1 Please help me solve this case Car Loan1 You have decided to purchase a new car. You have visited an auto dealership in San Francisco, picked a

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1 Please help me solve this case

Car Loan1

You have decided to purchase a new car. You have visited an auto dealership in San Francisco,

picked a model and specification of your preferable car, and are planning to pay cash for it.

The sales rep argues that it would be better to borrow the funds. He shows you the article

from the Los Angeles Times to prove his point (below). You read it carefully because you want

to make the most cost-efficient decision.

Should you pay cash for a new car?

Los Angeles Times

By S.J. Diamond, Reprinted in the NEWS-SUN, Saturday/Sunday, September 28-29.

AT FIRST, psychology Professor Geoffrey Keppel of Berkeley, California, 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 $15,100 in an 8 percent certificate of deposit than he’d pay out on a 14.2 percent

car loan, “but you just don’t believe it,” he says. “It’s counter-intuitive: Anyone can see 14 is bigger

than 8.”

He’s not unusual. Many people who spend their adult lives avoiding debt have heard from (usually

richer) friends that it’s generally better to spend borrowed money than savings, but they can never

clearly see why, particularly when loan rates are higher than investment yields. What’s more, Keppel

says, “when you’ve just spent several hours nickel-and-diming with the auto dealer, you’re not inclined

to jump when they say they have another good deal for you.”

That night, however, Keppel awoke and went to his computer to “work it out for myself, month by

month.” Calculating di_erent 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 6.9 percent investment, and, if he could

earn 10 percent, he’d make almost $2,600.

A COUPLE of points must be interjected here. First of all, this seems a rather exclusive quandary, the

concern only of affuent people who have the option of paying outright for their car. But it really isn’t.

According to J.D. Power & Associates, an automotive market research firm, one-third of the people

who buy cars do pay cash and some of the two-thirds who don’t probably could.

Second, it’s a quandary only today’s affuent can easily solve: Yesterday’s consumers didn’t have the

calculators and personal computers for such analysis, and it’s laborious to work out by hand.

They might otherwise have seen the advantage in borrowing without taking anyone’s word for it.

Keppel, for example, calculated that 48 months of interest on a 14.2 percent loan of $15,100 would be

$4,779.20, while the same principal invested at 8 percent, compounded monthly would earn interest

of $5,672.56 – a profit of $893.36.

Tracing both transactions month by month, he could also see that the reason it worked to his

advantage was that “the 14 percent is applied to a declining balance and the 8 percent is on an

increasing balance.” Indeed, over four years, the average outstanding balance of the loan – the average

1© 2016 by Paulina Roszkowska based on an original article from the Los Angeles Times.

Mini-case #1

Part of Individual Assignment Due on March 11

Note: Case is borrowed directly from Dr. Paulina Roszkowska

2

amount on which he’d be paying interest – was only about half the total amount borrowed. His

investment, on the other hand, would earn interest on his full deposited principal, plus continually

compounded interest throughout the term.

GENERALLY SPEAKING, “an easy rule of thumb is if you can earn an interest rate equivalent to half the

interest rate on your loan, you’ll come out ahead,” says Frank Sperling, vice president at Security Pacific

National Bank.

The same analysis, including the same assumptions could probably be applied to any consumer loan,

with Sperling’s Rule a good guide to potential consumer advantage. Certain other items, however, may

deserve consideration.

A home equity loan, for example could look good by Sperling’s Rule, given fixed interest rates similar

to regular auto loan rates, but such loans are essentially mortgages and may levy extra charges for

property appraisals, document work and title searches.

Questions:

1. What do you think of Prof. Keppel’s calculations? Verify that the numbers for interest

paid ($4,779.20) and interest earned ($5,672.56), quoted in the article, are correct

(within rounding). What should one conclude from them?

2. What do you think of “Sperling’s rule” [that it’s a good idea to borrow if you can earn

an interest rate equal to at least half the interest rate on your loan]? Do you agree?

Why might these numbers be not sufficient for deciding whether paying cash or taking

out the car loan is a better deal?

3. Evaluate the proposal that you borrow rather than pay cash using present value

calculations. by calculating the present value of your car payments if you pay

cash and the present value of your car payments if you take out the car loan (think

carefully about which interest rate to use in your present value calculations).

A note on taxes: When this article was written (in 1985), interest on auto loans was a taxdeductible

expense. This is no longer true (today, the only interest deduction allowed on

personal income tax returns is home mortgage interest). Thus, today, you would pay taxes on

any investment interest income, but receive no offsetting tax deduction on your loan interest

payments.

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