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Retirement Savings: How Much Do You Need

Retirement Savings

Retiring is one of the riskiest financial decisions you will make. On the day you retire, you can calculate your net worth. You won’t know, however, how much retirement savings you need because you don’t know:

  • how much you will actually spend on day-to-day expenses
  • how much those expenses will be impacted by inflation
  • whether you’ll have significant medical or other expenses
  • how long you will live or
  • what returns you will earn on your investments.

I retired a little over a year ago and realized that, even though I have a lot of money saved, it wasn’t enough to give me confidence we wouldn’t run out.  I took on a large consulting project to help cover our expenses for the next year or two. Researching this post, though, added even more confidence as we have more than enough to meet some of the simple rules of thumb.   We will see what happens.

In this post, I’ll provide some insights about how to think about a target you might want to set for your retirement savings.  As a follow up, I’ll talk about how much you need to save to meet your retirement savings goal in this post.

4% Rule and Multiply by 25 Rule

As I checked to see what others were saying on this topic, I found a very common theme for determining how much you need to save for retirement.  In some places, it was called the 4% Rule and, in others, the Multiply by 25 Rule.  Being the math geek that I am, my first thought was that 4% = 1/25 so they are the same thing!  It turns out that, in the nitty gritty details, the Multiply by 25 Rule is intended to tell you how much you need to have available on the day you retire while the 4% Rule guides you in how much you can spend in your first year of retirement.  Nonetheless, as explained below, they both result in the same amount needed in savings on your retirement date.

4% Rule for Retirement Spending

The 4% rule is intended to tell you how much you can spend from your retirement savings each year.  Let’s say you have $1,000,000 in invested assets when you retire.  It says you can spend 4% of that amount or $40,000 (including all of your expenses and taxes) in your first year of retirement.  In each subsequent year of your retirement, you can spend $40,000 increased for the cumulative impact of inflation since you retired.   The 4% Rule assumes that you are invested 50% in stocks and 50% in bonds.

4% Rule Illustration

The graph below shows the amount you can spend each year (blue bars which use the left axis scale) and the amount you’ll have remaining at each age (red line which uses the right axis scale) if you retire at 65, inflation is 3% per year, bonds earn 2.5% and stocks earn 7% annually. These assumptions are similar to long-term average assumptions that are common these days.

As you can see, in this scenario, the amount you can spend increases from $40,000 when you are 65 to almost $100,000 a year when you are 95 solely due to inflation. In the first few years, your spending is less than your investment returns, so your savings increases.  After you turn 72, your savings exceeds your investment returns so your savings starts to decrease.

4% Rule Background

The 4% rule was developed by William Bengen and is presented in detail in a 1994 study published in the Journal of Financial Planning.  (If you like numbers and graphs, check out this paper. It is a surprisingly easy read.)

Using historical data from 1926 to 1991, Bengen found that there were no 50-year periods in which a retiree would run out of money if his or her initial withdrawal rate was 3.5% or lower.  With a 4% initial withdrawal rate, the shortest time period in which the savings ran out was 33 years.  In only 10% of the scenarios did the money last for less than 40 years.

If you turn this rule around and know how much you want to spend in your first year of retirement, say $60,000, you can calculate the amount you need to have saved by dividing that amount by 4% (=0.04).  In this example, you need $1,500,000 (=$60,000/0.04) in savings on the day you retire using this rule.

Multiply by 25 Rule for Retirement Savings

The Multiply by 25 Rule says that the amount you need in retirement savings is 25 times the amount you want to spend in the first year of retirement.  Using the example above in which you want to spend $60,000 in your first year of retirement, you would calculate that you need $1,500,000 (=25 x $60,000) in savings.  As I said, the math is the same for determining how much you need to save because multiplying by 25 is the same as dividing by 0.04.  It is just that the rules are stated from different perspectives (how much you can spend given the amount saved as opposed to how much you need to save giving how much you want to spend).

When do you need more or less?

As indicated, those rules make assumptions that might not be right for you. There are a number of personal factors that impact how much you need in retirement savings.

Your Risk Tolerance

The 4% Rule assumes that you invest half in bonds and half in stocks. Some people are willing to take more risk by investing more heavily in stocks. Other people can’t tolerate the ups and downs of the stock market, so invest more heavily in bonds. As shown in this chart below, taken from my post on diversification and investing, the higher percentage of stocks in your portfolio, the higher your average return (the blue lines) but the more likely you are to lose some of your principal (the portion of the whiskers that fall below 0).


If you plan to put more than 50% of your retirement assets in stocks, you can withdraw a bit more than 4% each year. Turning that around, it means you need a bit less than 25 times your estimated expenses in your first year of retirement. The table below was copied with permission from a March 19, 2019 article from Schwab found at this link.  It shows how your time horizon (see below) and investment risk impact the 4% Rule.

Life Expectancy and Retirement Age

The analysis underlying the 4% Rule focuses on a retirement period of 30 years.  If you retire in your mid-60s, it would imply that you would most likely have enough money to last through your mid-90s.  If you are in poor health or have a family history of dying early, you could consider spending a bit more than 4% (that is, multiply by less than 25 to determine how much you need to save).

On the other hand, if you plan to retire at 45 and want to have enough money to last until you are 95, you’ll need to save more.  The Schwab table above shows planning horizons up to 30 years.  Based on the numbers in the table, it looks like you could subtract about 0.1 percentage points from the numbers in the 30-year row for each year your planning horizon extends beyond 30 years to estimate how much you need to save.

For example, if you want to be highly confident (90% sure in this case) you will have enough money to last for 50 years, you would be looking at 20 years beyond the 30-year horizon.  Multiplying 20 years by 0.1 percentage point is 2.0%.  According to the table, you can spend 4.2% of your savings in the first year with a Moderately Conservative portfolio and 90% (highly) confident that you won’t run out of money in 30 years.  My approximation would subtract 2.0% from 4.2% to estimate that you could spend about 2.2% of your savings in the first year if you wanted to be 90% confident you won’t run out of money in 50 years.  You could then divide your estimated first year expenses by 2.2% or multiply by 45 to estimate how much you need to save.

Other Sources of Income

Some people’s employers provide defined benefit retirement plans.  These plans generally pay a flat amount every month starting at normal retirement age (as defined by the employer) until death.  In the US, people who have worked or whose spouses have worked are eligible for Social Security benefits, as discussed in this post.  Many other countries have similar programs.

When you are estimating how much you need to save for retirement, you can consider these sources of income.  If all of your other sources of income increase with inflation, it is a fairly straightforward adjustment.  You just need to subtract the income from these other sources from your first-year-of-retirement expenses before applying the 4% Rule (as adjusted for other considerations).

For example, if you plan to spend $100,000 a year in retirement and have $40,000 of Social Security and defined benefit plan benefits,  you would subtract $40,000 from $100,000 to get $60,000.  Using the Multiply by 25 Rule, you would multiply $60,000 by 25 to get $$1.5 million instead of multiplying the full $100,000 by 25 which would indicate you need $2.5 million in savings.  In this example, you need $1 million less in savings because you have other sources of income.

Unfortunately, most defined benefit plan benefits do not increase with inflation.  The math for adjusting the Multiply by 25 Rule is fairly complicated.  I’ve developed a simple approximation that you can use that will get you close to the correct percentage.  To approximate the adjustment to the amount you Multiply by 25, divide your defined benefit plan income by 2 before subtracting it from your first-year expenses.

You Want to Leave Your Assets to your Beneficiaries

I remember being a teenager and having my father explain to me how much I needed to save for retirement.  The approach he proposed was that you could spend 2% of your assets which is equivalent to a Multiply by 50 Rule.  (No wonder I was nervous about my finances when I retired!)  His logic was as follows:

  • Invest in the stock market and get a 10% return.  (He did this analysis a long time ago, when stock market average returns, inflation and taxes were all considered to be a bit higher than they are today, but not by so much as to make the logic faulty.)
  • You will pay taxes of 40% of your returns, which makes your after-tax return 6%.
  • Inflation will be 4% per year.  Because he wanted his investment income in every year to cover his expenses without dipping into the principal, he had to re-invest 4 percentage points of his investment return so he would have 4% more investment income in each subsequent year.
  • Subtracting the 4% reinvestment from the 6% after-tax return leaves an amount equal to 2% of his investments that he could spend each year (excluding taxes because he separately considered them).

So, if you are like my father, you will want to save closer to 50 times your first-year retirement expenses, rather than 25 times.  It is important to remember that my father’s Multiply by 50 rule applies to your expenses excluding income taxes and the Multiply by 25 Rule applies to your expenses including income taxes, so they aren’t quite directly comparable.

Liquidity of your Assets

As indicated above, the 4% Rule assumes your assets are invested 50% in stocks and 50% in bonds. You may have other assets that contribute to your net worth, such as equity in your home, your personal property, a family farm and rental property, among others. These other assets are all consider illiquid – that is, you can’t convert them to cash easily. Further, some of them are assets that you never want to have to convert to cash to cover expenses, such as your home and personal property.

As you project how much you will have in retirement savings, you’ll want to exclude any equity in your house as it isn’t available to invest.  A portion of it may be available at some point if you plan to downsize, but you’ll want to be cautious about including it in your savings plan.  Other of these assets, such as rental property, could be liquidated to cover retirement expenses.  In your planning, though, you’ll need to make sure you consider the selling costs (e.g., real estate agent’s commission) and taxes you need to pay on capital gains and that they may not generate a return as high as underlies the 4% Rule.

Irregular Large Expenses

The analysis that supports the 4% Rule assumes that you have the same expenses every year and that they change due only to inflation. That’s not how life works! You may want to be like me and want to take an expensive vacation every three or four years in retirement, you’ll likely have to replace your car at least once in retirement or you could have major home repairs if you own your home.  In addition, end-of-life medical bills can be very expensive.

As you are determining your first-year retirement expenses, you’ll want to include amounts for any such expenses in your budget at their average annual cost.  For example, let’s say I want to take a vacation (in addition to my already budgeted travel expenses) every five years that has a total cost of $10,000.  I need to add $2,000 (= $10,000 per vacation divided by one vacation every 5 years) to my regular annual expenses for these big vacations.  Similarly, if I plan to buy a $25,000 car every 15 years, I need to add $1,667 (= $25,000/15) to my annual expenses.  In both cases, you would add these amounts to your budgeted expenses before you divided by 4%.

How to Set Your Personal Target

So, what can you do to estimate your personal retirement savings target? Follow the following steps.

Make a Budget for Today if You Don’t Already Have One

It is hard to estimate your expenses in retirement, but it is very helpful to understand what you are spending today.  If you don’t have a budget or haven’t tracked your expenses to see where your money is going, I suggest starting there.  Here is a link to a post I wrote with a spreadsheet to help you monitor your expenses.

Estimate Your Expenses in Your First Year of Retirement

Next, look at your current budget and/or spending and estimate how it would change if you were retired today.  On what types of things might you want to spend money in the future that you don’t spend now?  Might you want to buy special gifts for your grandchildren that are more extravagant than what you spend for your children’s gifts now?  Also think about expenses you have now that you won’t have in the future, such as commute expenses and possibly a separate wardrobe for work.

Be sure to think about Social Security (or equivalent) and income taxes. In addition to Federal income taxes, you may pay state or provincial and possibly local income taxes.  If you plan to live somewhere else in retirement, it might have a higher or lower tax rate.  In the US, Social Security taxes are 6.2% (12.4% I you are self-employed) of your wages up to the limit ($128,400 in 2019).  As you adjust your budget, you can eliminate Social Security taxes and will want to think about whether your state or provincial and local tax rate will be substantially different from their current rates.

Some people say that your expenses will decrease by 20% when you retire.  In my very short retirement, I find I’m spending more than I expected as I have more time to do things and many of them cost money.  This post from Financial Samurai provide some insights as to how retirement might impact your expenses.

Increase Your Retirement Expenses for Special Purchases

Do you want to travel? How often do you think you’ll need to buy replacement cars and how much do you think you’d spend if you bought one today? What other expenses might you have that aren’t in your budget? For each of these expenses, divide the amount by the time between them to estimate an average annual cost, as I illustrated earlier in this post.

Adjust Your Budget for Inflation

All of the amounts you’ve estimated so far are in today’s dollars.  That is, they reflect the current prices of every item.  You’ll want to increase these amounts for inflation between now and the time you retire.  Over long periods of time, annual inflation has averaged 3% to 3.5% though it has been a bit lower recently.  To adjust your budget for inflation, you’ll want to multiply it by 1.03n, where n is the number of years until you retire.  Don’t like exponents?  The table below provides approximate multipliers by number of years until you plan to retire.

Years 5 10 15 20 25 30 35 40 45
Factor 1.15 1.35 1.55 1.80 2.10 2.45 2.80 3.25 3.80

Subtract Other Sources of Income

If you think you’ll have a defined pension plan benefit or will receive social insurance (Social Security) benefit, you can subtract those amounts from your inflation-adjusted budget.  My post on Social Security provides insights on how to estimate your benefits for my US readers.

Figure Out your Risk Tolerance and Length of Retirement

If you want to be almost 100% confident you will have enough money to last for your full retirement, regardless of how long it is, and leave most or all of your principal to your heirs, multiply the difference between your inflated budget (excluding income taxes) and other sources of income by 50 to derive your retirement savings target.

If you plan to be retired for only 10 years, you can multiply by a number as low as 10, according to the chart from Schwab. Where between those two numbers you choose is up to you. The longer you expect to be retired, the more conservative your investments and the more confident you want to be that you won’t run out of money, the higher your multiplier.

 

 

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Credit Cards: What You Need to Know

Credit-Cards

Credit cards are a terrific convenience but also can be very costly.  Effective use of a credit card can make life easier and improve your credit score.  On the other hand, it is easy to buy more than you can afford using a credit card, leading to high interest charges and a lower credit score.  The latter process can lead to a downward spiral as the purchases you couldn’t afford lead to ever increasing finance and interest charges on your credit card.  At the same time, your credit score goes down which increases the interest rate on other loans, if you can get them at all as discussed in this post. For a real-world example of how credit cards and lead to a financial disaster, check out this post about a friend of mine.

In this post, I’ll explain how credit cards work, including how finance and interest charges normally apply.  Every credit card is different, so you’ll want to look closely at the terms of any credit cards you currently carry or for which you plan to apply.

How They Work

When a financial institution issues you a credit card, it is offering you a loan in an amount that you can choose based on the amount of your purchases up to your credit limit.

Credit Cards from Your Perspective

From your perspective, you:

  • Pay the annual fee, if there is one.
  • Make purchases or get a cash advance. When you get a cash advance, you are borrowing cash from your credit card company instead of borrowing money to buy something.  You can get a cash advance at an ATM, among other places.
  • Pay your bill – hopefully the full amount every month, but at least the minimum payment if at all possible. If you don’t pay your bill in full, issuers will add interest charges to your next bill, as discussed below.  If you don’t pay as much as your minimum payment, they will also add finance charges.
  • Get rewards. Many credit cards provide rewards in the form of cash back or “points” that can be used for travel or other purchases.

In addition, you have the option to transfer your balance from one credit card to another.  Many people make this type of transfer when they have at least one credit card with a very high interest rate and one with a low interest rate.  By transferring the balance from the high-rate card to the low-rate card, you can reduce the amount of interest you will pay.  Most issuers charge a fee of roughly 3% of the amount transferred when you make a transfer.  If your interest rate decreases by more than 3 percentage points and you are paying off your credit card debt fairly slowly, though, your interest savings will be more in one year or a little longer than the transfer fee. As discussed below, though, the transfer could impact the interest charged on other purchases, so you’ll want to look at the whole picture before making a transfer.

Credit Cards from the Issuer’s Perspective

Income

The credit card issuer generates revenue from several sources:

  • Your annual fees.
  • Interest and financial charges you pay.
  • Fees it receives from vendors who accept their credit cards. Most issuers require vendors to pay them 2% to 4% of the amount of your purchases.  Recently, some vendors have started passing these fees on to customers.  That is, they charge customers who use credit cards more than customers who use a check or pay cash.  I ran into that when paying for many of the costs of our daughter’s wedding.  To keep the cost down, I made sure I paid any vendors who charged these fees using an electronic transfer.
  • Finance charges. If you don’t make a payment toward your credit card bill at all or the amount you pay is less than the minimum payment, issuers charge you a fee in addition to the interest charges.
  • Cash advance fees.  Many issuers charge $10 to $25 or 5% of the amount every time you get a cash advance.  I never use my credit card for a cash advance as 5% of the cash is a steep charge to access cash.  There are emergencies, though, when having cash at any price is imperative.
  • Foreign transaction fees. Many issuers charge fees when you buy something outside your home country.  I carry two Visa cards one of which charges me 3% on my purchases every time I leave the US.  For years, I carried only one credit card but I was leaving the US for a month to travel and decided I wanted a back-up card.  I went to the bank where I keep my checking account and clearly didn’t read the fine print! In hindsight, it was silly to get a back-up credit card for travel with such a high foreign transaction fee.

Issuers’ Expenses

Credit card issuers have four primary expenses – their overhead costs (salaries, rent, etc.), the cost of the rewards they give customers, the cost of borrowing the money that they “loan” you between the time you make a charge and pay your bill, and the amount of money they have to write off because customers don’t pay their bills.

When Do You Pay Interest

If you pay your credit card bill in full every month, you don’t transfer a balance from another card and you don’t get a cash advance from your credit card, you won’t pay any interest.   When you do any of those things, you’ll get interest charges.

Interest on Unpaid Balances

You pay interest on unpaid balances from the day they are due until the day the issuer receives your payment for those charges.  Once you haven’t paid your previous bill in full by its due date, though, the issuer starts charging interest on the day you make each future purchase rather than starting on the day the bill is due until all charges have been paid in full.  I’ll provide an example of this difference below.

Interest on Cash Advances

You pay interest on cash advances from the day you withdraw the money until the day the credit card company receives your payment.  I looked at one of my credit cards and it has a higher interest rate on cash advances in addition to having interest charges from the date of the withdrawal.  The same is true with other credit cards I’ve seen on line or discussed with my friends.

Interest on Balance Transfers

Some issuers allow you to transfer the balance from one credit card to another. You might want to do this type of transfer if the interest rate on one card with a balance is significantly higher than another card you hold.  When you make this type of transfer, the issuer starts charging you interest on the day of the transfer and continues to do so until you pay the balance in full.

In addition, even if you had previously paid off the balance on the card to which you transferred your balance, you will pay interest on all new purchases starting on the date of purchase.  That is, until you have fully paid off your credit card balance including the amount transferred, you do not get a grace period between the date of purchase and the due date of your bill.  The additional interest could offset some or all of the savings you attain by reducing your interest rate when you transfer a balance.  This article from creditcards.com provides more details about some of the risks and benefits of transferring a balance.

