[SECTION II: HOW TO MANAGE YOUR INCOME & EXPENSES]
5. Managing credit

I’m going to do you a favor...

— anonymous car dealer

Most of us will borrow money to finance the purchase of a car and a home. Some will borrow money to buy stocks and bonds and to pay educational expenses. In this chapter, we will look at how loans can be used and misused. You will see how loan payments are determined and you also will learn why the common practice of comparing loans on the basis of the total payments is wrong.

USING LOANS TO LIVE BEYOND OUR MEANS

Having the option to buy things with borrowed money creates wonderful opportunities to improve our lives. If we couldn’t borrow money to buy a house, few of us would ever own homes. The availability of home mortgages allows many of us to be homeowners for most our lives, using money that would otherwise pay rent to instead be used to pay off our mortgage. At the end of 30 years, we have a valuable house instead of a worthless collection of rent receipts. (In Chapter 12, we will do a detailed financial comparison of renting versus buying.)

For another example, suppose that you can’t afford to pay $1000 for a clothes washer and dryer. So you spend $10 a week, or $40 a month, to clean your clothes at a laundromat. If you can borrow $1000 at a 10 percent interest rate to buy a washer and dryer, $40 a month will pay off the loan in 28 months. Then the monthly payments stop and you have your own washer and dryer. (The average clothes washer lasts 13 years, the average dryer 18 years.) And you don’t have to spend time traveling to and from the Laundromat and reading old magazines while you wait for your clothes.

Unfortunately, the opportunity to buy things with borrowed money sometimes sucks us into buying things we don’t really need—a BMW instead of a Toyota, a 42-inch Flat Screen Plasma TV instead of a 21-inch standard television, designer fashions, time-share condominiums, snowmobiles, jet skies, and dune buggies.

The cost of a luxury item is not just the monthly payments, but what you could alternatively buy with those payments. And we need to think broadly. The question is not just what you could buy today, but what you could buy in the future if you saved your money instead of repaying a loan used to buy something you don’t really need. Loans can finance instant gratification; one of the costs is future gratification. The question of whether someone is living beyond their means is not just whether they can make the current monthly payments on their debts, but whether they are saving enough for the future they want: college for their children, a house to call their own, a comfortable retirement.

Suppose that a 30-year-old is considering borrowing $10,000 (perhaps to buy a more expensive car than she really needs or costly sports equipment). At a 10% percent interest rate, this will cost her $400 a month for 28 months. (Later in this chapter, you will learn how to determine the monthly payments yourself). With admirable restraint, she stops for a moment and considers how much money she will have if she does without these luxury items and instead invests $400 a month for 28 months at a 7 percent interest rate.

Open the Annuities program and enter enter 400 for the first payment, 0 for the growth rate, 12 for the number of payments per year, 28 for the total number of payments, and 7 for the interest rate, so that the program boxes look like this:

Press the Calculate button and you will see that the future value at the end of 28 months is $12,098.32.

Now we’ll let this money continue to earn a 7 percent return for another 35 years, until she is 67 years old. Open the Future Value program and enter 12098.32 for the amount invested, 35 for the number of years, and 7 for the rate of return:

Press the Calculate button and you will see that the future value at the end of 35 years is $129,168.70.

What could she do with $129,168.70 at age 67? Well, she could retire a little earlier or live a little better during retirement. Open the Spending Wealth program and enter 20 years for the horizon, 129168.70 for current wealth, 7 percent for the rate of return, 0 percent for the rate of increase of spending:

Press the Calculate button and you will see that $129,168.70 would allow her to spend an extra $979.30 a month for 20 years.

So, she can make 28 monthly loan payments of $400 in order to buy something she doesn’t really need. Or she can save $400 a month for 28 months and be able to spend an extra $979 a month for 20 years when she is retired. What should she choose? The choice is hers, but she should make it consciously.

USING LOANS FOR LEVERAGE

We have been exploring the question of how using debt to finance a current lifestyle may have negative effects on your future lifestyles. A somewhat different question is whether we should have debts when we have assets that can be used to pay off debt. Does it make sense to take out a car loan when we could pay cash? If we could make a $50,000 down payment on a house, does it make sense to make a $30,000 downpayment and keep $20,000 to invest in stocks? If we inherit $20,000, should we put it in the bank or prepay part of our home mortgage?

