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^211

Companies, 2002

LOAN TYPES AND LOAN AMORTIZATION

Whenever a lender extends a loan, some provision will be made for repayment of the
principal (the original loan amount). A loan might be repaid in equal installments, for
example, or it might be repaid in a single lump sum. Because the way that the principal
and interest are paid is up to the parties involved, there is actually an unlimited number
of possibilities.
In this section, we describe a few forms of repayment that come up quite often, and
more complicated forms can usually be built up from these. The three basic types of
loans are pure discount loans, interest-only loans, and amortized loans. Working with
these loans is a very straightforward application of the present value principles that we
have already developed.

Pure Discount Loans

The pure discount loanis the simplest form of loan. With such a loan, the borrower re-
ceives money today and repays a single lump sum at some time in the future. A one-
year, 10 percent pure discount loan, for example, would require the borrower to repay
$1.10 in one year for every dollar borrowed today.
Because a pure discount loan is so simple, we already know how to value one. Sup-
pose a borrower was able to repay $25,000 in five years. If we, acting as the lender,
wanted a 12 percent interest rate on the loan, how much would we be willing to lend?
Put another way, what value would we assign today to that $25,000 to be repaid in five
years? Based on our work in Chapter 5, we know the answer is just the present value of
$25,000 at 12 percent for five years:

Present value $25,000/1.12^5

$25,000/1.7623

$14,186

Pure discount loans are very common when the loan term is short, say, a year or less. In
recent years, they have become increasingly common for much longer periods.

CONCEPT QUESTIONS

6.3a If an interest rate is given as 12 percent compounded daily, what do we call this

rate?

6.3bWhat is an APR? What is an EAR? Are they the same thing?

6.3c In general, what is the relationship between a stated interest rate and an effec-

tive interest rate? Which is more relevant for financial decisions?

6.3dWhat does continuous compounding mean?

CHAPTER 6 Discounted Cash Flow Valuation 181

6.4

EAR e.0525
 1

2.71828.0525
 1

1.0539026 
 1

5.39026%

This is what banks could actually pay. Check for yourself to see that S&Ls could effectively pay

5.65406 percent.