How Is Interest Calculated

Still confused about how and when interest is calculated?  Hopefully these examples will help.  Before going into the examples, I need to explain what the interest rate or APR (annual percentage rate) really means.

A 24% APR, for example, doesn’t mean you pay 24% interest if you carry your balance for a full year.  The 24% is divided by 365 (number of days in a year) to get a daily rate.  The daily rate is multiplied by your balance on each day and added to the balance for the next day.  As such, if you didn’t pay or charge anything on your balance for a year, the interest rate on the beginning balance would not be 24%, but rather 27.1%!  I calculated 27.1% as (1+.24/365)365 – 1.  By raising the term inside the parentheses to the 365 power, I’m compounding the daily interest charge for a full year (365 days).

Example 1 – Paid Bill in Full Last Month

In the first example, I’ll show how interest is calculated if you paid your bill in full at the end of the previous billing cycle.  Here are the assumptions for this example:

  • Interest rate on charges = 18%
  • Cash advance interest rate = 24%
  • The cash advance fee is the greater of $10 or 5% of the amount of the cash advance
  • You make a $500 purchase on Day 5
  • You take a $100 cash advance on Day 8
  • Your issuers receives your payment on Day 10 of the next billing cycle (i.e., 33 days after you took the cash advance)

In this example, you don’t pay any interest on the $500 purchase during this billing cycle.

The cash advance is different.  First, you are charged the cash advance fee.  5% of your cash advance is $5 which is less than the $10 minimum, so you will be charged $10 as a cash advance fee.  In addition, you will pay interest at a 24% APR.  The interest charge is $2.19 which is calculated as:

As such, you will re-pay the issuer $112.19 for the $100 cash advance you received. This example illustrates why it is often better to tap sources of cash other than your credit card, if at all possible.

Example 2 – Didn’t Pay Bill in Full Last Month

In this example, I’ll show how interest is calculated if you didn’t pay your bill in full at the end of the previous billing cycle.  Here are the assumptions for this example:

  • Interest rate on charges = 18%
  • Unpaid balance from last month = $750
  • You make a $500 purchase on Day 5
  • Your issuer receives your payment in full on Day 10 of the next billing cycle

I haven’t included a cash advance in this example because it will cost you the same amount regardless of whether you paid your bill in full in the previous month.

In this example, you will pay interest on your unpaid balance for the 30 days in the month plus the 10 days into the next billing cycle, for a total of 40 days. The interest on this balance totals $14.93 and is calculated as:

In addition, you pay interest on the $500 purchase for 25 days in this billing cycle plus the 10 days in the next billing cycle, for a total of 35 days.  The interest charge on this purchase is $8.70 for a total interest charge of $23.63. If you have gotten behind on your credit card balances, check on this post for strategies that will help you get caught up.

The Best Credit Card for You

As with every financial decision, picking the best credit card for you requires balancing the costs and benefits.  In large part, the best credit card for you depends on how you will use it.  The bottom line is that you want the credit card that will have the greatest net benefit or lowest net cost for you.  Here’s how you can calculate that benefit/cost.

Plusses

The plus in the equation that determines your net benefit is the value of any rewards you earn.  Some credit cards provide no rewards, so the total plusses equal 0.  Other credit cards provide rewards, such as  1% of all purchases or 5% of gas purchases plus 3% of food purchases plus 1% of everything else.

To calculate the value of the benefits, you’ll need to estimate how much you expect to charge on your credit for each category of expense.  You can then multiply those benefits by the corresponding reward percentage.  As an illustration, I’ll use the 5% for gas, 3% for food and 1% of everything else example I mentioned above.  The table below shows three different combinations of monthly expenses in those categories and the rewards you would earn.

Category Scenario 1 Scenario 2 Scenario 3
Gas 100 200 500
Food 300 500 300
Other 600 300 200
Monthly Rewards 17 23 33
Annual Rewards 204 276 396

By comparison, you would receive $10 a month or $120 a year with a credit card that provides 1% back on every purchase under all 3 scenarios.  I note that most credit cards do not give rewards for cash advances, so I have not included them in the table above.

Some rewards are harder than others to access or might be in a form that isn’t useful for you.  If that is the case with one of the credit cards you are considering, you might reduce the annual benefit by some amount, such as 50%, for the chance that you don’t use it.

Minuses

Offsetting the rewards are all of the fees and charges I mentioned above – the annual fee, cash advance fees, finance fees, foreign exchange fees and interest charges.

The table below shows the fees I’ve used for illustration for the two cards above.

Rewards 5%/3%/1% 1%
Annual fee $75 $0
Cash advance fee $10 $10
Cash advance APR 24% 18%
Purchase APR 18% 12%

To keep the examples simpler, I’ve assumed you make at least the minimum payment every month so there are no finance charges and you have no foreign transactions.

Example 1

In the first example, you have $1,000 a month in charges plus a $200 cash advance 30 days before your issuer receives your payment.  You pay your bill in full every month.

In this example, your annual costs are $243 using the higher reward card and $150 using the lower reward card.  The table below shows the net cost of using your credit card under each of the 3 scenarios above for both cards, remembering that the lower-reward card has the same rewards under all three scenarios.  A negative net cost means that you pay more in fees than you get in rewards, whereas a positive net cost means you get more in rewards than you pay in fees.

Card 5%/3%/1% 5%/3%/1% 5%/3%/1% 1%
Scenario 1 2 3 All
Rewards +240 +276 +396 +120
Costs -243 -243 -243 -150
Net Cost -3 +93 +189 -30

 

In this example, you don’t incur many fees, so the lower fees in the lower-reward credit card don’t help you.  As such, you are better off with the higher-reward credit card under all three spending scenarios.

Example 2

In the second example, you have $1,000 a month in charges plus a $200 cash advance 30 days before your issuer receives your payment.  Unfortunately, you got behind on your credit card payments so you average 60 days between the time you make each purchase and take out your cash advance and pay your bill.

Your annual costs are $652 using the higher reward card and $379 using the lower reward card.  The table below shows the net cost of using your credit card under each of the 3 scenarios above for both cards.

Card 5%/3%/1% 5%/3%/1% 5%/3%/1% 1%
Scenario 1 2 3 All
Rewards +240 +276 +396 +120
Costs -652 -652 -652 -379
Net Cost -412 -316 -220 -259

 

In this example, the lower-rewards credit card has a lower net cost than the higher-rewards card, unless you buy a lot of gas in which case you are somewhat better off using the higher-rewards card.

Summary

This comparison illustrates that high-rewards credit cards are not always the best.  To select the best credit card, you’ll want to balance the fees you are likely to pay based on your spending and payment patterns with the available rewards and their usefulness to you.

 

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Tax-Efficient Investing Strategies – USA

Tax-Effective-Investing-USA

You can increase your savings through tax-efficient investing.  Tax-efficient investing is the process of maximizing your after-tax investment returns by buying your invested assets in the “best” account from a tax perspective.  You may have savings in a taxable account and/or in one or more types of tax-sheltered retirement accounts.  Your investment returns are taxed differently depending on the type of account in which you hold your invested assets.  In this post, I’ll provide a quick overview of the taxes applicable to each type of account (since I cover taxes on retirement plans in much greater detail in this post) and provide guidelines for how to invest tax-efficiently.

The strategy for tax-efficient investing differs from one country to the next due to differences in tax laws so I’ll talk about tax-efficient investing strategies in the US in this post and in Canada in this post.

Types of Investment Returns

I will look at four different types of investments:

  • Individual stocks with high dividends
  • Mutual funds
  • Exchange-traded funds (ETFs)
  • Bonds

I will not look at individual stocks with little or no dividends.  The returns on those stocks are essentially the same as the returns on ETFs and are taxed in the same manner.

The table below shows the different types of returns on each of these investments.

Distributions by Investment Interest Dividends Capital Gains Capital Gain Distributions
High dividend stocks           x          x
Mutual Funds          x          x          x
ETFs          x
Bonds          x          x

Cash Distributions

Interest and dividends are cash payments that the issuers of the financial instrument (i.e., stock, fund or bond) make to owners.

Capital Gains

Capital gains come from changes in the value of your investment.  You pay taxes on capital gains only when you sell the financial instrument which then makes them realized capital gains.  The taxable amount of the realized capital gain is the difference between the amount you receive when you sell the financial instrument and the amount you paid for it when you bought it.  Unrealized capital gains are changes in the value of any investment you haven’t yet sold.  If the value of an investment is less than what you paid for it, you are said to have a capital loss which can be thought of as a negative capital gain.

Mutual Funds

Mutual funds are a bit different from stocks and ETFs.  They can have the following types of taxable returns.

  • Dividends – A mutual fund dividend is a distribution of some or all of the dividends that the mutual fund manager has received from the issuers of the securities owned by the mutual fund.
  • Capital gain distributions – Capital gain distributions are money the mutual fund manager pays to owners when a mutual fund sells some of its assets.
  • Capital gains – As with other financial instruments, you pay tax on the any realized capital gains (the difference between the amount you receive when you sell a mutual fund and the amount you paid for it) when you sell a mutual fund.

Tax Rates

The four types of distributions are taxed differently depending on the type of account in which they are held – Taxable, Roth or Traditional.  401(k)s and Individual Retirement Accounts (IRAs) are forms of retirement accounts that can be either Roth or Traditional accounts and are discussed in more detail in in this post.

Accounts other than Retirement Accounts

I’ll refer to accounts that aren’t retirement accounts as taxable accounts.   You pay taxes every year on dividends and realized capital gains in a taxable account, whereas you pay them either when you contribute to or make a withdrawal from a retirement account.  The table below shows how the different types of investment returns are taxed when they are earned in a taxable account.

Type of Investment Return Tax Rates
Interest Same as wages
Dividends, realized capital gains & capital gain distributions ·         0% if dividends, capital gains & capital gain distributions are less than $38,600 minus wages minus income from other sources.

·         15% up to roughly $425,000.

·         20% if higher

For many employed US residents (i.e., individuals with taxable income between $38,700 and $157,500 and couple with taxable income between $77,400 and $315,000 in 2018), their marginal Federal tax rate wages and therefore on interest is likely to be 22% or 24%.

In a taxable account, you pay taxes on investment returns when you receive them.  You are considered to have received capital gains when you sell the financial instrument.

Roth Retirement Accounts

Before you put money into a Roth account, you pay taxes on it.  Once it has been put into the Roth account, you pay no more income taxes regardless of the type of investment return unless you withdraw the investment returns before you attain age 59.5 in which case there is a penalty.  As such, the tax rate on all investment returns held in a Roth account is 0%.

Traditional Retirement Accounts

You pay income taxes on the total amount of your withdrawal from a Traditional retirement account at your ordinary income tax rate.  Between the time you make a contribution and withdraw the money, you don’t pay any income taxes on your investment returns.

After-Tax Returns by Type of Account

To illustrate the differences in how taxes apply to each of these four financial instruments, I’ll look at how much you would have if you have $1,000 to invest in each type of account at the end of one year and the end of 10 years.

Here are the assumptions I made regarding pre-tax investment returns.

Annual Pre-tax Investment Return % Interest Dividends Capital Gains
Stocks 0% 3% 5%
ETFs 0% 0% 8%
Mutual Funds 0% 3% 5%
Bonds 4% 0% 0%

Mutual funds usually distribute some or all of realized capital gains to owners.  That is, if you own a mutual fund, you are likely to get receive cash from the mutual fund manager related to realized capital gains in the form of capital gain distributions.  Whenever those distributions are made, you pay tax on them.  For this illustration, I’ve assumed that the mutual fund manager distributes all capital gains to owners, so they are taxed every year.

Here are the tax rates I used for this illustration.

Type of Income Tax Rate
Ordinary Income – This Year 24%
Dividends 15%
Capital Gains 15%

One-Year Investment Period

Let’s say you have $1,000 in each account.  I assume you pay taxes at the end of the year on the investment returns in your Taxable account.  If you put the money in a Traditional account, I assume that you withdraw all of your money and pay taxes at the end of the year on the entire amount at your ordinary income tax rate.  (I’ve assumed you are old enough that you don’t have to pay a penalty on withdrawals without penalty from the retirement accounts.)

The table below shows your after-tax investment returns after one year from your initial $1,000.  Note that the pre-tax returns are the same as the returns in the Roth row, as you don’t pay income taxes on returns you earn in your Roth account.

One-Year After-tax Investment Returns ($) Stocks Mutual Funds ETFs Bonds
Taxable $68 $68 $68 $30
Traditional 61 61 61 30
Roth 80 80 80 40

The table below shows the taxes you paid on your returns during that year.

Taxes Paid Stocks Mutual Funds ETFs Bonds
Taxable $12 $12 $12 $10
Traditional 19 19 19 10
Roth 0 0 0 0

When looking at these charts, remember that you paid income taxes on the money you contributed to your Taxable and Roth accounts and that those taxes are not considered in these comparisons.  This post focuses on only the taxes you pay on your investment returns.

Comparison of Different Financial Instruments in Each Type of Account

Looking across the rows, you can see that, for each type of account, stocks, mutual funds and ETFs have the same one-year returns and tax payments. In this illustration, all three of stocks, mutual funds and ETFs have a total return of 8%.  It is just the mix between appreciation, capital gain distributions and dividends that varies.  The tax rates applicable to dividends and capital gains are the same so there is no impact on the after-tax return in a one-year scenario.

In all accounts, bonds have a lower after-tax return than any of the other three investments.  Recall, though, that bonds generally provide a lower return on investment than stocks because they are less risky.

Comparison of Each Financial Instrument in Different Types of Accounts

Looking down the columns, you can see the impact of the differences in tax rates by type of account for each financial instrument.  You have more savings at the end of the year if you invest in a Roth account than if you invest in either of the other two accounts for each type of investment.  Recall that you don’t pay any taxes on returns on investments in a Roth account.

The returns on a taxable account are slightly higher than on a Traditional account for stocks, mutual funds and ETFs.  You pay taxes on the returns in a taxable account at their respective tax rates – usually 15% in the US for dividends and capital gains.  However, you pay taxes on Traditional account withdrawals at your ordinary income tax rate – assumed to be 24%.  Because the ordinary income tax rates are higher than the dividend and capital gain tax rates, you have a higher after-tax return if you invest in a taxable account than a Traditional account for one year.  For bonds, the taxes and after-tax returns are the same in a Traditional and taxable account because you pay taxes on interest income in taxable accounts and distributions from Traditional accounts at your marginal ordinary income tax rate.

Remember, though, that you had to pay income taxes on the money you put into your taxable account before you made the contribution, whereas you didn’t pay income taxes on the money before you put it into your Traditional retirement account.

Ten-Year Investment Period

I’ve used the same assumptions in the 10-year table below, with the exception that I’ve assumed that you will pay ordinary income taxes at a lower rate in 10 years because you will have retired by then. I’ve assumed that your marginal tax rate on ordinary income in retirement will be 22%.

Ten-Year After-Tax Investment Returns ($) Stocks Mutual Funds ETFs Bonds
Taxable $964 $931 $985 $349
Traditional 904 904 904 375
Roth 1,159 1,159 1,159 480

Comparison of Different Financial Instruments in Each Type of Account

If you look across the rows, you see that you end up with the same amount of savings by owning any of stocks, mutual funds and ETFs if you put them in either of the retirement account.  The mix between capital gains, capital gain distributions and dividends doesn’t impact taxes paid in a tax-sheltered account, whereas it makes a big difference in taxable accounts, as can be seen by looking in the Taxable row.

In taxable accounts, ETFs provide the highest after-tax return because they don’t have any taxable transactions until you sell them.  I have assumed that the stocks pay dividends every year.  You have to pay taxes on the dividends before you can reinvest them, thereby reducing your overall savings as compared to an ETF.  You have to pay taxes on both dividends and capital gain distributions from mutual funds before you can reinvest those proceeds, so they provide the least amount of savings of the three stock-like financial instruments in a taxable account.

Comparison of Each Financial Instrument in Different Types of Accounts

Looking down the columns, we can compare your ending savings after 10 years from each financial instrument by type of account.  You earn the highest after-tax return for every financial instrument if it is held in a Roth account, as you don’t pay any taxes on the returns.

For bonds, you earn a higher after-tax return in a Traditional account than in a taxable account.  The tax rate on interest is about the same as the tax rate on Traditional account withdrawals.  When you hold a bond in a taxable account, you have to pay income taxes every year on the coupons you earn before you can reinvest them.  In a Traditional account, you don’t pay tax until you withdraw the money, so you get the benefit of interest compounding (discussed in this post) before taxes.

Your after-tax return is higher in a taxable account than in a Traditional account for the three stock-like investments.  The lower tax rate on dividends and capital gains in the taxable account, even capital gain distributions, more than offsets the fact that you have to pay taxes on dividends and mutual fund capital gain distributions before you reinvest them.

Illustration of Tax Deferral Benefit

The ability to compound your investment returns on a tax-deferred basis is an important one, so I’ll provide an illustration.  To keep the illustration simple, let’s assume you have an asset that has a taxable return of 8% every year and that your tax rate is constant at 24% (regardless of the type of account).

The table below shows what happens over a three-year period.

Returns and Taxes by Year Taxable Account Retirement Account
Initial Investment $1,000 $1,000
Return – Year 1 80 80
Tax – Year 1 19 0
Balance – Year 1 1,061 1,080
Return – Year 2 85 86
Tax – Year 2 20 0
Balance – Year 2 1,125 1,166
Return – Year 3 90 94
Tax – Year 3 22 0
Balance – Year 3 1,194 1,260

By paying taxes in each year, you reduce the amount you have available to invest in subsequent years so you have less return.

The total return earned in the taxable account over three years is $255; in the tax-deferred account, $260.  The total of the taxes for the taxable account is $61.  Multiplying the $260 of return in the tax-deferred account by the 24% tax rate gives us $62 of taxes from that account.  As such, the after-tax returns after three years are $194 in the taxable account and $197 in the tax-deferred account.

These differences might not seem very large, but they continue to compound the longer you hold your investments.  For example, after 10 years, your after-tax returns on the tax-deferred account, using the above assumptions, would be almost 10% higher than on the taxable account.

Tax-Efficient Investing for Portfolios

It is great to know that you get to keep the highest amount of your investment returns if you hold your financial instruments in a Roth.  However, there are limits on how much you can put in Roth accounts each year.  Also, many employers offer only a Traditional 401(k) option.  As a result, you may have savings that are currently invested in more than one of Roth, Traditional or taxable accounts.  You therefore will need to buy financial instruments in all three accounts, not just in a Roth.