We begin with a discussion of the general principle that the investment of borrowed money can magnify the gains and losses from an investment. Then we will develop the framework for answering these questions.

We have all seen news reports of people, perhaps even relatives or neighbors, who lost their home, farm, or business because they could not repay a loan. This is one reason why many people consider debt to be one of those four-letter words that decent people avoid: If you can’t pay cash, then you can’t afford it. However, others swear by, not at, debt. Borrowing allows you to invest other people’s money, and many a fortune has been built with other people’s money.

Debt has these two sides, as a proverbial two-edged sword, because it creates leverage, in which a relatively small investment reaps the benefits or losses from a much larger investment. Suppose that you have $10,000 of your own money and borrow another $90,000, giving you $100,000 to invest. For simplicity, we’ll look a year into the future and assume that the $90,000 is a simple 1-year loan at 10 percent, so that you must pay $99,000 at the end of the year. Your net financial gain depends on the rate of return R that you earn on your $100,000 investment. The table shows some possible outcomes.

Look first at R = 10 percent. A 10 percent return on $100,000 is $10,000, enough to pay the $9,000 interest due on the $90,000 loan with $1,000 left over—a 10 percent return on the $10,000 that is your own money. Not very exciting so far. But this case illustrates the general principle that if you borrow at 10 percent in order to invest at 10 percent, then the borrowing is neither an advantage or disadvantage. If the rate of return on the total investment is equal to the rate of interest owed on other people’s money, then this will also be the rate of return on your own money.

What if the rate of return on the total investment turns out to be 20 percent? Twenty percent of $100,000 is $20,000, minus $9,000 interest leaves an $11,000 gain on your $10,000—a rewarding 110 percent return. You more than double your wealth in a year by borrowing at 10 percent and investing at 20 percent!

In general, the size of the gain can be determined by taking the degree of leverage into account. Because the total $100,000 investment is ten times the size of your own $10,000, you have 10-to-1 leverage. The consequence is that every percentage point by which the investment return exceeds the loan rate is multiplied by 10 in determining the return on your own money. A total return of R = 20 percent is a 10 percent excess over the 10 percent loan rate, and multiplication by 10 pushes your percentage return up 100 percentage points, from 10 percent to 110 percent.

The two-edged sword comes into play because leverage works on the downside too, multiplying shortfalls. If your $100,000 investment just breaks even, with R = 0 percent, this is 10 percentage points less than the loan rate and multiplication by the 10-to-1 leverage gives you a return of -90 percent. You have $100,000 at the end of the year and, after paying your $99,000 debt, are left with $1,000—a $9,000 loss on a $10,000 investment. Notice that your total investment doesn’t have to lose money for leverage to be a disaster; what hurts is that the investment’s rate of return is less than the rate you are paying on the borrowed money. You will lose money borrowing at 10 percent to invest at 5 percent, and the more you borrow the more you lose. Example 5.1 recounts how highly leveraged real estate investments have caused some to live and die by this two-edged sword.

CALCULATING LOAN PAYMENTS

When a bank loans you money, you sign an agreement promising to pay back the amount borrowed plus interest. Before the Great Depression in the 1930s, most mortgages were 3- to 5-year balloon loans: Interest is paid on the loan until maturity, at which time a balloon payment equal to the size of the original principal is due. For instance, on a $100,000 4-year balloon loan with annual 10 percent interest payments, the homeowner pays $10,000 in interest each year for 4 years and then either repays the $100,000 loan or, more likely, refinances it. On some balloon loans, nothing—not even interest—is paid until maturity. In our example, the homeowner would owe $146,410 after 4 years.

In the 1920s, balloon loans were routinely renewed at maturity. The next decade, the 1930s, was not routine, however, and many banks and other lending institutions were unable or unwilling to renew loans. Homeowners who were out of work or earning reduced wages had trouble paying the interest they owed, let alone balloon payments. By 1935, more than 20 percent of the assets of savings and loan associations was real estate, mostly foreclosed properties.

