Appendix. Present Value

• Pages: 523-529
• Author: Marvin A. Chirelstein,Lawrence Zelenak

523

Appendix

PRESENT VALUE

This book has used the concept of “present value” and

“discounting to present value” at many points. The excerpt below

(reprinted with permission) explains the concept and supplies the

relevant Tables.

Exercise: An investor expects to receive (i) a lump-sum payment

of $5,000 at the end of year 3 plus (ii) a 20-year an nuity of $1,000 a

year, the first payment to be received at the end of year 4. What is

the present value of the investor’s expectations, assuming a discount

rate of 10%?

Answer: $10,146. Do you agree? If not, write the authors.

ALCHIAN AND ALLEN,

UNIVERSITY ECONOMICS

205–209 (2d ed. 1967).

The more distant the deferred service (or income, or goods), the

lower its present price. A dollar deferred two years is worth less today

than a dollar def erred one year, if the rate of interest is positive. At

an interest rate of 6 percent, the current price o f $1 deferred a year

is 94 cents—the amount that will grow at 6 percent in one year to $1.

This is given by the formula

p1

=

A

=

$1.00

=

$.943.

(1 + r)

(1 + .06)

To get the present price for $1 deferred two years, simply repeat

the above operation. If $1 deferred one year from now is now worth

94 cents, then deferring the dollar an additional year again reduces

its present value by the same proportion. For two years, this is .943

× .943 = .890. A dollar due in two years is worth 89 cents today.

This same relationship can be expre ssed by noting that at 6

percent per year 89 cents will grow in one year to 94 cents, and then

in the seco nd year the 94 cents will grow to exactly $1. This can be

expressed in form

p2 (1 + r) (1 + r) = A.