Here are some guidelines that will help you figure out which financial instruments to buy in each account:

  • You’ll maximize your after-tax return if you buy your highest yielding financial instruments in your Roth.  Because they generate the highest returns, you will pay the most taxes on them if you hold them in a taxable or Traditional account.
  • Keep buying your high-yielding financial instruments in descending order of total return in your Roth accounts until you have invested all of the money in your Roth accounts.
  • If two of your financial instruments have the same expected total return, but one has higher annual distributions (such as the mutual fund as compared to the stocks in the example above), you’ll maximize your after-tax return if you put the one with the higher annual distributions in your Roth account.
  • Once you have invested all of the money in your Roth account, you’ll want to invest your next highest yielding financial instruments in your Taxable account.
  • You’ll want to hold your lower return, higher distribution financial instruments, such as bonds or mutual funds, in your Traditional account. There is a benefit to holding bonds in a Traditional account as compared to a taxable account.  The same tax rates apply to both accounts, but you don’t have to pay taxes until you withdraw the money from your Traditional account, whereas you pay them annually in your taxable account.  That is, you get the benefit of pre-tax compounding of the interest in your Traditional account.

Applying the Guidelines to Two Portfolios

Let’s see how to apply these guidelines in practice using a couple of examples.  To make the examples a bit more interesting, I’ve increased the annual appreciation on the ETF to 10% from 8%, assuming it is a higher risk/higher return type of ETF than the one discussed above.  All of the other returns and tax assumptions are the same as in the table earlier in this post.

Portfolio Example 1

In the first example, you have $10,000 in each of a taxable account, a Traditional account and a Roth account.  You’ve decided that you want to invest equally in stocks, mutual funds and ETFs.

You will put your highest yielding investment – the ETFs, in your Roth account.  The stocks and mutual fund have the same total return, but the mutual fund has more taxable distributions every year.  Therefore, you put your mutual funds in your Traditional account and your stocks in your taxable account.

Portfolio Example 2

In the second example, you again have $10,000 in each of a taxable account, a Traditional account and a Roth account.  In this example, you want to invest $15,000 in the high-yielding ETFs but offset the risk of that increased investment by buying $5,000 in bonds.  You’ll split the remaining $10,000 evenly between stocks and mutual funds.

First, you buy as much of your ETFs as you can in your Roth account.  Then, you put the remainder in your taxable account, as the tax rate on the higher return from the ETFs is lower in your taxable account (the 15% capital gains rate) than your Traditional account (your ordinary income tax rate).  Next, you put your low-yielding bonds in your Traditional account.  You now have $5,000 left to invest in each of your taxable and Traditional accounts.  You will invest in mutual funds in your Traditional account, as you don’t want to pay taxes on the capital gain distributions every year if they were in your taxable account.  That means your stocks will go in your taxable account.

Risk

There is a very important factor I’ve ignored in all of the above discussion – RISK (a topic I cover in great detail in this post).  The investment returns I used above are all risky.  That is, you won’t earn 3% dividends and 5% appreciation every year on the stocks or mutual funds or 10% on the ETFs.  Those may be the long-term averages for the particular financial instruments I’ve used in the illustration, but you will earn a different percentage every year.

If your time horizon is short, say less than five to ten years, you’ll want to consider the chance that one or more of your financial instruments will lose value over that time frame.  With perfect foresight, you would put your money-losing investments in your Traditional account because you would reduce the portion of your taxable income taxed at the higher ordinary income tax by the amount of the loss when you withdraw the money.  Just as the government gets a share of your profits, it also shares in your losses.

The caution is that financial instruments with higher returns also tend to be riskier.  If, in the US, you put your highest return investments – the ETFs in my example – in your Roth account, their value might decrease over a short time horizon.  In that case, your after-tax loss is the full amount of the loss.  If, instead, you had put that financial instrument in your Traditional account, the government would share 24% (your marginal ordinary tax rate) of the loss in my example.

In conclusion, if you plan to allocate your investments using the above guidelines, be sure to adjust them if your time horizon is shorter than about 10 years to minimize the chance that you will have to keep all of a loss on any one financial instrument.

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New vs Used Cars

Is buying a used car really all that important to your financial health?  I’ve seen lots of articles and posts that say that financially responsible people buy only used cars.  Being the data geek that I am, I was curious so looked into the question.  In this post, I’ll provide you with my insights on the importance of buying a new vs used cars.

Summary of Findings

Here are the important things I learned from studying this question.

  • The cost of your car is more important than whether it is new or used. For example, you will have more savings if you buy a new car for $15,000 than a used car for $20,000, assuming you own them for the same length of time.
  • How long you own your car can be more important than whether you buy a particular model when it is new or when it is three years old.
  • The accumulation of savings from buying less expensive cars and owning them longer, especially after the compounding benefit of investment returns, can be significant though not as large as the amounts I’ve seen reported by some other authors on this topic.

The chart at the very end of this post illustrates these points (so keep reading).

Cost of Buying A Car

How much you pay for a car depends on several factors – its make and model, how old it is, how many miles it has on it, whether it has been in an accident, among other things.  It also depends on how you pay for it – cash, lease or borrowing – as discussed in my post on that topic.  If one of your goals is to save as much as possible, you’ll want to buy the least expensive car that meets your needs, regardless of whether it is new or used.

The biggest argument against buying new vs used cars is that the value of the car decreases more per year when it is brand new than when it is older. This decrease in value is called depreciation.

Depreciation

The chart below illustrates estimates of the patterns of depreciation for five different makes and models – a Subaru Impreza, a Ford Fusion, a Toyota RAV4, a Ford F150 and a BMW M4.

These estimates are based on a combination of data from Edmunds and the National Automotive Dealers Association (NADA). These two data sources didn’t have always values that were consistent, so I applied some judgment in deriving these curves.

The graph shows that all five models depreciate between 18% (Impreza) and 29% (F150) in the first year.  In the next 10 years, depreciation is generally between 13% and 17% per year and is even lower when the cars are older than that.

Depreciation in Dollars

To look at these values from a different perspective, I created the next graph that shows the dollar amount of estimated depreciation each year.

This chart shows that, even though the Fusion has the second highest percentage depreciation in the first year, it has the smallest dollar depreciation.  When considering how much a car will cost you, it is the dollar depreciation that is important.

These graphs make it fairly clear that, if you plan to reduce the cost of a car purchase by buying used, you save the most money by buying a car when it is one year old. The amount you will save gets smaller with each additional year the car ages.

Costs of Owning a Car

In addition to depreciation and, if applicable, finance or lease costs, there are five other major costs of owning a car – fuel, insurance, taxes and fees, maintenance, and repairs.

Fuel

The cost of fuel (e.g, regular, premium or ethanol-free gas, diesel or electricity) will generally stay constant for each mile you drive, other than inflationary changes in fuel prices.  For modeling the total cost of ownership, I assumed you will drive the same number of miles every year so the real cost of fuel will be constant.  I used the first-year fuel cost from Edmunds True Cost to Own as the real cost of fuel in every year.

Insurance

The portion of insurance that covers liability will likely be constant for a particular car in real dollars.  The cost of liability insurance will be higher for makes and models of cars that are in more accidents (e.g., sporty ones) and larger cars (e.g., pick-ups that will cause more damage to another vehicle or more severe injuries).  For my analysis below, I have used the first-year insurance cost from Edmunds True Cost to Own.  I assumed that 40% of that amount was for liability insurance and would stay constant in real dollars.  That leaves the remaining 60% for physical damage coverage which I assumed would decrease, in real dollars, in proportion to the value of the car.

Taxes and Fees

Taxes and fees can be constant over time or decrease with the value of the car, depending on the state in which it is registered.  For my analysis below, I used the first-year amount for taxes and fees from the Edmunds True Cost to Own.  For subsequent years, I have assumed that taxes and fees, in real dollars, would decrease with the value of the car.

Maintenance

This component of the cost of owning a car includes regularly scheduled maintenance and parts replacement, such as oil and other fluid changes, tire rotation, balancing, alignments and replacement, brakes, transmissions, tune-ups and anything else included in the maintenance schedule provided by the dealer when new. It excludes repairs for damage to the car and repair or replacement of parts not on the schedule.

I have assumed that the real cost for maintenance is fairly constant per mile over the life of the car.  Because I am assuming that your annual mileage is fairly stable, I can assume that the real cost of maintenance is constant from year to year.

Warranties Reduce Maintenance Costs

The significant exception is that many manufacturers include the cost of up to five years of maintenance in the purchase price of a new car.  In my analysis below, I have relied on the information in the Edmunds True Cost to Own for the length of time that maintenance is covered by the manufacturer.  After that, I used the average maintenance cost for the remaining years included in the Edmunds data and assumed it was constant in real dollars for the rest of the life of the car.  I also assumed that the maintenance provided by the manufacturer is transferrable to a new owner.

If you are comparing the cost of a new car with that of a used car, you will want to make sure you understand which maintenance costs are covered by the warranty for each vehicle.  For most of the cars in this comparison, the average annual cost of scheduled maintenance was estimated by Edmunds to be between $750 and $1,150 a year.  The exception is the BMW for which the average annual cost after the warranty ends was closer to $3,000 a year.  The maintenance covered by the dealer could offset some of the higher depreciation you experience in the first few years of owning a new car.

Repairs

Repair costs include repair of damage to your car, such as cracked windshields, and repairs or replacement of parts that break.  For my analysis below, I used the repair costs provided by Edmunds for each of the first five years after the car is new.  I then looked at the results of a Consumers Report study to estimate how much repair costs would increase as the car got older.  Based on that study, I estimated that repair costs increased about 4% per year in real dollars.

Total

The graphs below show the components of the cost of ownership (excluding purchase price, financing cost and depreciation) for the five illustrative cars in each of the first and fifth years of ownership.

 

A comparison of these charts shows the much lower cost of owning a new car than a five-year old car if the costs related to its purchase are excluded.  While the insurance goes down from the first year to the fifth year, the cost of maintenance increases significantly as the manufacturer is no longer paying for it.  In addition, Edmunds shows no repair costs in the first year after it is first sold, but they can be significant, especially for the BMW M4, by the fifth year.

The chart below shows the total of these costs for each car by the number of years since it was new.

For most of these cars, the ownership cost is fairly constant starting in the second year. The Impreza, Rav 4 and Fusion all have annual ownership costs of about $3,500.  The F150 has a similar pattern, but its annual ownership cost is closer to $4,500.  The BMW M4 ownership cost is similar to that of the F150 for the first three years, but increases dramatically when BMW stops covering the costs of maintenance and repairs.

Total Cost of Ownership

To provide insights on the long-term costs of different car-buying decisions, I calculated the total cost (in real dollars, i.e., without adjustment for inflation) of owning a car assuming the same choice was made for 60 years.  I used 60 years as I thought it fairly closely represented the length of time people own cars – from the time they are about 20 until they are about 80.

In these comparisons, I included the initial purchase price of each car (using the new car costs from Edmunds and used car costs using my approximation of depreciation) and the other costs of ownership as discussed in the previous section. Also, whenever a replacement car was purchased, I assumed that the preceding car could be sold at the depreciated price.

New vs. Used

The two graphs below show the total cost over 60 years of owning each of the five cars. The three bars for each car correspond to buying a new car, a one-year old car and a three-year old car.  The first graph compares the total cost if you buy a replacement car every five years; the second, every 15 years.

If you replace your car every five years, it is clearly less expensive to buy a three-year-old car than a one-year-old car or a new one, though it becomes less important if you are buying inexpensive cars such as the Fusion.  The difference between buying a new car and a one-year-old car is quite large for the F150 and the BMW, both of which have high depreciation in the first year.

If you own each car for 15 years, the benefits of buying a used car are much smaller. In fact, the increased maintenance and repair costs of buying a one-year-old car essentially offset the high first-year depreciation for the Subaru, Toyota and Fusion.  Buying a three-year-old car is still clearly less expensive for all models.

More Expensive vs. Less Expensive

The Subaru and Fusion are fairly similar cars – both are basic 4-door sedans, though the Subaru has all-wheel drive.  If you don’t need all-wheel drive, you might be indifferent between the two cars.  By comparing the total costs of the Subaru and Fusion in the above charts, you can see that the long-term cost of ownership of the Fusion is less than that of the Subaru.  In particular, the cost of buying new Fusions is less expensive than buying three-year-old Subarus.

This comparison emphasizes the point I made in the Summary that the initial purchase price of your vehicle is a more important factor than whether you buy new vs used cars.

Length of Time Owned

The graph below compares the total cost of ownership if you buy new cars and own them for different lengths of time.

The longer you own your cars, the fewer times you need to replace them. Replacing cars fewer times is less expensive over the long run, even though you get less for them when you sell them.  One consideration when you own your cars for a long time is that you’ll need to save up more for the replacement car because you will get less when you sell the old car.

For the Subaru, Toyota and Fusion, there is a small difference in total cost between replacing your car every three years and replacing it every five years.  For the BMW and F150, which have higher depreciation, the benefit of keeping your car for five years is larger.

For all five cars, you will save a significant amount over your lifetime if you replace your cars every 15 years as compared to replacing them every three or five years.

The graph below emphasizes the importance of how long you own your car.  The blue bars represent the total cost of ownership if you buy new cars and own them for 15 years.  The orange bars correspond to buying a three-year old car and replacing it every five years.

For all fives makes and models, replacing a new car every 15 years is about the same total cost or slightly less expensive than replacing three-year old cars every five years.

Compounded Value of Savings

Many of my readers look at how much more money they will have when they retire if they make certain financial decisions.  I think this perspective is terrific, as it focuses on long-term financial objectives.  It also encourages financial responsibility in that these analyses assume that you will save the money in a tax-advantaged retirement account, such as an IRA or 401(k), rather than spend your savings on something else.  My post at this link provides more information about tax-advantaged retirement accounts.

Common Assumptions

I’ve read a few other posts that look at how much money will accumulate if you buy used cars instead of new cars and invest the difference in stocks.  These posts tend to make the following assumptions:

  • You have enough money to pay cash for a new car every certain number of years (such as 10), but buy a used one instead. One example I saw assumed that a three-year old car would cost 50% of a new car.
  • You replace your car when it is a certain number of years old, such as 10, regardless of whether you buy it new or used (three years old, for example).
  • You are able to invest the difference between (a) the stream of cash needed to buy the new car every 10 years and (b) the stream of cash needed to buy the used car every seven years in the stock market at 8% to 10%.

Better Assumptions

There are a few aspects of this process that most posts I’ve seen overlooked.

  • They exclude the cash you get when you sell your car.
  • They overstate the cost savings from buying a three-year old car. My analysis indicates that cars depreciate between 35% and 45% in that time frame, not 50%.
  • They ignore the other costs of ownership, especially the much lower repair costs and the maintenance costs covered by manufacturers’ warranties in the first few years of ownership.
  • They ignore the riskiness of investing in the stock market. That is, if you invest the savings from buying a used car in the first year, there is as much as a 15% to 20% chance that you will not have enough money in the seventh year to replace your used car.

In the discussions below, I will use essentially the same paradigm, but will refine some of the assumptions.  In particular, I will revise the investment assumptions so they:

  • better reflect the cash flow needs,
  • use the higher purchase costs for the used car,
  • include all costs of ownership, and
  • eliminate the risk that you might not have enough money to buy your second car.

This analysis is simpler than it could be.  In the entire analysis, I stated all of the cash flows in current or real dollars. That is, your actual savings will likely be higher than is estimated in this analysis because, with inflation, the cost of the more expensive strategy will be even more expensive than if we had assumed that all costs were subject to the same inflation rate.

Reasonable Investment Assumptions

To avoid the risk that you won’t have enough money to pay for the second used car, I will assume that you can earn 3% in an essentially risk-free investment for the first 10 years (until you replace your new car for the first time). In the current interest rate environment, you can earn close to 3% on CDs, corporate bonds or high-yield savings accounts.  After that, you have enough savings built up from buying two used cars instead of two new cars that you can afford to take on the risk of investing in the stock market.

I have used the annual returns on the S&P 500 from 1950 through 2018 to model the amounts you will have accumulated by selecting the less expensive strategies.

New vs Used Cars

For the first comparison, I will look at the example discussed above – buy a new car every 10 years or a used car every 7 years.  In this comparison, I calculated how much you would have at the end of 40 years if you invested the difference between the new car costs and the used car costs.  For the first 10 years, I assumed you would earn 3%.  For the remaining 30 years, I used the time series of 30 years of S&P 500 returns starting in each of 1950 through 1968 (for a total of 39 time series).  To reiterate, this comparison assumes that you invest the difference in a tax-advantaged account and don’t spend it on something else.

If you buy used F150s instead of new ones, the historical stock market returns indicate that you will have an average of $390,000 more in retirement savings at the end of 40 years with a range of $200,000 to $800,000.   For the Subaru, the average is $160,000 in a range of $75,000 to $350,000.

This analysis indicates that, if you prefer to drive fairly expensive cars that depreciate quickly when they are new, you can accumulate a substantial amount of money if you buy used cars for 40 years.  For less expensive cars that don’t depreciate as quickly, the additional savings amount isn’t as large but is still significant.

More Expensive vs. Less Expensive

You can get almost as much additional retirement savings if you buy a less expensive new car and own it for 10 years as you can if you buy the used F150 instead of a new one and more than if you buy a used Subaru instead of a new one. For example, if you buy the Fusion (currently about $15,300 new) instead of the Subaru Impreza (currently about $26,000 new according to Edmunds) every 10 years, you would have an average of about $300,000 more in retirement savings.  That additional money comes from:

  • the $11,000 of up front savings from the first car purchase,
  • the $8,000 of savings for purchase of the three replacement cars after trade-in,
  • the $250 to $350 a year less it costs to own the Fusion, and
  • the investment returns on those savings.

This analysis shows that you can save more by buying a less expensive new sedan (the Fusion) every 10 years than by buying a three-year old Subaru every seven years. That is, if instead of buying new Subarus you buy new Fusions, you will have an average of $300,000 in additional retirement savings, but only $160,000 if you buy used Subarus.

Length of Time Owned

You can also accumulate savings by buying cars less often.  For this comparison, I looked at comparison of buying new Subarus and F150s every five years and every 15 years.  If you replace the Subaru every 15 years, you will accumulate an average of $300,000 of additional retirement savings in 40 years as compared to replacing it every five years.  With the faster depreciation and higher cost of the F150, the average additional savings in 40 years is about $600,000.

Comparison of Options

The box and whisker plot below (discussed in more detail in my post on risk) compares the amount of additional retirement savings you will have under the options above.  Briefly, the boxes represent the range between the 25th and 75th percentiles, while the whiskers (lines sticking out of the boxes) represent the range between the 5th and 95th percentiles.  Recall that the only source of variation in these results is the different time periods used for stock returns – the 39 30-year periods starting in each of 1950 through 1988.

The first three boxes relate to the purchase of fairly modest sedans – the Subaru and Fusion.  The graph shows how much more retirement savings you will have if you either buy new Fusions instead of new Subarus (second box) or replace your new Subaru every 15 years instead of every 5 years (third box) than if you buy three-year-old Subarus instead of new ones (first box).

The last two boxes relate to the purchase of the more expensive F150.  Again, you will accumulate much more in your retirement savings if you replace your F150 every 15 years instead of every 5 years (last box) than if you buy three-year-old trucks instead of new ones (second to last box).