Today, most consumer loans and mortgages are amortized, in that the periodic payments are not just interest but, in addition, repay the loan gradually rather than with a single balloon payment at the end. (The word amortized comes from mors, a Latin word meaning death: amortized payments kill the loan.) The most common amortized loan involves constant monthly payments over the life of the loan.

No matter how the payments are structured, the general rule for all loans is very simple:

If the loan payments are made monthly, they must be discounted by a monthly interest rate, which is equal to the annual percentage rate (APR) divided by 12. For a conventional amortized loan with constant monthly payments, we use this notation:

The size of the monthly payment is the value of X that solves the present value equation

Let’s use the Amortized Loan computer program to do the calculations for us. Open the program and select the button for calculating the Size of Periodic Payments. Enter 4000 for the amount borrowed, 12 percent for the interest rate, 12 for the number of payments per year, and 12 for the total number of payments:

Press the calculate button and you will see that the monthly payment is $355.40. Twelve monthly payments of $355.40, discounted at a 12 percent annual rate, have a present value equal to $4000.

The Unpaid Balance

The present value logic can be confirmed by dividing each monthly payment into interest and principal. Continuing with the example of a 12-month $4000 loan at 12 percent, the Amortized Loan program shows these figures for the first 5 months:

After the first month the borrower owes one month’s interest on $4000. At a 12 percent annual rate, the monthly interest rate is 1 percent and the interest due is 0.01($4000) = $40. The $355.40 monthly payment covers this $40 in interest and, in addition, the extra $355.40 - $40.00 = $315.40 reduces the principal (or unpaid balance) to $4000 - $315.40 = $3684.60.

For the second month, the amount borrowed is only $3684.60, and the interest due at the end of the month is 0.01($3684.60) = $36.85. The monthly $355.40 payment includes this interest and $355.40 - $36.85 = $318.55 repayment of principal, reducing the unpaid balance to $$3684.60 - $318.55 = $3366.05.

The table from the computer program gives the month-by-month details. To see the months at the end of the loan, replace payment numbers 4 and 5 with 11 and 12 and press the Calculate button:

At the end of eleven months, the principal is down to $351.82 and the final monthly payment covers this balance plus interest, so that, as intended, the loan is fully repaid after twelve months (with a 6 cents rounding error). Thus a present value calculation of the appropriate level of the monthly payments is logically consistent with the month-by-month payment of the interest and principal:

Since the total payments on the loan are 12($355.40) = $4264.80 and the total principal payments are $4000, the total interest payments are $4264.80 - $4,000 = $264.80, although 12 percent interest on a $4000 loan seemingly should be almost twice this amount, 0.12($4000) = $480. The answer to this paradox is that $480 in interest would be due if you borrowed the $4000 for a full year, but the unpaid balance on an amortized loan shrinks month by month. Here, $4000 is borrowed for the first month, then $3684.60 for the second month, $3366.06 for the third month, and so on until the last month, when only $351.88 is borrowed. The average amount borrowed is only about half of $4000, and, therefore, the interest is only about half of what would be due if $4000 were borrowed for the entire year.

The table also shows that as time passes and the unpaid balance declines, the monthly payments increasingly contain less interest and more repayment of principal. This inherent shift from interest to principal is particularly pronounced for a long-term loan, such as a 30-year mortgage. This table shows some highlights for a 30-year loan of $100,000 at 12 percent:

The initial monthly payments are almost entirely interest, so that after two years, the unpaid balance is only down to $99,228.29, and after five years to $97,663.43. The loan is not half repaid until the twenty-fourth year. In the twenty-fourth year, the monthly payments finally become more principal than interest and the unpaid balance then shrinks rapidly during the last six years of the loan. It takes 24 years to pay off half the loan and 6 years to pay off the remaining half.

People who buy a house and then move, paying off their mortgage after only a few years, are often surprised to find that all the money they have paid month after month after month has made barely a dent in the principal. They have not been cheated. Each month, they paid the interest due on their loan, fairly calculated, and every dollar beyond that did reduce the principal. What they don’t realize, is that an amortized loan does not reduce the principal equally each month because more interest is due when the loan is large and less when it is small.

