Introduction to Finance

DISCUSSION QUESTION 1
What do you expect the infl ation rate to be over the next several years? Why?
9.3
Discounting to Determine Present Values
Most fi nancial management decisions involve present values rather than future values. For 
example, a fi nancial manager who is considering purchasing an asset wants to know what 
the asset is worth now rather than at the end of some future time period. The reason that an 
asset has value is because it will produce a stream of future cash benefi ts. To determine its 
value now in time period zero, we have to discount, or reduce, the future cash benefi ts to their 
present value. 
Discounting
is an arithmetic process whereby a future value decreases at a 
compound interest rate over time to reach a present value.
Let’s illustrate discounting with a simple example involving an investment. Assume that 
a bank or other borrower off ers to pay you $1,000 at the end of one year in return for using 
$1,000 of your money now. If you are willing to accept a zero rate of return, you might make 
discounting 
arithmetic process 
whereby a future value decreases 
at a compound interest rate over 
time to reach a present value

---

226
C H A PT E R 9 Time Value of Money
the investment. Most of us would not jump at an off er like this! Rather, we would require 
some return on our investment. To receive a return of, say, 8 percent, you would invest less 
than $1,000 now. The amount to be invested would be determined by dividing the $1,000 
that is due at the end of one year by one plus the interest rate of 8 percent. This results in an 
investment amount of $925.93 ($1,000 ÷ 1.08), or $926 rounded. Alternatively, the $1,000 
could have been multiplied by 1 ÷ 1.08, or 0.9259 (when carried to four decimal places) to get 
$925.90, or $926 rounded.
Let’s now assume that you will not receive the $1,000 for two years and the compound 
interest rate is 8 percent. What dollar amount (present value) would you be willing to invest? 
In word terms, we have,
Present value = Future value × {[1 ÷ (1 + Interest rate)] × [1 ÷ (1 + Interest rate)]}
For our two-year investment example, we get,
Present value = $1,000 × (1 ÷ 1.08) × (1 ÷ 1.08)
= $1,000 × (0.9259) × (0.9259)
= $1,000 × 0.8573
= 
$857.30
A time line also can be used to illustrate this two-year example as follows: