Introduction to Corporate Finance

3: The Time Value of Money

3-7 ADVANCED APPLICATIONS OF

TIME VALUE

The techniques we have studied thus far have many different applications in business as well as in

personal finance. Some of those applications involve compounding interest more frequently than once

per year. When interest compounds more often, the stated interest rate on a loan or an investment

doesn’t always accurately measure the true rate of return, or the effective rate of interest. In this section,

we relax the assumption maintained so far that interest compounds once per year, and we examine

several additional applications of the time value of money.

3 -7a COMPOUNDING MORE FREQUENTLY THAN ANNUALLY

In many applications, interest compounds more frequently than once a year. Financial institutions compound

interest semiannually, quarterly, monthly, weekly, daily or even continuously. This section explores how the

present-value and future-value techniques change if interest compounds more than once a year.

LO3.5

Assume that Zark Muckerberg is a wealthy individual

who now wishes to endow a medical foundation with

sufficient money to fund ongoing research. Zark is

particularly impressed with the research proposal

submitted by the Strangelove Cancer Institute (SCI).

The Institute requests an endowment sufficient to

cover its expenses for medical equipment, which will

total $15 million next year, and then grow by 4% in

perpetuity afterwards.

Assume the Institute can earn a 12% return on

Zark’s contribution. How much must Zark contribute

to finance the institute’s medical equipment

expenditures in perpetuity? Equation 3.11 tells us

that the present value of these expenses equals $125

million, computed as follows:

PV

$15,000,000

0.12 0.04

$15,000,000

0.08

= $187,500, 000

−

==

Zark would have to make an investment of only

$125,000,000 ($15,000,000 ÷ 0.12, using Equation

3.10) to fund a non-growing perpetuity of $15 million

per year. The remaining $62.5 million supports the

4% annual growth in the payout to SCI.

example

See the concept explained

step by step on the

CourseMate website.

SMART

CONCEPTS

10 You are given a mixed cash-flow stream and an interest rate, and you are asked to calculate both

the present and future value of the stream. Explain how the two numbers you calculate are related.

11 How is the present value of an annuity due related to the present value of an identical ordinary

annuity?

12 Does a perpetuity pay an infinite amount of cash? Why is the present value of a perpetuity not

infinite?

13 How would you calculate the present value of a perpetuity that had payments that were declining

by a fixed percentage each year?

CONCEPT REVIEW QUESTIONS 3-6