Final Words

Ultimately, you’ll need to buy a car that best fits in your budget and meets your needs. As you make your choice, though, you might want to remember that there are clearly ways you can save money even if you prefer to buy new cars.

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My Next Car: Pay Cash, Borrow or Lease?

The finances of buying a car can be tricky.  In addition, there are so many other things to consider. What kind of car do I like?  How often do I want to replace my car?  How many people (and pets) do I need to be able to transport comfortably?  Through what weather conditions do I need to drive? Do I want a new or used car (as discussed here)? In this post, I’ll focus on the finances of purchasing a car once you’ve decided generally what car(s) fit your other needs.  Specifically, I’ll describe the financial considerations of three options for buying your next car: pay cash, borrow or lease. I will also provide a spreadsheet to allow you to compare the finances of specific deals.

The Basics of Leases and Loans

I have a post that provides all the basics you need to understand about loans.

There are plenty of resources available to provide you with information about leases, so I won’t repeat that information here.  Here are a few resources:

  • This article focuses on teenagers, but it covers a lot of important aspects of leasing. Consumer Reports is considered an independent source for information about purchases.
  • Edmunds is a company that values and researches cars, as well as having a platform for selling used cars. Its guide on leasing can be found here.
  • The first several sections of this post by Debt & Cupcakes (@debtandcupcakes) provide details about leasing, along with the pros and cons.
  • Real Car Tips also has a guide for leasing. Here is the link for the leasing guide.

Your credit score is an important driver of the terms you will be offered whether you lease or borrow.  When I looked for examples on line, all of the offers were contingent on your credit score being above 800.  A credit score of 800 is excellent.  I have a post on how you can check and improve your credit score.

The Finances of Owning a Car

Cars are expensive to own.  This post will focus on the cost of buying a car under three different options – cash, borrowing and leasing.  As you evaluate which of the options works for you, you’ll also want to make sure you are able to afford the other costs of ownership of a car.  In addition to the purchase costs discussed below, there are four other categories of expenses:

Fuel

Your car needs gas, diesel or electricity.  As you are selecting a car, you’ll want to consider the type of fuel your car needs, the miles per gallon the car gets and how many miles you are going to drive.

Registration

You will need to register your car every year.  In the states in which I’ve owned cars, registration is a function of the value of the car – the higher the value, the higher the registration fees. I recall that a car worth $20,000 cost about $300 to $400 a year to register, whereas the minimum charge (for older cars) was about $50 a year in Minnesota, but the amounts vary widely across states.  In other states, registration fees are a flat amount regardless of the age or value of your car.

Insurance

In all states you are required to buy car insurance. This post provides information on insurance you are required to purchase and coverages you might want to purchase.  Liability insurance usually doesn’t depend on the value of the car, though can be higher for sportier and faster cars.  The premiums for physical damage coverages (comprehensive and collision which protect you against damage to your car) increase with the value of your car.

Maintenance & Repairs

Cars need regular maintenance – oil changes, replacement brakes and tires, among other things.  Some dealers provide regular maintenance at their location for one or more years if you buy a new car, but that is not always the case.  In addition to regular maintenance, cars break down and need to be repaired.  Repair expenses tend to be higher on older cars.  Even on new cars, repairs can be expensive and unexpected.

You’ll want to keep some money in your designated savings for car repairs, as discussed in this post.  Another option is to buy an extended warranty to cover repairs to your car.  Extended warranties can be quite expensive, but cover the cost of some major repairs if they are needed.  I’ll write about extended warranties in another post in the future. If you choose to purchase an extended warranty, you’ll need to include that cost as part of your expenses related to owning the car, along with a provision for repairs not covered by the warranty.

How to Think About the Finances of Buying a Car

Determine Your Needs

I always find it helpful to define what I want and can afford before I go shopping for anything expensive, cars in particular.  My husband does all of the negotiating on price for our cars because that is a skill I never acquired and I don’t like the process so don’t want to acquire it.  I figure out what I need, what’s available in our price range that meets those needs and make a very detailed list so he can go to different dealers to negotiate the terms.

As part of your needs, you’ll want to think about the length of time you’d like to own your car.  Some people like to drive a new or at least a different car every few years.  I was that way when I was young – I bought a different car every 3 years for a bit.  I’ve always regretted selling the first one – a 1969 Mustang convertible. Live and learn!

Other people drive cars until they die or become unreliable.  Now that I understand the finances of cars better, I have moved to the second category.  The most recent two cars I’ve sold (both Honda Preludes) had 250,000 and 150,000 miles on them respectively.  The only reason I sold the second one is because I moved to a place with hills and snow, as opposed to flat and snow, and a Honda Prelude just wasn’t going to get me home reliably in the winter.

Figure Out What You Can Afford

The second step in the process – figuring out what’s in your price range – can involve several perspectives.

  1. How much cash do you have available to either pay for the entire car or put as an initial payment towards a loan or lease? As you consider that amount, you’ll want to take the total cash you have available and reduce it for the other costs of ownership I’ve listed above.
  2. If you aren’t going to pay cash for the car, how much you can afford to pay every month? Again, don’t forget that you’ll need to pay for registration, insurance, fuel, maintenance and repairs, too.
  3. If you can’t find new cars that fit in your budget, you might need to look at used cars. I have another post planned that will address the finances of buying new versus used.

Gap Insurance

Gap insurance is another expense you may have to pay if you don’t pay cash for your car. In some cases, you’ll want to buy it for your peace of mind.  In other cases, the lender or lessor may require it.

Gap insurance protects you against the difference between the value of the car and your outstanding balance at any point in time during the loan or lease.  Although it may not be clearly stated in your lease agreement, lessors think of your lease payments as including compensation to them for the reduction in the value of the car as you use it (depreciation) and interest on the value of the car (similar to loan interest).  As such, both loans and leases have outstanding balances at all times during their terms.

The chart below compares the outstanding balance on a loan with an estimate of the value of a $23,000 car over the term of an 84-month loan.  For this illustration, I’ve assumed that the borrower paid $1,000 towards the value of the car as a down payment and the loan has a 3% interest rate. I estimated the value of the car by looking at the clean trade-in value of a Ford Fusion from prior model years on the National Automobile Dealers Association (NADA) web site, a common source for lenders to get car values.

For the Ford Fusion, the loan balance is more than the value of the car between 4 and 36 months.  If the car is totaled, your car insurer will reimburse you for the value of the car minus your deductible.  During that time period, you will owe the lender not only your deductible but the difference between the blue line and the orange line.  To protect yourself from having to pay the additional amount, you can buy gap insurance.

You’ll want to investigate the cost and need for gap insurance for the particular make and model you are buying.  Cars depreciate at different rates.  For example, when I looked at the NADA web site for a Subaru Impreza, the value never went below this illustrative loan balance.

The Finances of Cash, Leases and Borrowing

Now that I’ve covered the preliminaries, we can get to the main topic of this post – the details of paying cash, borrowing and leasing.

Cash

When you pay cash for a car, there is only one number on which you need to focus. It is the out-the-door cost of buying the car.  This amount will include some or all of the following:

  • The cost of the car,
  • The additional cost of options you choose,
  • Sales tax (called excise tax in some jurisdications),
  • Processing and documentation fees,
  • Delivery charges, and
  • Title and registration fees.

Not all of these charges are included in every state or by every dealer.  I recently bought a new car in Montana. There is no sales tax in Montana, there wasn’t a delivery charge and you pay the state for title and registration fees directly, so the only things on my invoice were the cost of the car, the cost of the two options I added and a $100 documentation fee.  If you are comparing prices from different sources, you’ll want to make sure that they consistently treat all of these possible costs. For example, you should make sure they either all include or all exclude title and registration fees.   If not, you’ll need to add them to your analysis of the total amount you can pay for the car.

Leasing

The finances of leasing involve many important numbers, even more than borrowing.  All of these numbers should be available to you in the contract and from the dealer or leasing company. 

Up-front Payment

You’ll want to make sure you know the total amount of the up-front payment, including sales taxes, title and registration fees and the base charges from the dealer and finance company. The up-front payment often includes the first month’s lease payment, but not always, so you’ll want to be sure to know whether it is included for each offer you consider.

Monthly Payment

The amount that you’ll pay every month.

Sales Tax Rate

You pay sales tax on your monthly lease payments.You’ll need to know if the sales tax is included in the monthly payment you’ve been quoted and, if not, what sales tax rate applies.

Term

The term is the number of months you are committed to the lease. It is important to note that my spreadsheet assumes the lease term is 36 months and you will honor your commitment to the lease for its entire term.  There can be significant penalties if you choose to return the car before the lease ends.

Allowed Annual Mileage

Every lease contains a maximum number of “free” miles you can drive on average each year.

Estimated Actual Annual Mileage

You can use your actual annual mileage to estimate how much you will have to pay in excess mileage charges to understand the full cost of a least.

Cost Per Extra Mile

If you exceed the total allowed mileage (the allowed annual mileage times the term), you will pay an extra fee when you return the car. To calculate the extra amount, you first take your actual mileage and subtract the total allowed mileage.  You then multiply the excess miles by the cost per extra mile.  As I’ve looked on line at leases, I’ve seen several that charge 15 cents per extra mile.  If, for example, you drive 50,000 in three years on a car with 12,000 miles allowed and a 15 cent per mile charge, you will pay an extra $1,800 when the lease ends.

You may also need to pay a fee if your car experiences more than the normal amount of wear and tear. For example, if you live on a gravel road or a busy street, your car may have many more nicks and dings than someone who lives on a quiet paved cul-de-sac.

Residual Value

If you think you might want to buy the car at the end of the lease, you’ll need to know the residual value.This amount is what you will pay to keep the car.

Monthly Cost of Gap Insurance

If you want or need to buy gap insurance, you’ll want to know by how much it costs each month. You can buy gap insurance from your car insurer and, sometimes, the dealer, though I’ve read that buying it through the dealer tends to be more expensive.

Borrowing

The finances of taking out a loan for a car are a bit less complex than leasing. Here are the important numbers you need to know.

  • Up-front payment – You’ll want to make sure you know the total amount of the up-front payment, including sales taxes, title and registration fees and the base charges from the dealer and finance company. The up-front payment often includes the first month’s lease payment, but not always, so you’ll want to be sure to know whether it is included for each offer you consider.
  • Amount financed – This amount is equal to the total value of the car minus the portion of your up-front payment that goes towards paying for your car.
  • Monthly payment – The amount that you’ll pay every month. There is no sales tax on loan payments.  The sales tax was considered in the total amount of the car used to determine your up-front and monthly payments.
  • Interest rate – The interest rate, along with the amount financed and monthly payment, are used to determine the remaining principal on your loan at point in the future. If you want to sell your car before you have paid off your loan, you’ll want to be sure to know the amount financed and the interest rate so the spreadsheet can calculate the remaining principal.
  • Loan term – The term determines how many monthly payments you will make.
  • Monthly cost of gap insurance – If you need or want to buy gap insurance, you’ll want to know by how much it costs each month.

Illustrative Comparison

Because I just purchased a Subaru Impreza for around $23,000, I use it and two other cars advertised as having similar costs as illustrations.

The Offers

The table below summarizes the values I found on line and/or created for a Subaru Impreza, a Toyota Camry and a Ford Fusion

Although the cash prices are similar, the Lease and Borrow options have fairly different terms. The amount due at signing and monthly payment are much lower for the Toyota Camry lease than for the other two cars. The interest rates on the loans are very different, even though the monthly payments are all essentially identical. The Subaru has a lower interest rate and shorter term than the other two cars.  Because the payments are the same and the interest rate is higher, the amount due at signing must cover more of the cost of the Toyota than for the other two cars.

Not all of these values were clearly identified in the terms I found on-line.  The actual offers could be somewhat to significantly different from the values I’ve shown above.  Nonetheless, the differences in the terms help differentiate the total financial cost of these offers.

Look at Just the Subaru

We will first look at a comparison of the three options for the Subaru Impreza. Before we can do that, you need to determine for how long you want to own the car.  For illustration, I’ve looked at two options – own it for the term of the lease (assumed to be 36 months) or own it until it dies (or at least until you’ve made all of your loan payments).

Sell in Three Years

The first row of the table below shows the total of all of the payments you will make under each of the three options over the course of the first three years.  For the Cash option, it is your out-the-door cost. For the Borrow and Lease options, it is the sum of the amount due at signing, your monthly payments and the monthly cost of gap insurance.  For the Lease option, I added sales tax to the monthly lease payments.

Three Years Cash Borrow Lease
Upfront Cost + Monthly Payments $23,691 $14,133 $15,971
Amount on Sale 12,000 761 -1,350
Net Cost 11,691 13,372 17,321

The second row shows how much you would get or pay at the end of 36 months.  For all three cars, I have assumed you can sell them for $12,000 after three years. For the Cash option, the second row shows the total sales price of the car.  For the Borrow option, it is the difference between the $12,000 sales price and the loan balance.  For the Lease option, the value is negative meaning it is an amount you have to pay instead of receive.  It is the charge for the extra miles put on the car.  If you look at the inputs table, you’ll see that there is a 15 cent per mile charge for every mile over 12,000 a year and I have assumed you will drive 15,000 miles a year.

The third row shows the total net cost, calculated as the first row minus the second row.  For the offers for the Subaru Impreza, the Cash option is cheapest if you plan to sell after 3 years.  If you can’t afford to pay cash up front, the Borrow option is preferred to the Lease option.

Drive Forever

Under the Drive Forever option, the sales price of the car is assumed to be essentially zero, so we can look at just the cash outflows.  The table below summarizes the total cost of the three options.

Drive Forever Total Cost
Cash $23,691
Borrow 25,581
Lease 31,321

The total cost of the Cash option is the same as in the Three Years table.  There are no purchasing costs other than the amount paid at signing under this option.  For the Borrow option, the total cost has increased from the Three Years option because it now includes the monthly payments after three years until the loan is fully re-paid.  For the Lease option, the cost has increased by the residual value of the car, $14,000 in this case.  That is, in addition to the up-front and monthly lease payments, you’ll need to pay the $1,350 for the extra miles and $14,000 to buy the car from the lessor.

Using the longer time frame, the Lease option is even more expensive than the Borrow option.  Because the interest rate is fairly low, the additional interest paid after three years isn’t a lot so the difference between the Borrow and Cash options doesn’t increase by a large amount from what was observed for the Three Years option.

Look at All Three Cars – Three Years

The relative order of the three options varies depending on the terms of the offer. The graph below compares the net costs of ownership of the three cars if you anticipate selling the car in three year.

The values for the Subaru Impreza are the same as the ones in the third row of the Three Years option table above.  As can be seen, leasing isn’t always the worst option as was the case for the Subaru. The Lease option is less expensive than the Borrow option for the Camry and is only slightly more expensive than the Borrow option for the Ford, using the three-year time frame.

If you are indifferent among the three cars, you could also compare the costs among the cars.  For example, let’s say you don’t have enough cash to pay for the car up front, so you are looking at the Lease and Borrow options. The net cost of the Lease option for the Camry is about the same as the Borrow option for the Impreza.  The risk of the Lease option is that you will drive even more miles than you’ve estimated adding to the net cost of the Camry Lease option.  You would want to offset that risk with the risk that you might not get $12,000 for the Impreza when you sell along with the hassle of having to sell the Impreza.

This comparison highlights the importance of getting all of the detailed terms of every option.

Look at All Three Cars – Drive Forever

The graph below shows the same comparison for the “Drive Forever” option.

Other than the total costs of ownership being higher (because you are owning the car until it dies instead of having to replace it or selling it in three years), the relationships among the three options for each car are essentially the same. That is, the order and relative costs of the Cash, Borrow and Lease options are the same for each vehicle.

Of the Lease and Borrow options, the Impreza Borrow option is the least expensive in this example.  The Camry Borrow and Lease options and Ford Borrow option are all $3,000 to $4,000 higher, so you might choose from one of those if you didn’t like the Impreza.  If you have cash to buy the car outright, the Ford Cash option is the least expensive, though the Camry is only a few hundred dollars more.

In addition to comparing different makes and models, you can make similar comparisons among offers you obtain from different dealerships for the same car.

Can I Invest my Cash and Use it to Pay Off my Lease or Loan?

For those of you who read my post about Chris’s mortgage, you know that I suggested he consider paying the minimum payments on his mortgage and investing the rest of his money.  You may be wondering why I haven’t talked about the benefits of investing money under the Lease and Borrow options.

There are a few reasons.

  • Most people who buy a car using a lease or borrowing don’t have the cash available to pay for the car up front. If you don’t have cash to invest, there is no possibility of investment returns.
  • The term of a lease or loan is much shorter than the length of a fairly new mortgage. In Chris’s case, he had 26 years of payments left on his mortgage.  As I discussed in my post on investments and diversification, the likelihood you will earn the average return increases the longer you invest. With the short time span of a car loan or lease, investing in stocks with the expectation of having money to pay off your lease or loan would be very risky.  There is a fairly high probability your investments wouldn’t return enough to make those payments.
  • To avoid the chance that your investments wouldn’t cover your car payments, you could invest in something with very low risk, such as a money market account, certificates of deposit (of which you would need a lot to match the timing of your loan or lease payments) or high yield savings account. Low risk investments currently have very low returns – generally less than 2.5% pre-tax and even less than that after tax.  There are very few loans or leases that have interest rates (implicit in the case of a lease) that are less than 2.5%, so there isn’t much benefit in investing cash in risk-free assets until your loan or lease payments are due.

How To Use the Spreadsheet

To help you create your own comparisons similar to the ones above, I’ve provided you my spreadsheet at the link below.

Overview

The flowchart below will help guide you through the financial aspects of the car-buying process.  It assumes that you have identified one or more cars that will meet your needs and possibly fit in your budget.

The hexagonal boxes in a flow chart correspond to decision points. The rectangular boxes contain action items.

The first step is to determine whether you can afford to pay cash.  If not, you won’t have to negotiate a price for the Cash option for any of the cars you are considering.

Next, take a look at estimates of the up-front and down payments for the Lease and Borrow options.  If you can’t afford either of them in addition to the other costs of car ownership, you will need to find a less expensive option – either new or used – and go back to the top of the flowchart.

The next decision point is how long you want to own the car – the term of the lease (which I have assumed will be three years) or a much longer time (at least as long as the term of the loan in the Borrow option).  When you are done entering the values, you’ll look at the summary at the top of the Lease Term tab if you plan to own the car for the lease term and the Drive Forever tab if you want to own it longer.

If you want to own the car beyond the end of the lease, you’ll need to be able to afford to pay the residual value at the end of the lease.  If not, you’ll want to exclude the Lease option from consideration and focus on the Borrow option.

Collect Terms

Once you’ve narrowed down your choices to a few cars and figured out which of the Cash, Lease and Borrow options work for you, you will be ready to talk to dealers and other car sellers.  The Inputs tab of the spreadsheet lists all of the information you need for each type of purchase.  I defined each of the inputs earlier in this post.  For every deal you are offered, be sure to get all of these values.  I found that there are some of these values that are consistently unavailable if you look on line.  You may need to ask for some of these items specifically.  If you aren’t sure you are getting straight answers, you can always ask for the actual contract.  It is required to have all of the terms.

Enter Values in Spreadsheet

Next, enter all of the values into the Inputs tab.  Then, go to the tab that corresponds to the time period you plan to own your car – Lease Term or Drive Forever.  You can see the total cost of the options for which you entered the data.

If you have deals for more than one car, I suggest making one copy of the spreadsheet for each car.  You can then compare not only between the Cash, Lease and/or Borrow options for a single car, but can compare whichever options are available to you across cars.

Your final choice of car and deal could be the least expensive or a different one. It will all depend on your personal financial situation, your qualitative considerations and their relative importance.  Buying a car is an important decision, so cost may not be the only factor to influence your decision.

Download Car Comparison Spreadsheet

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Savings Accounts for Kids

Many parents want to create savings accounts for their kids – for one or both of funding their education or giving them a head start on life.  In this post, I’ll focus on the different types of accounts you can use for the latter purpose – giving them a little (or maybe more than a little) money to get started.  Savings accounts for kids can also be used if your children receive an inheritance, such as from a grandparent or other relative.  I’ll talk about saving for education in a separate post, as it is a lengthy topic all by itself.

Ways to Save for your Kids

There are several ways to save for your kids.  They range from easy – for example, just open an account in your name with the intention of giving the money to the kids – to quite complicated and possibly expensive – for example, setting up trusts.  Besides the ease of the process and the expense, your choice will also depend on when you want your children to be able to access the money and your and your kids’ tax situations.

Starting from simplest to most complex, I will explain the following options here:

  • Open an account in your name.
  • Open a joint account.
  • Create an account under the Uniform Gift to Minors Act (UGMA) or Uniform Transfer to Minors Act (UTMA).
  • Create a trust.

A Caution about Gifts and Taxes

Before making gifts to your children, you need know that there are tax rules in the US about gifts themselves as well as any investment returns your children earn.

Gift and Inheritance Taxes

Information from the Internal Revenue Service (IRS) about gifts can be found at this link.  Each individual can give another individual a gift of up to the gift tax limit ($15,000 in 2019) each year without any tax consequences.  For example, each of a father and mother could give their daughter a gift of $15,000 for a total of $30,000 in a year and there would be no additional tax reporting or taxes.

If you make a larger gift, the portion in above the gift limit is called an excess gift and needs to be reported to the IRS.  According to Schwab’s web site, you do not have to pay gift tax to the IRS as long as the combination of your gifts in excess of the limit and the amount you give to people as part of your estate when you die doesn’t exceed a stated threshold ($11.18 million for 2019 through 2025).  I believe that the excess gift and estate tax limit in some states is much, much lower.  If you are fortunate enough to be able to make large gifts, I suggest you contact your tax advisor to ensure you understand the tax ramifications.

Taxes on Children’s Income

A child’s unearned income (e.g., interest, dividends and capital gains) exceeds $2,100 may be subject to tax, according to the IRS web site.  As outlined at that link, in some cases, parents can report the child’s income on their own tax return.  In other cases, the child must file its own tax return.

The 2019 Federal tax rates on child’s taxable income go up very quickly, as shown in the table below.  Taxable income includes all earned and unearned income.

Taxable Income Taxes
Up to $2,550 10% of taxable income
$2,550 – $9,150 $255 + 24% of taxable income in excess of $2,550
$9,150 – $12,500 $1,839 + 35% of taxable income in excess of $9,150
More than $12,500 $3,011.50 + 37% of taxable income in excess of $12,500

If you choose to gift large amounts of money to your children, you will want to consider whether you can include your child’s income on your return, the complexity of filing a separate return for your child and the difference in the taxes on your income as compared to your child’s income.

Separate Bank or Brokerage Account (in Your Name)

The easiest way to open a savings account for your kids is to open a bank or brokerage account in your name and know “in your mind” that you intend to give the money to you kids.  The advantage of this type approach is that you have complete access to the money and can change your mind about giving it to your children.  Of course, that defeats the purpose of setting aside money for your kids!

You will report any interest, dividends or capital gains from the account on your tax return, as you own the account.  If you use this approach, you’ll want to be careful of the gift tax rules when you transfer it to your child.  The value of the account may exceed the gift tax limit when you give the money to your child if you have been contributing to it for many years and/or it has grown through investment returns.

Joint Bank or Brokerage Account

Another form of savings accounts for kids is a joint account at a bank or brokerage account. That is, both your and your child’s name will be on the account.  We took this approach for our children to teach them about saving.

Some of these accounts allow your child to deposit or withdraw money at any age, while others allow only you to make transactions on the account.  If you choose a truly joint account (which means your child can make withdrawals), you need to be certain you can stand watching them withdraw the money and spend it on their own.  I will admit I was surprised at my emotional reactions to watching my children spend money.  They were much stronger than I would have guessed.

According to Pocket Sense, if your child doesn’t file a tax return, you will report the income, gains and losses on the account on your tax return – the same as if you open the account on your own.  If your child files a tax return, you’ll report all of the income as yours, but you then deduct your child’s share from your return and report it on his or her return.  In addition, the amount you deposit into the account is considered a gift to your child in the year it which it is withdrawn.

UTMA/UGMA Accounts

There are two types of savings accounts for kids that give you a bit more control over the money than a joint account.  These accounts are Uniform Transfer to Minors Act (UTMA) and Uniform Gift to Minors Act accounts.

UTMA and UGMA accounts are easy to set up at a bank or brokerage firm. Someone, often the parent or person who opens the account, is identified as the custodian on behalf of the minor (the beneficiary).  The money in these accounts can be used by the custodian for the benefit of the minor, though there are fewer restrictions on how money in an UTMA account can be spent than an UGMA account.  Broadly, expenses that parents usually pay for their children, such as food, housing and clothes, are considered to be “for the benefit of the minor.”  At ages established by each state individually for each type of account, often 18 for UGMA accounts and 21 for UTMA accounts, the beneficiary becomes solely responsible for the account.

These accounts have the benefit that your child can’t access the money until they are at least 18.  They have the drawback, relative to a joint account, that you can use the money only for the benefit of your child.

The money you put in an UTMA or UGMA account is considered a gift when you deposit it.  Any interest, dividends or capital gains will be reported as the child’s income, so you might have to file a tax return for your child if he or she has enough income.

Trusts

Another legal structure you can use when you open a savings account for kids is a trust.  A trust is a legal entity that requires a trust agreement and gets its own tax ID number.  The trustee is the person who oversees the trust until the child receives the money.

We created a trust for each of our children, as they each received an inheritance that stipulated that the money be put in trusts, and had a lawyer draft the trust agreement.  I suspect there are books and websites that will help you do it yourself as well, but you’ll want to consider the cost of establishing a trust as you decide it this option is best for you.

Once you have created the trust, you can then open a bank or brokerage account on its behalf.  The trust agreement will specify who can withdraw money and for what purposes. One of the advantages of a trust over an UTMA or UGMA account is that you determine the age at which your children receive the money.  In some cases, people even release portions of the money to their children at two or three different ages.  If you are concerned about your child’s ability to handle money responsibly, a trust will allow you to delay distribution of the money to them until they are more mature.

Trusts always needs to file a tax return separate from you and your child.  The 2018 tax rates for trusts are the same as those shown above for children shown earlier in this post.  Any deposits into a trust are considered as gifts by the IRS.

Summary

This table shows a quick comparison of the four different options I’ve described here.

  Account in your name Joint Account UTMA/UGMA Trust
Who owns the account You Both Child, with custodian oversight Child, with trustee oversight
When can child spend money Only when you transfer it Anytime At age established by state At age established by trust agreement
Purposes for which you can withdraw money Anything Anything For benefit of child As specified by trust agreement
When considered a gift When you transfer money When spent by child When deposited When deposited
Who pays taxes You 50% by you/50% by child Child Trust

 

For other tips on how to help your kids become financial literate adults, check out my guest post for Grokking Money in honor of Financial Literacy Month.

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Should Chris Pay off his Mortgage?

Chris @Money$tir asked other financial literacy and financial independence (FI) bloggers, in a post on March 9, 2019, whether he should pre-pay his mortgage or invest the money. He provided his thought process and calculations. In this post, I will review his calculations and then show that his decision will be easier if he narrows his question and analysis. I will also provide my findings and analysis to help inform his decision.

Background

Chris’s post provides all of the background. You might want to read his post quickly to understand his calculations and other considerations before you read the rest of this post.

Briefly, he will have just under $310,000 left on his mortgage on July 1, 2019. His payments are $1,525 and he will have an additional $4,000 a month available to either pre-pay his mortgage or invest.

I followed up with Chris and learned that he expects to take the standard deduction on his tax return, so he will have no tax benefit from his mortgage interest. His marginal tax rate on ordinary income is 22%; on capital gains and dividends, 15%. I also confirmed that Chris does not have any pre-payment penalties associated with his mortgage.

Three Re-Payment Options

Chris suggested three options in his article, two of which involve making pre-payments. The three options are:

1. Make $1,525 a month in mortgage payments until his mortgage is fully re-paid in July 2045, while investing the remaining $4,000 at 8% per year.

2. Take a middle-of-the road option and make mortgage payments of $3,525 each month and invest the remaining $2,000. Under this option, his mortgage will be re-paid in 2027.

3. Pay $5,525 each month – $1,525 in scheduled payments and $4,000 in pre-payments – until his mortgage is fully re-paid in 2024.

Chris calculated his pre-tax savings using an 8% return through July 2045. The values he calculated are:

• Option 1 – $4,145,000
• Option 2 – $3,772,000
• Option 3 – $3,594,000

In his post, Chris indicated he is leaning towards Option 3 – pre-pay his mortgage as quickly as possible.

Chris’s Math

One of Chris’s questions is whether his calculations are correct. I re-created Chris’s calculations. While I did not get his ending balances exactly, my results were within a couple of percentage points, so I suspect we made slightly different assumptions regarding either the timing of the interest charges (beginning or end of month) and/or his exact mortgage balance. I’m quite comfortable that the calculations he performed are what he intended.

I also confirmed that increasing his payments by $2,000 or $4,000 a month shortens the time until his mortgage is fully re-paid as he indicated in his post.

Re-framing the Question

Many of Chris’s considerations relate to additional flexibility he will have after his mortgage is fully re-paid. I believe that Chris has not correctly separated the mortgage re-payment question from his other decisions – renting out his house and buying a new one, not having a mortgage if he decides to downsize, freeing up money for other purchases and so on. That is, as discussed below, he can use his first five years of savings in Options 1 and 2 to make the rest of his mortgage payments. By understanding that, he can independently decide to do with the $5,525 a month after five years doesn’t depend on his choice of payment option.

If Chris changes his calculations consistent with the re-framed question (i.e., looking at only the $5,525 a month for the first five years), he can eliminate all of the noise of these other questions as they will become independent of his mortgage decision. In his calculations, Chris has set aside $5,525 every month until his mortgage would be fully re-paid in 2045 if he made the minimum payments. Instead, I propose that he set aside $5,525 a month only until 2024 (and not after) – that is, only until his mortgage would be fully paid under Option 3. Except in certain situations discussed below, Chris will make his mortgage payments starting in August 2024 from the savings that accumulates from the money he saved up until then and not from his future income or other savings. That stream of payments, if invested in a hypothetical risk-free, tax-free financial instrument at 3.625% would exactly pay off his mortgage regardless of which of his three re-payment options he chooses.

By focusing on this shorter stream of payments until 2024, he can do whatever he wants with the $5,525 a month after his mortgage is paid off under all three re-payment options. As a result, his decision-making process can focus solely on the risks and rewards of his three re-payment options without any consideration of other, unrelated financial decisions.

My re-framed question does not eliminate one of his considerations – his peace-of-mind from not having a mortgage. Chris will need to include this subjective consideration in his decision-making process, along with the considerations regarding risk and rewards presented below.

My Math

There are four changes I made to Chris’s calculations:

1. I assumed that Chris set aside $5,525 a month from July 2019 through August 2024, rather than until 2045. In addition, except as noted below, after July 2024, he will make his remaining mortgage payments from the savings he has accumulated and not from his income. Therefore, starting in August 2024, he can use the $5,525 a month however he wants as I excluded it from my analysis.

2. I introduced the impact of income taxes. Chris will pay taxes on his investment returns which will make the first two options look less attractive than is shown in his analysis.

3. I quantified the risk Chris will assume by investing in the first two re-payment options.

4. I focused on Chris’s financial position not only in 26 years (when his mortgage would be paid off making the minimum payments), but also in 10 years (when he might want to down-size).

Three Investment Strategies

Chris’s first and second options assume he will invest in an S&P 500-like ETF returning 8%. His calculations do not quantify the riskiness of the S&P 500, though he does mention the risk in his subjective considerations. I will provide explicit insights on the risk. In addition, because Chris is concerned with the riskiness of the S&P 500, I also looked at two other options, for a total of three investment strategies:

1. Invest in 100% in stocks, such as an S&P 500 ETF.

2. Invest in 100% bonds, such as a bond fund. I used the Fidelity Investment Grade Bond Index (FBNDX), as a proxy.

3. Invest 50% in each of stocks (an S&P 500 ETF) and bonds (the Fidelity bond index).

Under all three strategies, I assumed the Chris would re-invest all interest, dividends and capital gains, after tax, and would not withdraw it except to make his mortgage payments.

In my analysis, I calculated Chris’s financial position as if stocks and bonds had the monthly returns observed historically for the 10-year periods starting on the first of each month from January, 1980 through October, 2008 (10 years before my time series ended). There are 345 overlapping 10-year periods. For the 26-year time frame, there are only 153 overlapping periods covered by the Fidelity bond index data. I therefore looked at only the S&P 500 investment option when doing the calculations of Chris’s financial position in 2045.

Timeline

The infographic below clarifies the key dates under all three options and provides a teaser of the results.

Option 1

Under Option 1, Chris will make payments of $1,525 a month to his lender from July 2019 to August 2024 from his income. He will also save $4,000 a month over the same time period. This time period is represented in green. From August 2024 until July 2045, he will withdraw $1,525 from the savings he accumulated in the first five years to pay his mortgage. This period of time is shown in orange.

Option 2

Under Option 2, Chris will make payments of $3,525 a month to his lender from July 2019 to August 2024 (the green segment) from his income. He will also save $2,000 a month over the same time period. From August 2024 until December 2027 (the orange segment), he will withdraw $3,525 a month from his accumulated savings to pay his mortgage. He will have fully re-paid his mortgage by December 2027, so any leftover savings will remain invested until July 2045. This time period is represented in yellow.

Option 3

Under Option 3, Chris will make payments of $5,525 a month to his lender from July 2019 to August 2024 (the green segment) at which point his mortgage will be fully re-paid. Because he hasn’t put any money in savings, he will have no savings so nothing will happen related to the money from the green time period during the yellow time period.

Check-In Dates

The infographic also calls out July 2029 and July 2045. These are the two dates that Chris mentions in his post as being possible decision dates. In ten years (July 2029), he might want to sell his house and downsize. In July 2045, his mortgage will be fully paid if he makes his minimum payments and it offers another point at which to consider selling the house.

The infographic shows the balance of his mortgage and the average amount of his after-tax savings if he invests 100% in stocks. As will be discussed below, there is a lot of risk around this average and it is calculated using historical returns, so there is also uncertainty around it.

Summary of Findings

Here are the key findings of my analysis. They will be discussed in detail below.

● Chris’s time horizon is important in making his decision.

o If he plans to keep his house until 2045, the historical data indicate he is better off in three-quarters of the scenarios making his minimum payments and investing in stocks. The average values of his after-tax savings are shown in the infographic above and show that he will have more savings on average with lower monthly mortgage payments.

o If he plans to sell his house or use the money he has saved to fully re-pay his mortgage 10 years from now, the decision is not as clear cut and will need to consider his risk tolerance. Because Chris plans to continue to work for many years, he may be able to tolerate more risk than someone who plans to retire before their mortgage is fully re-paid.

● Chris’s investment mix is important in making his decision.

o If he plans to keep his house until 2045, the historical data indicate that he is better off investing 100% in stocks.

o If he plans to sell his house or use the money he has saved to fully re-pay his mortgage 10 years from now, the mix of investments will depend on his risk tolerance.

● The historical data indicate Chris’s downside risk is not significantly changed by the stock market possibly being near its peak.

Discussion

I will start by providing insights on Chris’s financial position on average across all of the time series of historical investment returns – first for the 10-year period and then for the full 26-year period. I will then discuss the riskiness of the options. The last part of this discussion will focus on how I evaluated his results if the stock market were at a peak.

Average Results – 10 Years

The table below summarizes Chris’s average financial position, based on the historical investment returns, in 10 years on July 1, 2029, the time frame he referenced as possibly wanting to downsize. The invested asset row shows the balance of his investments if he sells all of his positions on that date and pays the related taxes. The “net worth” row shows the average amount Chris will have left if he pays off the balance of his mortgage with his after-tax investments.

Payment Option 3 2 2 2 1 1 1
Mortgage Payment $5,525 $3,525 $3,525 $3,525 $1,525 $1,525 $1,525
Investment Option All 100% Bonds 50% Bonds/ 50% Stocks 100% Stocks 100% Bonds 50% Bonds/ 50% Stocks 100% Stocks
Invested Assets $0 $10,620 $25,515 $34,396 $248,941 $285,615 $324,269
Mortgage Balance 0 0 0 0 221,928 221,928 221,928
“Net Worth” 0 10,620 25,515 34,396 27,033 64,687 102,341

I use “net worth” in quotes because it includes only the assets emanating from the $5,525 per month for the next five years and only his mortgage balance as a liability. In addition, Chris will have his house, all of his other taxable savings, his retirement accounts, and so on and so forth. Because all of these other assets are the same regardless of which option he chooses for his mortgage re-payment, I have excluded them from the comparison.

The positive “net worth” numbers mean Chris will get to keep the entire proceeds of his house if he sells it in 10 years plus the positive “net worth.” If there were negative “net worth” numbers (which there are in the graphs below), Chris would need to use that portion of the proceeds from his house to contribute to the settlement of his remaining mortgage balance.

The farthest left column – paying off his mortgage as quickly as possible – is the option Chris indicated is his initial preference. Under this strategy, he will have saved no invested assets from the $5,525 a month for five years and have no mortgage balance, so would get exactly the proceeds of his house if he were to sell it then. The remaining columns show that, on average using the historical returns, Chris will have more savings than his mortgage balance if he makes his lower mortgage payments and invests the rest of his $5,525 per month than if he pre-pays his mortgage as quickly as possible.