EVALUATING LOANS: TOTAL PAYMENTS VERSUS PRESENT VALUE

Truth-in-Lending laws require lenders to reveal not only the annual percentage rate, but also the total amount (principal plus interest) that will be paid over the life of the loan. Unfortunately, the prominent display of this information encourages borrowers to make the mistake of judging loans by the total payments. (See Example 5.3.) Why is this a mistake? Because it doesn’t take into account when the payments are made, and a dollar paid today is more burdensome than a dollar paid 30 years from now.

The Right Way to Think About It

A simple-minded comparison of total payments says that a 1-year loan at a 100 percent interest rate is better than a 150-year loan at a 1 percent interest rate, a conclusion that present value logic says is nonsense. A total payments analysis also implies that, for any given loan rate, you are always better off borrowing less money and repaying the loan as soon as possible, because this reduces your total payments. The very best strategy, according to a total-payments analysis, is to never borrow any money at all—no matter what the loan rate! A comparison of total payments is misleading because it completely ignores present values. A present-value analysis implies that if the loan rate is favorable (perhaps a loan at 0 to 2 percent from your employer), you want to borrow as much as you can for as long as you can.

Remember our discussion of leverage earlier in this chapter. Borrowing at 10 percent in order to invest at 10 percent, is neither an advantage or disadvantage. It is financially advantageous to borrow at 5 percent in order to invest at 10 percent, and it is financially disadvantageous to borrow at 10 percent in order to invest at 5 percent. Now we can answer the questions posed earlier in this chapter:

• Does it make sense to take out a car loan when we could pay cash? Yes, if the interest rate on the car loan is less than the rate of return we will earn on our cash.
• If we could make a $50,000 down payment on a house, does it make sense to make a $30,000 downpayment and keep $20,000 to invest in stocks? Yes, if the rate of return on our stocks is higher than the mortgage rate.
• If we inherit $20,000, should we put it in the bank or prepay part of our home mortgage? You will come out ahead with money in the bank if it earns a rate of return that is higher than your mortgage rate.

Example 5.4: Can You Make Money Borrowing at 12 percent To Invest at 7 Percent? Car buyers can either pay cash or borrow money, usually through the dealer who sells the car. Those who try to pay cash are sometimes dissuaded by sales managers who claim that a car buyer can save hundreds of dollars by leaving, say, $12,000 in the bank earning 7 percent and borrowing through the dealer at 12 percent. Here is their persuasive, but fallacious, argument. If the $12,000 is kept in the bank for 4 years, the total interest, compounded monthly, comes to $3864. The monthly payments on the amortized car loan are $316, and the total interest comes to $3168, which is $696 less than the interest earned on the bank account. How can 7 percent interest come to more than 12 percent interest? The gimmick is that the loan is amortized, so that the amount borrowed is $12,000 only for the first month. Each month’s $316 payment covers the interest due and also reduces the principal, so that, each month, the amount still borrowed declines, until it hits zero at the end of the last month. Instead of borrowing $12,000 for four years, the car buyer borrows $12,000 at the beginning and almost nothing at the end, and the average amount borrowed is about half the initial loan. This is the sales manager’s trick: comparing 7 percent interest on $12,000 with 12 percent interest on roughly half of $12,000. It is also the basis for Sperling’s rule, named after a bank vice-president who advised that borrowers come out ahead if the loan rate is less than twice the interest rate earned on the bank deposit. But this apples-and-oranges comparison is illogical and Sperling’s rule is wrong. If the sales manager’s advice is followed, the car buyer won’t earn interest on the entire $12,000 for four years. At the end of the first month, the bank deposit will have earned only $12,000(0.07/12) = $70 in interest and the $316 car payment reduces the amount in the bank account by $316 - $70 = $246. Month after month, the bank account balance declines in order to pay off the loan. The sales manager uses the fact that, on average, the buyer pays interest on roughly half of $12,000, but ignores the fact that, on average, the buyer only earns interest on half of $12,000 too. The buyer would break even earning 7 percent and paying 7 percent, but must inexorably lose money earning 7 percent and paying 12 percent. Here, the bank account runs dry midway through the fourth year and the buyer must find other funds to make the last five car payments. At the end of four years, the buyer is not $696 ahead, but $1581 behind. What if the buyer leaves the $12,000 in the bank untouched and makes the car payments out of monthly income? The answer is the same, since each $316 monthly car payment could have been deposited to earn 7 percent interest. At the end of four years, the $12,000 will have grown to $15,865, but the buyer will have lost 48 deposits plus interest, a total of $17,446: on balance, a deficit again of $1581. It really doesn’t matter whether each $316 monthly payment comes out of old savings or new. Either way, intuition is right. You can’t make money borrowing at 12 percent in order to invest at 7 percent.

