This term is called the present value factor or the discount factor. It equals the present value of $1 received in n years when the discount rate is i, compounded annually. For example, if a company receives $1 in 30 years time, and it uses a discount rate of 7 percent, then the present value factor is 1/(1 + .07)30 = 0.13. In other words, $1 in 30 years’ time is equivalent to 13 cents today. As amounts are received further in the future, n increases and the present value of that amount decreases.
Table 10.1 supposes that firms receive an incremental increase in revenues each year over a fixed number of years, 55 or 30. Such payment streams are called an annuity. The present value of an annuity of $1 received each year for 30 years, denoted , equals
This can be shown to equal
Thus, for example, the present value of an annuity of $1 per year received for 30 years at a discount rate of 7 percent would equal $12.41. Consequently, the present value of $7.02 million per year1 for 30 years at a discount rate of 7 percent would equal $7.02 × 12.41 million = $87.1 million. This amount is rounded down to $85 million in Table 10.1.