The smaller his mortgage payment, the higher his “net worth” or the more he will have available in excess of his mortgage balance in 10 years. For example, Chris will have a “net worth” of $34,396 at the end of 10 years, on average using historical returns, if he pays $3,525 a month towards his mortgage and invests the rest in 100% stocks as compared to $102,341 if he pays $1,525 a month towards his mortgage and invests the rest in 100% stocks. Because the average historical after-tax returns on his investments are higher than Chris’s pre-tax mortgage interest rate, he will accumulate savings above the balance of his mortgage.

In addition, at the average, Chris is better off if he invests more heavily in stocks. For example, if Chris makes his minimum mortgage payments and sells his house in 10 years, he will have $27,033 in after-tax savings if he invests 100% in bonds as compared to $102,341 in after-tax savings if he invests 100% in stocks.

I also calculated the averages for the 100% stocks investment strategy using the longer time period (back to 1950). While the results are slightly less favorable, they show generally the same results as are shown in the 100% stocks columns in the table above.

Average Results – 26 Years

The table below summarizes Chris’s average financial position on July 1, 2045, based on the historical investment returns. As discussed above, I don’t believe there is enough historical data regarding bond returns to include those investment strategies in this analysis. This table therefore shows results only based on the 100% stocks investment strategy and is based on stock returns going back to 1950.

Mortgage Payment Option 3 2 1
Mortgage Payment $5,525 $3,525 $1,525
Investment Option 100% Stocks 100% Stocks 100% Stocks
Invested Assets $0 $84,534 $373,269
Mortgage Balance 0 0 0
“Net Worth” 0 84,534 373,269

This table shows that the smaller mortgage payments Chris makes, the higher his savings will be 26 years from now on average using the historical returns.

Risky Results – 10 Years

So far, I have focused on Chris’s average returns. I mentioned in my introduction that one of the aspects of his decision that Chris does not quantify is risk. By looking at his “net worth” under 345 different historical scenarios (i.e., the number of complete 10-year time periods in my historical data) regarding bond and stock returns, we can get a sense for the riskiness of Chris’s choices.

Box & Whiskers – 10 Years

The graph below is called a box and whisker plot. My post on risk provides additional information about these graphs. The boxes represent the 25th to 75th percentiles of Chris’s “net worth” at 10 years. That is, I put the 345 “net worth” results in order from smallest to largest. The 25th percentile is the 86 th one on the list; the 75th percentile, the 259th. The whiskers (lines sticking out from the ends of the boxes) represent the 5th percentile to the 95th percentile and correspond to the 17th and 328th in order from smallest to largest.

Taller boxes and wider spreads between the top and bottom of the whiskers represent more risk. The placement of the boxes up and down on the graph show the overall level of the results. That is, boxes that are higher on the graph have higher returns than boxes that are lower.

This graph shows Chris’s “net worth” after 10 years under each of the investment and re-payment strategies.

Chris’s Re-payment Option 3 – pay off his mortgage as fast as possible – is shown on the far left. Because he makes no investments under this option, there is no risk and he always has no savings at the end of 10 years. As either the percentage of investments in stock increases or the amount of savings increases (moving to the right on the graph), both the risk and level increase. That is, with more savings, the boxes are higher on the graph and taller (e.g., compare the $1,525/0% Stocks box with the $3,525/0% Stocks box). The same comparison can be seen as the percentage of stock increases, by looking at the $1,525/0% Stocks relative to the $1,525/50% Stocks and $1,525/100% Stocks.

The tops of the boxes, tops of the whiskers and average values (shown in the table above) are all clearly higher with lower mortgage payments and a higher investment in stocks. The bottoms of the boxes and bottoms of the whiskers are all lower, though, so those options have more risk.

Efficient Frontier – 10 Years

Making a decision from the box & whisker plot can be challenging. If Chris is willing to view his risk-reward trade-off as being between his average “net worth” and his worst “net worth,” he can narrow down his choices. The drawback of this approach is it considers only one point in the range of possible results for measuring risk.

The graph below is a scatter plot showing the different options. My post on financial decision-making provides more insights on this type of graph. The x-axis (the horizontal one) shows Chris’s average “net worth” in 10 years. The y-axis (the vertical one) shows the worst “net worth” result observed based on the historical returns. Points on this chart that are up (worst results aren’t as bad) and to the right (higher average result) are better than points that are lower or to the left.

I have drawn a dashed line, called the efficient frontier, that connects those strategies (dots) that are optimal in that there are no other dots that have a higher average with the same worst result or have a higher worst result with the same average. Using the worst result as the sole measure of risk would allow Chris to narrow his choices down to the four on the efficient frontier, depending on how much risk he is willing to take.

You’ll see that there are two orange dots on this graph. They represent the points using the S&P 500 returns going back to 1950, whereas the blue points all use data starting in 1980. What I found most interesting is that the worst results are the same for both time series, though the average results are somewhat lower using the longer time series. The worst results occurred using the time series starting in February 1999.

Risky Results – 26 Years

The graph below shows the box & whisker plot of Chris’s “net worth” in July 2045, using the historical returns.

The 25th percentile of Chris’s “net worth” under all three options is about $0. As such, in 75% of the historical scenarios, Chris will be somewhat to significantly better off making smaller mortgage payments than making larger payments.

The much clearer results shown in this chart as compared to the one at 10 years results from the benefits of diversification over time. That is, the longer time period over which Chris is invested, the less risk there is in his financial results. Diversification is one way a portfolio can be diversified. Investing in both stocks and bonds is another. My post on how diversification reduces investment risk discusses these concepts in more detail.

The scatter plot below shows that in the worst scenario, Chris ends up losing about $120,000 over 26 years if he is 100% invested in stocks. The trade-off is that in 75% of the historical scenarios, he will have at least some savings and more than $370,000 in savings on average.

Current Market Cycle

Another concern that Chris and others on Twitter expressed is that the stock market has been going up for many years and is at risk of going down significantly in the near future.

Selection of Prior Peaks

To address that concern, I have reviewed the historical stock market returns to find points that would correspond to the market being at a peak. The two graphs below show the cumulative returns on the S&P 500 since 1950. (I had to create two charts so that the ups and downs from older periods could be seen. Even then the first peak on the second chart is a little tough to see even though it includes the largest single monthly decline in the entire time period.)

The eight green circles correspond to important peaks in the market, similar to Chris’s concern about today’s market.

“Net Worth” After Prior Peaks

I looked at Chris’s “net worth” ten years after each of those peaks, as shown in the table below. Recall that the bond index data are available starting only in 1980, so we can’t look at any strategies that include bonds for the earlier peaks.

Mortgage Payment $5,525 $3,525 $3,525 $3,525 $1,525 $1,525 $1,525
Investment Option All 100% Bonds 50% Bonds/ 50% Stocks 100% Stocks 100% Bonds 50% Bonds/ 50% Stocks 100% Stocks
1/1/1962 $0 $4,528 $184
11/1/1965 0 -5,103 -62,533
11/1/1968 0 -36,596 -76,978
1/1/1973 0 -1,543 27,375
12/1/1980 0 44,331 61,920 79,509 99,120 138,282 177,444
8/1/1987 0 27,585 40,490 53,394 57,535 151,014 244,493
3/1/2000 0 -5,747 1,033 2,198 -13,435 -33,178 -52,922
6/1/2007 0 2,848 25,314 47,780 -8,634 62,814 134,263
Average – Last 4 0 17,254 32,189 45,720 33,646 79,733 125,819
Average – All 8 0 18,021 48,916
All Scenarios 0 10,620 25,515 34,396 27,033 64,687 102,341

In some of the time periods, particularly the ones starting on November 1, 1965 and November 1, 1968, Chris would have been better off pre-paying his mortgage as quickly as possible rather than investing. In others though, he would have been much better off making his minimum mortgage payments.

The average result for the most recent 4 “bad” time periods (third-to-bottom row) is slightly better than the average result across all possible time periods (bottom row). If all eight periods are included, Chris is better off making minimum payments, but not by as much as was observed in all scenarios.

Dollar Cost Averaging

In several of the “bad” periods (e.g., the ones starting on 12/1/1980, 8/1/1987 and 6/1/2007), Chris ends up with a very high “net worth” if he invests 100% in stocks. Although Chris buys some stocks at the peak of the market, he will also buy stocks as the prices go down (generally taking a year or two). The graphs above show that the market often re-bounds fairly rapidly after it has fallen. In these situations, Chris will achieve a high return on the stocks bought at or near the bottom of the market, thereby boosting his overall return.

Dollar cost averaging is the process of making regular investments regardless of the market cycle. It is a common investing approach and, although it may not be intentional, it is exactly what you do when you contribute to a 401(k) through payroll deductions. Dollar cost averaging lets you buy stocks at all levels, without timing the market, which can produce better total returns than trying to time the market and make your investment on a single day or just a few days a year. If Chris invests monthly, he is implementing a dollar cost average strategy.

Assumptions

The findings presented here depend on a large number of assumptions.

Investment Returns

I used historical monthly returns on the S&P 500 and the Fidelity Investment Grade Bond Index (FBNCX) downloaded from Yahoo Finance. I assumed that any dividends and distributions, reduced by any related income taxes, were immediately reinvested.

Yahoo Finance provides a Closing Price and an Adjusted Closing Price. I used the percentage changes in the Adjusted Closing Price to calculate the total return for each financial instrument. For the S&P 500, the Closing Prices and Adjusted Closing Prices were identical. For the Bond Index, they were not. I assumed that the difference in the percentage changes between the Adjusted Closing Price and the Closing Price were interest payments.

I assumed that Chris would fund any shortfalls from current income or other after-tax savings and that there would be no borrowing costs or additional taxes.

Income Taxes

I made several key assumptions about income taxes:

● All investments will be held in taxable accounts. Chris is already contributing the maximum amounts to his tax-sheltered retirement plans. In addition, he might encounter penalties if the withdrawals needed to make his mortgage payments did not meet the guidelines of the specific tax-sheltered account to which he made contributions. See my post on retirement plans for more details on such withdrawals.

● The interest payments from the Bond Index will be taxed at Chris’s marginal rate on ordinary income of 22%.

● Chris will pay tax at his marginal capital tax rate of 15% capital gains and losses when he sells his investments, either to make mortgage payments or withdraws the money at the end of 10 years or 26 years.

● Chris’s marginal tax rates won’t change over the time horizon of the analysis.

● There were no tax implications of borrowing.

Fine Print

Having been a consultant for over 20 years, I feel it necessary to touch on the many limitations on the findings of the analysis.

Variability

Most importantly, actual results will vary from those presented herein. I have used historical data as a proxy for what might happen in the future. However, it is unlikely that future results will exactly replicate any results previously seen. If any of the assumptions discussed above or otherwise made do not turn out to be appropriate to Chris’s situation, the findings may similarly be relevant to his decision-making process.

Economic Environment Differences

An important component of these differences is the interest rate environment. As shown in the chart below, interest rates (as measured by the 10-year Treasury in this chart) declined or were flat during almost the entire period from 1980 to the present – the time period for which data were available for the Bond Index.

It is more likely than not that interest rates will increase during the time horizon of this analysis. When interest rates increase, bond prices tend to decrease. If that were to happen, the findings based on historical bond returns likely overstate the results that might be observed in the future.

Data Used in My Analysis

I downloaded S&P 500 and the Fidelity bond index monthly returns from Yahoo Finance. Data were available for the S&P 500 going back to 1950, but only to 1980 for the Fidelity bond index. To the extent that these data are incorrect, the findings herein might also be incorrect (i.e., garbage in, garbage out).

Intended Use

The purpose of this analysis was to provide insights to help Chris make a more informed decision. It should not be interpreted as making a recommendation for any financial decision. The only information I have about Chris’s financial situation is what is outlined above and in his post. As such, there may be other aspects of his financial situation that cause this analysis to not apply correctly to his specific situation.

Lastly, the analysis may not be applicable to anyone else’s specific situation.

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Investing in Bonds

Bonds are a common investment for people targeting a low-risk investment portfolio. One of the pieces of advice I gave my kids (see others in this post) is to never buy anything you don’t understand. In this post, I’ll tell you what you need to know so you can decide whether investing in bonds is appropriate for you.

What is a Bond?

A bond is a loan you are giving the issuer.  The parties to the transaction are exactly opposite of you taking out a loan. You’ll see the parallels if you compare the information in this post with that provided in my post on loans!  When you buy a bond, you are the lender.  The issuer of the bond is the borrower.

How Do Bonds Work?

The issuer of a bond sells the bonds to investors (i.e., lenders).  Every bond has a face amount.  Common face amounts are $100 and $1,000.  The face value of the bond is called the par value.  It is equivalent to the principal on a loan.  When the issuer first sells the bonds, it receives the face amount for each bond.

The re-payment plan for a bond is different than for a loan.  When you take out a loan, you make payments that include interest and a portion of your principal.  Over the life of your loan, all of your payments are the same (unless the interest rate is adjustable).   By comparison, a bond issuer’s payments include only the interest until the maturity date when it pays the final interest payment and returns the principal in full.

Before selling bonds, the issuer sets the coupon rate and the maturity date of the bond.  The coupon rate is equivalent to the interest rate on a loan.  The maturity date is the date on which the issuer will pay the par value to the owner of the bond.  It can vary from something very short, like a year, all the way to 30 years.  In Europe, there are even bonds with maturity dates in 99 years.  In the meantime, the issuer will pay coupons (interest) equal to the product of the coupon rate and the par value, divided by the number of coupons issued per year. Coupons are often issued quarterly. For example, if you owned a bond with a $1,000 par value, a 4% coupon rate and quarterly payments, you would get 1% of $1,000 or $10 a quarter in addition to the return of the par value on the maturity date.

What Price Will I Pay

You can buy bonds when they are first issued from the issuer or at a later date from other people who already own them.  You can also sell bonds you own if you want the return of your initial investment before the bond matures.  If you buy and sell bonds, the sale prices will be the market price of the bonds.

Present Value

Before explaining how the market value is calculated, I need to introduce the concept of a present value. A present value is the value today of a stated amount of money you receive in the future.  It is calculated by dividing the stated amount of money by 1 + the interest rate adjusted for the length of time between the date the calculation is done and the date the payment will be received.  Specifically, the present value at an interest rate of i of $X received in t years is:

The denominator of (1+i) is raised to the power of t to adjust for the time element.

Market Price = Present Value of Cash Flows

The market price of a bond is the present value of the future coupon payments and principal repayment at the interest rate at the time of the calculation is performed.

Interest Rate = Coupon Rate When Issued

The interest rate when the bond is issued is the coupon rate!  Because the issuer sells the bonds at par value (the face amount of the bond), the par value has to equal the market value.  For the math to work, the coupon rate must equal the interest rate at the time the bond is initially sold.

Interest Rates after Issuance

If interest rates change (more on that in a minute) after a bond is issued, the market value will change and become different from the par value because the “i” in the formula above will change.  When the interest rate increases, the price of the bonds goes down and vice versa.

Also, as the bond gets closer to its maturity date, the exponent “t” in the formula will get smaller so it will have less impact on the present value, making the present value bigger. As such, all other things being equal, a bond that has a shorter time to maturity will have a higher market price than a bond that has a longer time to maturity.  Remember that the par value is all paid at the end, so the market price formula is highly influenced by the present value of the repayment of the par value.

How is the Interest Rate Determined

There are two factors specific to an individual bond that influence the interest rate that underlies its price – the bond’s time to maturity and the issuer’s credit rating. In addition, there are broad market factors that influence the interest rates for all bonds.  These factors influence the overall level of interest rates as well as the shape of the yield curve.

What is a Yield Curve

The interest rate on a bond depends on the time until it matures.  If I look at the interest rates on US government bonds today (March 7, 2019) at this site, I see the following:

The line on this graph is called a yield curve.  It represents the pattern of yields by maturity.  In this case, there is some variation in yields up to 5 years and then the line goes up.

A “normal” yield curve would go up continuously all the way from the left to the right of the graph.  Up to five years, the chart above would be considered essentially “flat” and, above five years, would be considered normal.  If the entire yield curve went down, similar to what we see in the very short segment from one year to two years in this graph, it would be considered inverted.

Time to Maturity

The yield curve along with the maturity date of a bond influencethe interest rate and therefore its market price.  Looking at US Government bonds, the interest rates for bonds with maturities between 0 and 7 years are all around 2.5%.

The price of a 30-year bond will reflect interest rate of about 3%.  If the yield curve didn’t change at all, the same 30-year bond would be priced using a 2.5% interest rate in 23 years (when it has 7 years until maturity).  With the lower interest rate, the market value of the bond will increase (in addition to the increase in market value because the maturity date is closer).

Credit Rating

The other important factor that affects the price of a bond is its credit rating.  Credit ratings work in the same manner as your credit score does.  If you have a low credit score (see my post on credit scores for more information), you pay a higher interest rate when you take out a loan.  The same thing happens to a bond issuer – it pays a higher interest rate if it has a low credit rating.

Instead of having a numeric credit score, bonds are assigned letters as credit ratings.  There are several companies that rate bonds, with Standard and Poors (S&P), Moodys and Fitch being the biggest three.    When you buy a bond (more on that later), the credit rating for the bond will be quite clearly stated.

The graph below summarizes information I found on the website of the St. Louis Federal Reserve Bank (FRED).

It shows the interest rates on corporate bonds with different credit ratings on February 28, 2019. As you can see, there is very little difference in the interest rates of bonds rated AAA, AA and A, with a slightly higher interest rate for bonds rated BBB.  Bonds with BBB ratings and higher are considered investment grade.

Bonds with ratings lower than BBB are called less-than-investment grade, high yield or junk. You can see that the interest rates on bonds with less-than-investment grade ratings increase very rapidly, with C-rated bonds having interest rates close to 12%.

What are the Risks

There are two risks – default and market – that are inherent in bonds themselves and a third – inflation – related to using them as an investment.

Defaults

Default risk is the chance that the issuer will default or not make all of its coupon payments or not return the full par value when it is due.  When an issuer defaults on a bond, it may pay the bond owner a portion of what is owed or it could pay nothing.  The percentage of the amount owed that is not repaid is called the “loss given default.”  If the loss given default is 100%, you lose the full amount of your investment in the bond, other than coupon payments you received before the default.  At the other extreme, if the loss given default is only 10%, you would receive 90% of what is owed to you.

Issuers of bonds with low credit ratings are considered riskier, meaning they are expected to have a higher chance that they will default than issuers with high credit ratings. I always find this chart from S&P helpful in understanding default risk.

It shows two things – the probability of an issuer defaulting increases as the credit rating gets lower (e.g., the B line is higher than the A line) and the probability of default increases the longer the time until maturity.

These increases in the probability of default correspond to increases in risk.  Recall from the previous section that interest rates increase as there is a longer time to maturity when the yield curve is normal and as the credit rating gets lower. The higher interest rates are compensation to the owner of the bond for the higher risk of default.