Exercises

5.1	You have inherited $50,000 and hope to multiply your new wealth by buying undeveloped land in a resort area. You are considering borrowing $50,000 and buying a $100,000 parcel or, else, borrowing $450,000 and buying a $500,000 property. Assume that either way you will have to pay back your loan plus 12 percent interest after a year and that each property will appreciate equally. If, for instance, property in this area appreciates by 20 percent, you will either make $20,000 - $6,000 = $14,000 or $100,000 - $54,000 = $46,000, depending on which property you buy. Fill in the rest of the table below, showing the net gain on your $50,000 wealth. For what rate of property appreciation, do these two strategies do equally well? How much leverage do you have with each strategy? Property Profit if Borrow $50,000 Profit if Borrow $450,000 Appreciation (percent) Dollars Percent Dollars Percent -10 0 10 20 $14,000 28 $46,000 92 30 40
5.2	In 1980 Chrysler announced that interest rates (then about 20 percent on car loans) were “7 percent too high” and that it was consequently giving a 7 percent rebate on new cars financed by car loans. Consider a new car costing $10,000 for which you will put $2000 down and pay the remainder over five years with a conventional amortized monthly car loan. Would you rather have the price reduced 7 percent to $9300 or have the loan rate reduced to 13 percent?
5.3	Before the 1969 Truth-in-Lending law, a finance company using the “add-on” method could loan you $1000; charge you $100 interest (with $1100/12 = $91.67 due each month for 12 months); and say that the interest rate was only 10 percent. Use the Amortized Loan program to determine the true annual percentage rate on such a loan. If the annual percentage rate were really 10 percent, how big would the monthly payments be?
5.4	At age 82, Fred Benson won a $50,000 state lottery, paying $100 a month for 500 months. He sold his claim to a local bank for $13,500 and threw the biggest party in the history of Block Island. What is the bank’s implicit rate of return on its investment? (That is, if this were a $13,500 mortgage, to be repaid in 500 monthly $100 installments, use the Amortized Loan program to determine the mortgage rate.)
5.5	Rent-A-Center rents televisions and other appliances by the week to customers without a credit check, allowing them to apply the rental payments towards eventual purchase; for example, for a 19-inch portable TV that can be purchased from a discount store for $229, Rent-A-Center charges $9.95 a week for 78 weeks. If a customer buys the set by paying $9.95 a week for 78 weeks, use the Amortized Loan program to determine the implicit annual interest rate on this $229 TV.
5.6	On August 28, 1986, General Motors announced “The Big One,” a 2.9 percent interest rate on 36-month loans for its 1986 models; Ford and Chrysler followed with similar deals. If you are buying a $12,000 car and have $2000 for a downpayment, would you rather borrow the difference at 2.9 percent or have the price reduced by $1000 and borrow from a credit union at 10 percent?
5.7	You need $100,000 to start your new business. One lender requires 60 monthly payments of $2150, due at the end of each month (beginning a month from the signing of the loan papers). A second lender requires 20 quarterly payments of $6450 due at the beginning of each quarter (starting on the day the loan is signed). Which charges the higher loan rate? How much higher?
5.8	Find the error in this comparison of car leasing with buying: Consider a moderately equipped Pontiac Grand Am that would sell for $11,288. GM calculates that the standard lease on the car would be $229 a month for 48 months, or a total of $10,992. With a 5% tax on the monthly payments, the cost would total $11,542. If a person were to buy the car with the standard minimum down payment of 13%, or $1,481, and finance the rest at 11% for 48 months, the monthly payments would be $253, or a total of $12,144. Including the down payment and lost interest earnings on that amount, as well as the 5% sales tax, the buyer’s cost would be $14,840. But with the loan paid, the buyer would own a car with a value of at least $4,400, according to GM. If the buyer sold the car for that price, his net cost would be $10,440, compared with the lessee’s $11,542
