Introduction to Corporate Finance

Ross et al.: Fundamentals

of Corporate Finance, Sixth

Edition, Alternate Edition

III. Valuation of Future

Cash Flows

6. Discounted Cash Flow
   Valuation

© The McGraw−Hill^209

Companies, 2002

EARs and APRs

Sometimes it’s not altogether clear whether or not a rate is an effective annual rate. A
case in point concerns what is called the annual percentage rate (APR)on a loan.
Truth-in-lending laws in the United States require that lenders disclose an APR on vir-
tually all consumer loans. This rate must be displayed on a loan document in a promi-
nent and unambiguous way.
Given that an APR must be calculated and displayed, an obvious question arises: Is
an APR an effective annual rate? Put another way, if a bank quotes a car loan at 12 per-
cent APR, is the consumer actually paying 12 percent interest? Surprisingly, the answer
is no. There is some confusion over this point, which we discuss next.
The confusion over APRs arises because lenders are required by law to compute the
APR in a particular way. By law, the APR is simply equal to the interest rate per period
multiplied by the number of periods in a year. For example, if a bank is charging 1.2 per-
cent per month on car loans, then the APR that must be reported is 1.2%  12 14.4%.
So, an APR is in fact a quoted, or stated, rate in the sense we’ve been discussing. For ex-
ample, an APR of 12 percent on a loan calling for monthly payments is really 1 percent
per month. The EAR on such a loan is thus:

EAR [1 (APR/12)]^12 
 1

1.01^12 
 1 12.6825%

The difference between an APR and an EAR probably won’t be all that great, but it
is somewhat ironic that truth-in-lending laws sometimes require lenders to be untruthful
about the actual rate on a loan.
There are also truth-in-saving laws that require banks and other borrowers to quote
an “annual percentage yield,” or APY, on things like savings accounts. To make things
a little confusing, an APY is an EAR. As a result, by law, the rates quoted to borrowers
(APRs) and those quoted to savers (APYs) are not computed the same way.

CHAPTER 6 Discounted Cash Flow Valuation 179

annual percentage rate

(APR)

The interest rate charged

per period multiplied by

the number of periods

per year.

q.0139  12

16.68%

Therefore, the rate you would quote is 16.68 percent, compounded monthly.

What Rate Are You Paying?

Depending on the issuer, a typical credit card agreement quotes an interest rate of 18 percent

APR. Monthly payments are required. What is the actual interest rate you pay on such a credit

card?

Based on our discussion, an APR of 18 percent with monthly payments is really .18/12 

.015 or 1.5 percent per month. The EAR is thus:

EAR [1 (.18/12)]^12 
 1

1.015^12 
 1

1.1956 
 1

19.56%

This is the rate you actually pay.

EXAMPLE 6.10