Introduction to Corporate Finance

3: The Time Value of Money

the company pays to remove the equipment in eight years, and the $855.55 represents an inflow when

the company charges this fee to its customer at the beginning of the lease.^3

3-3c A GRAPHIC VIEW OF PRESENT VALUE

Figure 3.4 illustrates the relationship between the present value of a future lump sum, the discount rate

and the ‘waiting time’ before the future lump sum is paid. For investors who expect to receive cash in the

future, Figure 3.4 contains two important messages. First, the present value of a future cash payment

declines the longer investors must wait to receive it. Second, the present value declines as the discount

rate rises. Note that for a discount rate of 0%, the present value always equals the future value ($1).

However, for any discount rate greater than zero, the present value falls below the future value.

5 How are the present value and the future value of a lump sum related in words? How are they

related mathematically?

6 How would the present value be affected by: (a) an increase in the discount rate; or (b) a decrease

in the time period until the cash flow is received? Why?

CONCEPT REVIEW QUESTIONS 3-3

FIGURE 3.4 THE POWER OF DISCOUNTING: PRESENT VALUE OF $1 DISCOUNTED AT DIFFERENT INTEREST RATES

This figure shows the present value of receiving $1 at various points in the future, discounted at different discount rates.
For example, if the discount rate is 5%, the present value of $1 received in six years is about $0.75. Note that the present
value of $1.00 falls as the interest rate rises. For example, the present value of $1 received in year six is only $0.75 if
the discount rate is 5%, but only $0.43 if the discount rate is 15%. Similarly, the longer one must wait to receive a $1.00
payment, the lower the present value of that payment.

1.00

0.5

0.25

0 2 4 6 8 10 12 14 16 18 20

Periods

Present value of one dollar ($)

0%

5%

10%

15%

20%

0.75

3 Just remember that when using a calculator or spreadsheet, the PV and FV will have opposite signs. Which sign you use really doesn’t
matter. In this example, for instance, if you enter the FV ($1,200) as a positive number, then the answer you get back for PV will be negative
(–$855.55).