5.9	Consumer Reports gave the following advice about auto loans: The nice thing about auto loans is that you can locate the lemons before you sign on the dotted line. Just keep your eye on the APR—the Annual Percentage Rate.... Obviously, the lower the APR, the better. Another point to keep in mind: the shorter the loan the better....a one-year loan is much cheaper than a four-year loan. Say you borrow $4000 at 11%. For a one-year loan, the total interest would be $242. The total interest for a four-year loan would be $963—about four times as much. Of course, the monthly payments for the longer loan would be smaller, but remember that you pay heavily for that convenience. a.Why is the $242 total interest on a 1-year loan far less than 11 percent of $4000? b.Why is the total interest on a 4-year loan more than on a 1-year loan? c.Why are the monthly payments smaller on the 4-year loan? d.What is the present value of each stream of monthly payments, discounted at a 11 percent required return? e.Assuming the same interest rate on each loan, are there any circumstances in which “the shorter the loan, the better” is not true?
5.10	In December 1991, The Wall Street Journal reported that a Denver concert promoter had pawned his Cadillac with Autopawn USA, using the car as collateral for a one-month loan of $1,000 at a 10% monthly interest rate. If Autopawn USA is able to loan $1,000 every month at a 10% monthly interest rate, use the Amortized Loan program to determine the implicit annual interest rate.
5.11	Do not do any calculations, but explain why you either agree or disagree with this reasoning: At first, Berkeley psychology professor Geoffrey Keppel rejected out of hand his Toyota dealer’s offer of financing. He had saved up the price of a new Corolla and, like many people, didn’t want a loan because “that’s the way I’d been brought up.” The dealer even told him he could earn more on the same $8300 in an 8% certificate of deposit than he’d pay out on a 14.2% car loan, “but you just don’t believe it,” he says.... That night, however, Keppel awoke and went to his computer to “work it out for myself, month by month.” Calculating different investment yields and weighing them against the total interest that he’d pay on the 14.2% loan, he saw that he’d break even with only a 7% investment, and, if he could earn 10%, he’d make almost $1,500.
5.12	The owner of Dial Auto Pawn in Long Beach, California says, “We aren’t lenders” and “we aren’t pawnbrokers.” In December 1991, The Wall Street Journal reported that the company will make a $10,000 “cash advance” to a customer who leaves a luxury car with Dial Auto Pawn; the customer can reclaim the car by paying back the $10,000 plus a storage fee of $39 a day. If the cash advance is considered a loan, use the Amortized Loan program to determine the implicit annual interest rate.
5.13	You can afford to pay $2500 a month in mortgage payments. Use the Amortized Loan program to determine how much you could borrow at a 6% interest rate with a conventional 30-year loan.
5.14	Seth currently spends $60 a month cleaning his family's clothes at a Laundromat He is thinking about borrowing $1000 at a 7 percent interest rate so that he can buy a clothes washer and dryer. If his monthly loan payments are $60, use the Amortized Loan program to determine how many months it will take to pay off his loan.
5.15	Beth wants to impress her friends by driving a car while he is in college. He pays for the car with a 48-month $25,000 loan at a 12% interest rate. Use the Amortized Loan program to determine his monthly payments. Now use the Annuities program to determine how much money he will have after 4 years if, instead of buying a car, he invests his monthly car payments at an 8 percent interest rate. Now use the Future Value program to determine the value of these savings 40 years later if his savings continue to be invested at an 8 percent rate of return. Finally, use the Spending Wealth program to determine the amount of monthly spending over the next 30 years that could be paid for by his accumulated savings if he continues to earn an 8 percent rate of return.