When you read the previous section and saw you could earn between just under 12% on a C-rated bond, you might have gotten interested.  However, it has almost a 50% chance of defaulting in 7 years!  The trade-off is that you’d have to be willing to take the risk that the issuer would have a 26% chance of defaulting in the first year and a 50% chance by the seventh year!  It makes the 12% coupon rate look much less attractive.

Changes in Market Value

As I mentioned above, you can buy and sell bonds in the open market as an alternative to holding them to maturity.  In either case, you will receive the coupon payments while you own the bond, as long as the issuer hasn’t defaulted on them.  If you buy a bond with the intention of selling it before it matures, you have the risk that the market value will decrease between the time you purchase it and the time you sell it.  Decreases in market values correspond to increases in interest rates. These increases can emanate from changes in the overall market for bonds or because the credit rating of the bond has deteriorated.

If you hold a bond to maturity and it doesn’t default, the amount you will get when it matures is always the principal.  So, you can eliminate market risk if you hold a bond to maturity.

Interest Doesn’t Keep Up with Inflation

The third risk – inflation risk – is the risk that inflation rates will be higher than the total return on the bond.  Let’s say you buy a bond with a $100 par value for $90, it matures in 5 years and the coupons are paid at 2%.  Using the formulas above, I can determine that your total return (the 2% coupons plus the appreciation on the bond from $90 to $100 over 5 years) is 4.3%.  You might have purchased this bond as part of your savings for a large purchase.  If inflation caused the price of your large purchase to go up at 5% per year, you wouldn’t have enough money saved because your bond returned only 4.3%.  Inflation risk exists for almost every type of invested asset you purchase if your purpose for investing is to accumulate enough money for a future purchase.

How are They Taxed

There are two components to the return you earn on a bond – the coupons and appreciation (the difference between what you paid for it and what you get when you sell it or it matures).

Tax on Coupons and Capital Gains

The coupons are considered as interest in the US tax calculation.  Interest is included with your wages and many other sources of income in determining your taxes which have tax rates currently ranging from 10% to 37% depending on your income.

The difference between your purchase price and your sale price or the par value upon maturity is considered a capital gain.  In the US, capital gains are taxed in a different manner from other income, with a lower rate applying for most people (0%, 15% or 20% depending on your total income and amount of capital gains).

States that have income taxes usually follow the same treatment with lower tax rates than the Federal government, but not always.

Some Bonds are Taxed Differently

Within this framework, though, not all bonds are treated the same.  The description above applies to corporate bonds.  Bonds issued by the US government are taxed by the Federal government but the returns are tax-free in most states.

Some bonds are issued by a state, municipality or related entity.  The interest on these bonds is not taxed by the Federal government and is usually not taxed if you pay taxes in the same state that the issuer is located.  Capital gains on these bonds are taxed in the same manner as corporate bonds.

Included in this category of bonds are revenue bonds. Revenue bonds are issued by the same types of entities, but are for a specific project.  They have higher credit risk than a bond issued by a state or municipality because they are backed by only the revenues from the project and not the issuer itself.

The manner in which a bond is taxed is important to your buying decision as it affects how much money you will keep for yourself after buying the bond.  You should consult your broker or your tax advisor if you have any questions specific to your situation.

Do They Have Other Features

If you decide to buy bonds, there are some features you’ll want to understand or, at a minimum, avoid. Some of the types of bonds with these distinctive features are:

Treasury Inflation-Protected Securities or TIPS

TIPS are similar to US Government bonds except that the par value isn’t constant.  The impact of inflation as measured by the Consumer Price Index is determined between the issue date and the maturity date.  If inflation over the life of the bond has been positive, the owner of the bond will be paid the original par value adjusted for the impact of inflation.  If it has been negative, the owner receives the original par value.  In this way, the owner’s inflation risk is reduced.  It is completely eliminated if the owner purchased the bond to buy something whose value increases exactly with the Consumer Price Index.

Savings or EE Bonds

Savings bonds are a form of US Government bond.  You can buy them with par values of as little as $25.  They can be purchased for terms up to 30 years.  Currently, savings bonds pay interest a 0.1% a year.  The interest is compounded semi-annually and paid to the owner with the par value when the bond matures.   With the currently very low interest rates, these bonds are very unattractive.

Zero-Coupon Bonds

The issuer of a zero-coupon bond does not make interest payments.  Rather, when it issues the bond, the price is less than the par value. In fact, the price is the present value of just the principal payment.  So, instead of paying the par value for a newly issued bond and getting coupon payments, the buyer pays a much lower price and gets the par value when the bond matures.

I don’t know all the details, but believe that, in the US, the owner needs to pay taxes on the appreciation in the value of the bond every year as if it were interest and not as a capital gain on sale.  As such, it is better to own a zero-coupon bond in a tax-deferred or tax-free account, such as an IRA, a 401(k) or health savings account.  I’ve owned one zero-coupon bond – it was my first investment in an IRA.  If you want to buy a zero-coupon bond, I suggest talking to your broker or tax advisor to make sure you understand the tax ramifications.

Callable Bonds

A call is a financial instrument that gives one party the option to do something.  In this case, the issuer of the bond is given the option to give you the par value earlier than the maturity date.  When the issuer decides to exercise this option, the bond is said to be “called.”  The bond contract includes information about when the bond is callable and under what terms. If you purchase a callable bond, you’ll want to understand those terms.

Issuers are more likely to call a bond when interest rates have decreased. When interest rates go down, the issuer can sell new bonds at the lower interest rate and use the proceeds to re-pay the callable bond, thereby lowering its cost of debt.

In a low-interest rate environment, such as exists today, a callable bond isn’t much different from a non-callable bond as it isn’t likely to get called.  If interest rates were higher, a non-callable bond with the same or similar credit quality and coupon rate is a better choice than a callable bond. If the callable bond gets called, you will have cash that you now need to re-invest at a time when interest rates are lower than when you initially bought the bond.  (Remember that the reason that callable bonds get called is that interest rates have gone down.)

Convertible Bonds

Convertible bonds allow the issuer to convert the bond to some form of stock.  As will be explained below, stocks are riskier investments than bonds.  If you buy a convertible bond, you’ll want to understand when and how the issuer can convert the bond and consider whether you are willing to own stock in the company instead of a bond.

How Does Investing in Bonds Differ from Other Investments

There are two other types of financial instruments that people consider buying as common alternatives to bonds – bond mutual funds and stocks.  I’ll briefly explain the differences between owning a bond and each of these alternatives.

Bond Funds

There are two significant differences between owning a bond fund and own a bond.

A Bond Fund with the Same Quality Bonds Has Less Default Risk

If you own a bond fund, you are usually buying an ownership share in a pool containing a relatively large number of bonds.  Owning more bonds increases your diversification (see this post for more on that topic).  With bonds, the biggest benefit from diversification is that it reduces the impact of a single issuer defaulting on its payments.  If you own one bond, the issuer defaults and the loss given default is 50%, you’ve lost 50% of your investment.  If you own 100 bonds and one of them defaults with a 50% loss given default, you lose 0.5% of your investment.

A Bond Fund Has Higher Market Risk than Owning a Bond to Maturity

Recall that you eliminate market risk if you hold a bond until it matures.  Almost all bond funds buy and sell bonds on a regular basis, so the value of the bond fund is always the market price of the bonds.  Because the market price of bonds can fluctuate, owners of bond funds are subject to market risk.

Stocks

When you buy stock in a company, you have an ownership interest in the company.  When you own a bond, you are a lender but have no ownership rights. To put these differences in perspective, owning a stock is like owning a share in vacation home along with other members of your extended family.  By comparison, owning a bond is like being the bank that holds the mortgage on that vacation home.

Stocks Have More Market Risk

The market risk for stocks is much greater than for bonds.  Ignoring defaults for the moment, the issuer has promised to re-pay you the par value of the bond plus the coupons, both of which are known and fixed amounts.  With a stock, you are essentially buying a share of the future profits, whose amounts are very uncertain.

Stocks Have More Default Risk

The default risk for stocks is also greater than for bonds.  When a company gets in financial difficulties, there is a fixed order in which people are paid what they are owed.  Employees and vendors get highest priority, so get paid first.  If there is money left over after paying all of the employees and vendors, then bondholders are re-paid.  After all bondholders have been re-paid, any remaining funds are distributed among stockholders.  Because stockholders take lower priority than bondholders, they are more likely to lose some or all of their investment if the company experiences severe financial difficulties or goes bankrupt.

Companies often issue bonds on a somewhat regular basis.  When a bond is issued, it is assigned a certain seniority.  This feature refers to the order in which the company will re-pay the bonds if it encounters financial difficulties.  If you decide to invest in bonds of individual companies, especially less-than-investment grades bonds, you’ll want to understand the seniority of the particular bond you are buying because it will affect the level of default risk.  Lower seniority bonds have lower credit ratings, so the credit rating will give you some insight regarding the seniority.

When is Investing in Bonds Right for Me

There isn’t a right or a wrong time to buy a bond, just as is the case with any other financial instrument.  The most important thing about buying a bond is making sure you understand exactly what you are buying, how it fits in your investment strategy and its risks.

Low-Risk Investment Portfolio

If you are interested in a low risk investment portfolio, US Government and high-quality corporate bonds might be a good investment for you.  As you think about this type of purchase, you’ll also want to think about the following considerations.

How Long until You Need the Money

If you are saving for a specific purchase, you could consider buying small positions in bonds of several different companies or US government bonds with maturities corresponding to when you need the money.  If you’ll need the money in less than a year or two, you might be better off buying a certificate of deposit or putting the money in a money market or high yield savings account.  If it is a long time until you’ll need the money and you think interest rates might go up, you’ll want to consider whether you can buy something with a maturity sooner than your target date without sacrificing too much yield so you can buy another bond in the future at a higher interest rate.

How Much Default Risk are You Willing to Take

If you aren’t willing to take any default risk, you’ll want to invest in US government bonds.  If you are willing to take a little default risk, you can buy high-quality (e.g., AAA or AA) corporate bonds.  You’ll want to buy small positions is a fairly large number of companies, though, to make sure you are diversified.

How Much Market Risk are You Willing to Take

If you are willing to take some market risk, you can more easily attain a diversified portfolio by investing in a bond mutual fund.  As mentioned above, you’ll want to consider whether you think interest rates will go up or down during your investment horizon.  If you think that are going to go up, there is a higher risk of market values going down than if you think they will be flat.  In this situation, a bond fund becomes somewhat riskier than buying bonds to hold them to maturity.  If you think interest rates are going to go down, there is more possible appreciation than if you think they will be flat.

High-Risk Investment Portfolio

If you want to make higher return and are willing to take more default risk, you can consider buying bonds of lower quality.  As shown in the chart above, non-investment grade bonds pay coupons at very high interest rates.  However, you need to recognize that you are taking on significantly more default risk. One approach for dabbling in high-yield bonds is to invest in a mutual fund that specializes in those securities. In that way, you are relying on the fund manager to decide which high-yield bonds have less default risk. You’ll also get much more diversification than you can get on your own unless you have a lot of time and money to invest in the bonds of a large number of companies.

Where Do I Buy Bonds and Bond Funds

You can buy individual bonds and bond mutual funds at any brokerage firm.  Many banks, particularly large ones, have brokerage divisions, so you can often buy bonds at a bank.  This article by Invested Wallet provides details on how to open an account at a brokerage firm.

All US Government bonds, including Savings Bonds and TIPS can be purchased at Treasury Direct, a service of the US Treasury department.  You’ll need to enter your or, if the bond is a gift, the recipient’s social security number and both you and, if applicable, the recipient need to have accounts with Treasury Direct.  US Savings Bonds can be bought only through Treasury Direct.  You can buy all other types of government bonds at any brokerage firm, as well.

As discussed in this post, it is best to buy bonds in a tax-advantaged account, such as an IRA, 401(k), Tax-Free Savings Account (TFSA) or Registered Retirement Savings Plan (RRSP) than a taxable account. You pay tax on the coupons every year when bonds are held in a taxable account, but you get the benefit of compounding without paying taxes along the way in a tax-advantaged account.

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How to Budget Step 9 – Monitoring your Budget

You may have thought you were done when you created and balanced your budget.  However, there is one very important step left in the budgeting process – making sure you are living within the guidelines set by your budget, i.e., monitoring your budget.  That is, are you earning as much income as you planned? Are you limiting your expenses to the amounts in your budget?  Did you put aside the savings you included in your budget, whether for expenses you pay infrequently, for retirement or something in between?

In this post, I’ll tell you how to use a new, budget-monitoring worksheet to compare your budget with your actual income and expenses.

Entering Your Budget

Since the purpose of the spreadsheet is to compare your actual expenses with your budget, the first thing to do is to enter your budget.  Most people find it easiest to monitor their budget on a monthly basis, even if they created an annual budget.  If you created an annual budget, you’ll want to divide all of the values in your budget by 12.

Once you have your monthly budget, you’ll enter it on the Budget Monitoring tab of the budget-monitoring spreadsheet at the link below.  Note that this spreadsheet is different from the one you used to track your expenses and create your budget, though many aspects of it will work the same as the budget creation spreadsheet (named Budget Template).

Enter Your Category Names

To enter your budget, enter the names of the categories from your budget in Column A starting in Row 8. Here are three different ways you can input your category names:

  1. Type the names directly into Column A.
  2. Use Excel’s copy and paste features to copy them from your Budget Template spreadsheet.
    1. On the Budget tab in your Budget Template spreadsheet, highlight all of your category names by putting your cursor on cell A11, holding down the shift key and moving the down arrow until all of them are highlighted. Let go of the shift key.
    2. Hold down the Ctrl key while you hit C or hit the copy button if you have one.
    3. Go to the Budget Comparison tab of the monitoring spreadsheet.
    4. Put your cursor in A8.
    5. Hold down the Alt key while you hit E, S and V or hit the paste-values button if you have one. If you just use a regular paste button, you will get errors because the cells from which you are copying have formulas in them.
  3. Link your monitoring spreadsheet to your Budget Template spreadsheet.
    1. Put your cursor in A8 of the Budget Comparison tab of your Budget Monitoring spreadsheet.
    2. Hit the equal sign on your keyboard.
    3. Go to the Budget Template spreadsheet.
    4. Go to the Budget tab.
    5. Put your cursor in A11.
    6. Hit Enter.
    7. Excel should return you to cell A8 of your Budget Monitoring spreadsheet.
    8. Hit the F2 (edit) key.
    9. Hit the F4 key 3 times. Hit Enter. There should now be no $ in the cell reference.
    10. Copy the formula in A8 and paste it in as many cells in Column A as needed until all of your category names appear.

When you enter the category names, make sure that the row with the total amount of income is called “Total Income,” the row with the expense total is called “Total Expenses,” and the difference between those two values is called “Grand Total.”

Enter Your Budget Amounts

Next, enter the monthly budget amounts in Column B next to each of the category names in Column A. You can use any of the three approaches described above for the category names. If you have an annual budget, you’ll need to divided the values by 12 before copying them if you use the second approach or add “/12” (without the quotes) in step (i) before you hit enter if you use the third approach.

Entering Your Actual Income and Expenses

You can enter your actual income and expenses using the same instructions as were used for entering them in the Budget Template spreadsheet.  See my posts on tracking expenses and paychecks and income for more details or review the instructions at the top of each tab.  Be sure to use the same category names as you used in your budget so all of your income and expenses will be included in the Actual column on the Budget Comparison tab.

For monitoring your actual income and expenses, you don’t need to enter the number of times per year you receive each type of income or pay each bill since your goal is compare what you actually received and paid with your budget.

Options for Expenses You Don’t Pay Monthly

Here are three different ways to monitor expenses that you don’t pay monthly:

  1. Enter them in the Monitoring Spreadsheet as you pay them and keep them in mind as known variances from your budget each month. This approach is the easiest to implement but also the least helpful for comparing your actual expenses to your budget.
  2. Adjust the budget amounts to reflect the amount of those expenses you expect to pay in each month. For example, if you pay your car insurance bill four times a year in March, June, September and December, you would
    • take your budget amount
    • adjust it to a full year if you budgeted on a monthly basis by multiplying by 12
    • divide the annual amount by 4
    • include the result in your budget for March, June, September and December
    • put 0 in your budget column in all other months

This approach is a little more complicated to implement, but will make comparing actual expenses with your budget much easier.

  1. Add an expense transaction every month equal to 1/12thof your annual expense on the Bank Transactions, Cash Transactions or Credit Card Transactions tab. In the months in which you actually make the payment, you’ll enter 1/12th of your actual annual expense.  If the total of the amounts you set aside in previous months differs from the amount you actually pay, you’ll need to include this difference in the actual payment amount in the month you make the payment. This approach is equivalent to moving money from your checking account to your savings account in every month you don’t have this expense and moving it back to your checking account in the month in which you pay the expense.

You can also use any one of the above approaches for income you don’t receive monthly.  If you use the third approach, you’ll put 1/12th of your actual annual income on the Income tab.

Monitoring Your Budget – What Happens When Your Actual Isn’t as Good as Your Budget

There are many reasons why your actual income and expenses might look worse than your budget.  You may have been planning to work overtime or get a second job to increase your income.  Those lifestyle changes can be challenging, so you might not have done them.

More likely, you spent more than you budgeted, either due to an emergency, an impulse purchase or difficulty in breaking long-standing habits.  Emergencies happen to everyone.  If possible, you’ll want to include building or re-building your emergency savings (see this post for more on that topic) in your budget. While overspending your budget can be problematic, especially if you do it continuously, don’t be too hard on yourself. Changing your spending habits is really hard.

A Few More Words about Budget

Congratulations!  You made it through the entire budgeting process. As I said in my first post on budgeting, staying on a budget is like being on a diet.  Just as every calorie counts, so does every dollar spent.  Sticking to your budget will increase the likelihood you will meet your financial goals, so do your best!

Download Budgeting Monitoring Spreadsheet Here

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Traditional vs Roth Retirement Plans

The difference between Roth vs Traditional plans for retirement is primarily about tax rates. Other differences relate to when you can or must withdraw your savings.  With one exception, the same withdrawal rules apply to both 401(k)s and Individual Retirement Accounts (IRAs), so I’ll refer to both 401(k)s and IRAs collectively as Roth and Traditional plans.  In this post, I will:

  • Describe the four different combinations of tax-advantaged retirement savings plans in the US.
  • Provide information about contribution limits.
  • Talk about the major differences between Roth vs Traditional plans.
  • Give you the nuts and bolts of the tax considerations so you can make an informed decision as to where to put your retirement savings.

Key Take-Aways – Roth vs Traditional Plans

While there are several differences between Roth vs Traditional plans, some of which may be important to some of you, the biggest difference has to do with when you pay taxes on the money you have saved.  As will be explained below, you pay taxes before you put money in a Roth plan and you don’t pay taxes on Traditional plan money until you withdraw it.

Characteristics that make a Roth plan a better option than a Traditional plan for you include:

  • Your salary and spending are likely to go up a lot before you retire.
  • You anticipate having a lot of taxable income in retirement, such as from a part-time job, a pension or savings not in a tax-sheltered retirement plan.
  • The expectation that tax rates will increase.

If none of these characteristics apply to your situation, a Traditional plan is likely to be better for your than a Roth plan.

As you are thinking about saving for retirement, you’ll want to think about not only where to save, but also a target for your retirement savings and how much you need to save each year.

Mechanics of Tax-Advantaged Retirement Savings Plans

In the US, there are two types of tax-advantaged retirement savings plans, each with two variations.

Types of Plans

The two types of plans are:

  • Individual Retirement Accounts (IRAs). An IRA is an account that you establish on your own at a bank, brokerage house or other financial institution that offers IRAs.  You make contributions to your IRA and can select one of many different choices for investments.  Allowed investment classes include stocks, bonds, real estate, mutual funds, ETFs, money market and other savings accounts and annuities, among other.
  • 401(k)s. A 401(k) is usually an employer sponsored plan, though you can open an individual 401(k) if you are self-employed. You can contribute a portion of your salary to the 401(k).  Many employers will match some or all of your contribution.  In a 401(k), you are restricted to the investment options offered by your employer, usually mutual funds and ETFs.

Two Variations

The two variations of each of IRAs and 401(k)s are Roth and Traditional plans.  When you set up an IRA, you have the choice of designating it as a Roth vs a Traditional IRA.  Your employer (or you if you have an individual 401(k)) determines whether to offer a Roth vs a Traditional plan. For information about the types of investments that are best held in each type of account, check out these posts for and Canada.

Maximum Contributions

For 2019, the maximum combined contribution to all of your IRAs combined is $6,000, plus another $1,000 if you are 50 or older.  The maximum combined contribution to your 401(k) plan is $19,000 ($25,000 if you are 50 or older).  The 401(k) contribution limits apply to money you deposit in your 401(k) and excludes any funds contributed by your employer.

Major Differences between Roth vs Traditional Plans

There are four major differences between Roth vs Traditional plans.

  • Roth contributions are restricted if your income is high, as discussed below.
  • You pay a penalty on any withdrawals you make from Traditional plans before the year in which you turn 59.5.
  • There are required minimum distributions on all plans except Roth IRAs.
  • The timing of paying taxes on the money in Roth and Traditional plans is different.

Restrictions on Roth Contributions

If your modified adjusted gross income is more than a certain threshold ($137,000 for single taxpayers in 2019, $193,000 for taxpayers who are married filing jointly), the tax law does not allow you to put as much in a Roth IRA and, if your income is high enough, do not allow you to directly contribute to a Roth IRA. However, you can contribute to a Traditional IRA and then very quickly transfer the money to a Roth IRA.  This transfer is called a “roll over.”  If you fall in this category, I suggest talking to your tax advisor or broker to make sure the process follows the IRS rules.

Early Withdrawal Penalty on Traditional Plans

If you withdraw money from your Traditional retirement plan before the year in which you turn 59.5, you will have to pay income taxes on the withdrawal (see below for more) and you will have to pay a tax penalty equal to 10% of your withdrawal amount.

With a Roth plan, you can make withdrawals at any time without paying a penalty, as long as you are either at least 59.5 or you made contributions in each of the previous five years.  If you are younger than 59.5, you can withdraw your contributions without paying any tax, but will pay taxes on any investment earnings (interest, dividends or appreciation) on your contributions.  I’ve read in some places that the every withdrawal is assumed to be a mix of your contributions and earnings, but I read the IRS web site as saying that you are assumed to withdraw your contributions first and then any earnings. If you want to make withdrawals before you are 59.5, I suggest talking to a tax advisor to make sure you understand the tax consequences.

Required Minimum Distributions

All tax-advantaged retirement accounts, except Roth IRAs, have minimum distribution requirements. By April 1 of the year in which you turn 70.5, you need to start withdrawing money from these accounts.

The amount you need to withdraw is the balance at the beginning of the year divided by your life expectancy, as calculated by the IRS.  The same life expectancy is used for everyone, based on their age, except people whose sole beneficiary is their spouse and their spouse is more than 10 years younger.  For most people, your life expectancy, according to the IRS web site, in the year you turn 70.5 is 27.4 years. So, if you have $50,000 at the beginning of that year in a Traditional IRA or any 401(k), the minimum withdrawal would be $1,824.  The penalty for not making the minimum withdrawal is very steep – 50% of the amount that you were required to withdraw but didn’t!

Even though I am retired and able to start withdrawing from my retirement savings, this minimum distribution requirement difference between a Roth IRA and the other accounts has not seemed important to me, as I assume I will need to withdraw money from my other retirement plans to support my expenses.  I may change my mind as I get older and have to start making withdrawals, as these withdrawals may increase my taxes more than necessary if I have other funds available to cover expenses.

Dollars and Cents of Taxes

The biggest difference between Roth vs Traditional retirement plans is the way they are taxed.

Taxes on Contributions

Briefly, Roth contributions are made with after-tax money, while Traditional contributions are made with pre-tax money.  After-tax money means that you have already paid income taxes on the money you contribute. Pre-tax money means that you do not pay income taxes on the money when you contribute it.

In practice, you can deduct the amount of any contributions to Traditional plans from your income on your tax return, but you don’t get to deduct Roth contributions.  The amount of your wages reported by your employer on your W-2 has usually already been reduced for contributions you have made to a Traditional 401(k).  There is a specific line on your tax return for Traditional IRA contributions.

Taxes on Withdrawals

You do not pay any taxes on withdrawals from Roth plans, but you do on Traditional plans.  Just the opposite of when you contribute the money.

Comparison

If the tax rate applicable to your contributions and withdrawals (a lot more on that in a minute) were the same, it wouldn’t matter whether you put your money in a Traditional vs Roth plan!   For a Traditional plan, you contribute the amount you have available, earn a return and withdraw it after paying taxes.  That is:

Money in Traditional plan = Contribution x (1 + compound investment return) x (1 – tax rate)[1]

For a Roth plan, you start with the amount you have available, pay taxes on it, contribute what you have left, earn a return and withdraw it.  That is:

Money in Roth plan = Contribution x (1 – tax rate) x (1 + compound investment return)

Because you can change the order of the terms when multiplying (the associate property for math geeks like me), these two amounts are equal as long as the applicable tax rate when you make your contribution is the same as when you make your withdrawal.

What You Need to Know About Taxes

The Federal government and most states tax your income.  There is a small handful of states with no income tax.  Because state income taxes vary so widely, I will focus only on Federal income taxes.  If you want more information about your state income taxes (and you’ll want to know at least a bit about them for your decision-making process), I suggest visiting your state’s web site or contacting your tax advisor.

The Federal income tax system is very complicated.  In this post, I will focus on aspects of the calculation that impact your choice between Traditional vs Roth retirement plans.  As with state income taxes, if you have questions about your specific situation, I suggest you contact a qualified tax advisor.

There are two steps in calculating your Federal income tax.

  1. Calculate your taxable income.
  2. Determine the taxes that apply to your taxable income.

Taxable Income

Your taxable income is the sum of all sources of income minus your deductions.

Income

The most common sources of income include:

  • Wages
  • Interest and dividends, other than those from US Government bonds
  • Capital gains and losses
  • Pension income and withdrawals from retirement plans, other than Roth plans
  • A portion of your social security benefits, as discussed in this post
  • Self-employment income
  • Alimony

Reductions and Deductions

These amounts are reduced by a number of items, including the following:

  • Contributions to Traditional retirement plans
  • Contributions to Health Savings Accounts
  • Alimony paid
  • Some student loan interest

The total of your income excluding this amounts is called your Adjusted Gross Income.

You can then choose to either itemize your deductions or use the standard deduction.  The standard deduction is $12,000 if you file individually and $24,000 if you file jointly with your spouse.  (There are also separate thresholds for most aspects of the tax calculation for married filing separately and head of household.  I will not provide the specifics for these filing statuses.  You can find more information at www.irs.gov.)

Itemizing your deductions is quite complicated.  Briefly, here are the most common deductions:

  • Medical expenses, but only the portion that exceeds 7.5% of your adjusted gross income
  • State and local income and property taxes, up to $10,000
  • Some or all of your mortgage interest
  • Charitable donations

People usually use the standard deduction unless their itemized deductions are higher than the standard deduction in which case they use their itemized deductions.

Taxable income is adjusted gross income minus deductions.

Calculating Your Taxes

For most people, the regular tax rates are applied to your taxable income.  People with high incomes and especially those with a large amount of deductions have to calculate a second tax called alternative minimum tax. According to the Tax Policy Center, a very small percentage of people with income between $200,000 and $1 million and about 10% – 15% of people with income more than $1 million will pay the alternative minimum tax. I am going to assume that most of you are not subject to the alternative minimum tax, so will not discuss it here.

If you do not have any dividend income or capital gains, you can calculate your taxes from tables provided by the IRS.

Tax Table for Single Taxpayers

Here is the table for single taxpayers for tax year 2018.

Taxable Income is More Than: But Not More Than: Fixed Part of Tax Tax Rate Threshold Above Which Tax Rate is Applied
$0 $9,525 $0 10% 0
9,525 38,700 952.50 12% 9,525
38,700 82,500 4,453.50 22% 38,700
82,500 157,500 14,089.50 24% 82,500
157,500 200,000 32,089.50 32% 157,500
200,000 500,000 45,689.50 35% 200,000
500,000 150,689.50 37% 500,000

Tax Table for Taxpayers Who Are Married Filing Jointly

Here is the table for taxpayers who are married filing jointly for tax year 2018.

Taxable Income is More Than: But Not More Than: Fixed Part of Tax Tax Rate Threshold Above Which Tax Rate is Applied
$0 $19,050 $0 10% 0
19,050 77,400 1,905 12% 19,050
77,400 165,000 8,907 22% 77,400
165,000 315,000 28,179 24% 165,000
315,000 400,000 64,179 32% 315,000
400,000 600,000 91,379 35% 400,000
600,000 161,379 37% 600,000

How to Use Tax Tables

To calculate your taxes from these tables, you:

  • Determine the range in which your taxable income falls.
  • Take your taxable income and subtract the value in the last column.
  • Multiply the difference by the percentage in the second-to-last column.
  • Add the amount in the middle column.

For example, if you are single and your taxable income is $50,000, your tax is

($50,000 – $38,700) x .22 + $4,453.50 = $7,093.50

If you have dividend and capital gain income, the calculations are a bit more complicated as those types of income are sometimes taxed at different rates.

Key Points about Taxes as They Relate to Contributions

Let’s look at a couple of examples to see how Roth and Traditional retirement plans affect your taxes today.

John’s Contributions

In the first example, John’s sole source of income is wages of $60,000.  He doesn’t have a lot of expenses to itemize, so takes the standard deduction of $12,000.  The table below compare the taxes he will pay if he makes contributions of $5,000 to either a Roth and a Traditional retirement plan.

Traditional Roth Difference
Wages $60,000 $60,000 $0
Deduction for IRA 5,000 0 5,000
Standard Deduction 12,000 12,000 0
Taxable Income 43,000 48,000 5,000
Tax 5,400 6,500 1,100

 

If we take the tax difference and divide by the difference in taxable income, i.e., $1,100/$5,000 = 22%, we get what is known as the marginal tax rate on your IRA contribution. A “marginal” rate is the amount by which the result changes if you make an addition or subtraction to one value in the calculation.  It differs from the average tax rate which would be the total tax divided by taxable income. For the Roth column, the average tax rate is 13.5%.  It is the weighted average of the 10%, 12% and 22% tax rates that are combined to determine your taxes if your taxable income is between $38,700 and $82,500.

The marginal tax rate will be important because it is the tax rate we need to evaluate whether you are better off making a contribution to a Roth or Traditional plan.

Jane’s Contributions

Let’s look at another example.  Jane’s situation is similar to John’s except she makes $90,000.  She also takes the standard deduction and has no other income.

Traditional Roth Difference
Wages $90,000 $90,000 $0
Deduction for IRA 5,000 0 5,000
Standard Deduction 12,000 12,000 0
Taxable Income 73,000 78,000 5,000
Tax 12,000 13,100 1,100

Her marginal tax rate is also 22% (=1,100/5,000), calculated using the differences in the table above.

Key Points about Taxes as They Relate to Withdrawals

The key focus of the Roth vs. Traditional decision is how the marginal tax rate compares at the time contributions are made with the marginal tax rate at the time withdrawals are made.  So, now we will look at what John’s and Jane’s situations might look like if they were retired and making withdrawals.  For this part of the illustration, we will assume that there hasn’t been any inflation or changes in tax rates between now and the time they retire.

We will assume John’s Social Security benefit is $2,000 per month and he has expenses (including income taxes) of $60,000 a year in retirement.  His Social Security totals $24,000, so he needs an additional $36,000 from his retirement accounts to cover his expenses.  (He will actually need to withdraw more from a Traditional account to cover the taxes on his Social Security benefits and withdrawals, but I will ignore those for now as they add a lot of complication without having much impact on the conclusion.)

John’s Withdrawals

Let’s look at John’s tax calculation in his retirement.  As a reminder, a portion of your Social Security benefits become taxable if the value in the Test Sum row is greater than $25,000.  For more details on this calculation, see my post on Social Security benefits.

Traditional Roth Difference
Social Security benefits $24,000 $24,000 $0
Taxable Withdrawal 36,000 0 36,000
Test Sum = 50% of SS + Taxable Withdrawal 48,000 12,000 36,000
Taxable SS benefit 16,400 0 16,400
Adjusted Gross Income 52,400 0 52,400
Standard Deduction 12,000 0 12,000
Taxable Income 40,400 0 40,400
Tax 4,828 0 4,828

John’s marginal tax rate in retirement is 12% (=$4,828/$40,400).  He is better off if he contributes to a Traditional retirement plan, as he would reduce his taxes at a 22% marginal rate when he makes his contributions with the Traditional plans as compared to reducing his taxes at a 12% marginal rate when taking his withdrawals with the Roth plans.  That is, a Traditional plan is better if the marginal tax rate when you withdraw the money is less than the marginal rate when you contribute it.

Jane’s Withdrawals

Now we will look at Jane’s situation in retirement.  In her profession, most people she knows get significant raises between her age and retirement.  She anticipates that her salary will be more than $150,000 (before inflation) when she retires. With her higher income, her monthly Social Security benefit will be $3,000 or $36,000 a year.  Jane expects to have gotten accustomed to her higher salary so has estimated that she will have $120,000 a year in expenses.  She plans to save some money in taxable accounts (i.e., not in tax-advantaged retirement accounts) and will get a pension from her employer. These two amounts contribute $44,000 a year to her retirement income.  She will need to withdraw $40,000 from her retirement savings accounts to cover her expenses. Her tax calculation in retirement is as follows:

Traditional Roth Difference
Social Security benefits $36,000 $36,000 $0
Taxable Withdrawal 40,000 0 40,000
Other Taxable Income 44,000 44,000 0
Test Sum = 50% of SS + Taxable Withdrawal 102,000 62,000 40,000
Taxable SS benefit 30,600 23,800 6,800
Adjusted Gross Income 114,600 67,800 46,800
Standard Deduction 12,000 12,000 0
Taxable Income 102,600 55,800 46,800
Tax 18,914 8,216 10,698

Her marginal tax rate in retirement is 23% (=$10,698/$46,800).  In her case, her marginal tax rate in retirement is higher than when she makes her contributions, so she is better off putting her contributions in a Roth retirement plan.  That is, it is better for to pay the taxes at the lower rate before she contributes money to a Roth plan than to pay the taxes at a higher rate on Traditional plan withdrawals in retirement.

How John’s and Jane’s Situations Differ

Jane’s situation differs from John’s in two ways:

  1. Her retirement expenses are expected to be much higher than her current salary, pushing her into a higher tax bracket in retirement than she is in today.
  2. She is funding some of her retirement expenses with other sources of income that are taxable which causes the marginal tax rate on her Traditional withdrawals to be higher than if all of her non-Social Security income were from her retirement plans.

How Taxes Have Changed

It is pretty clear that your spending when you retire would have to be much higher than your current income before a Roth retirement plan would be preferred under the current tax structure.  However, the tax structure changes frequently so it is impossible to know your marginal tax rate in retirement.  To shed some light on how much tax rates might change, I’ve compiled information from this site on historical tax rates.

Marginal Tax Rates Over Time

The graph below shows the marginal tax rate for four different taxable income levels: $40,000; $60,000; $100,000 and $200,000.  I adjusted these four amounts for inflation from 2018 back to each year shown in the chart. For example, the Social Security wage adjustment from 2000 to 2018 is 1.565.  I therefore looked up the marginal tax rate in 2000 for $25,559 (=$40,000/1.565) when creating the $40,000 line in this chart.

Tax rates prior to 1985 were much higher than they are today.  They were fairly constant from 1985 to 2014 with a few ups and down primarily at the higher income levels.  In 2015, the marginal tax rates for all but the $60,000 level in the chart increased. The increase for the $40,000 level brought the tax rate for people at that income to its highest level ever. In 2018, all of the tax rates decreased.

For people with taxable income in the $60,000 to $100,000 range, current tax rates are about as low as they have been in the past 35 years.  There is also a common sentiment that those with higher incomes should pay even higher taxes than they currently do.  Given the current financial condition of the Federal government, it seems more likely than not that tax rates will go up, making Roth plans more attractive.  One possible exception is people with lower incomes, e.g., at or below the $40,000 threshold in the graph, as their tax rates are high by historical standards.

How to Decide

Here are some guidelines you can use to decide whether a Roth or a Traditional plan is better for you. Characteristics that make a Roth plan better include:

  • Your salary and spending are likely to go up a lot before you retire.
  • You anticipate having a lot of taxable income in retirement, such as from a part-time job, a pension or savings not in a tax-sheltered retirement plan.
  • An expectation that tax rates will increase.

One suggestion I have seen that is interesting is to put some of your retirement savings in each of a Roth and a Traditional plan which you can do as long as the total doesn’t exceed the limit on contributions.  In this way, a portion of your retirement savings is protected from large increases in tax rates, but you still have the benefit of reducing your taxes now. This approach is similar to what I did. All of my 401(k) savings is in Traditional plans, while my IRA savings is all in a Roth plan.

[1]Here is a quick explanation of the (1 – tax rate) term in these formulas.  The pre-tax value is Contribution x (1 + compounded investment return) which can be thought of as Contribution x (1 + compounded investment return) x 1.  The tax on that amount is equal to Contribution x (1 + compounded investment return) x tax rate.  To get the after-tax return, we subtract the tax from the pre-tax value.   When we pull out the common term and group them (i.e., apply the distributive property of multiplication over subtraction for you math geeks), we get Contribution x (1 + compounded investment return) x (1 – tax rate).