Introduction to Corporate Finance

Ross et al.: Fundamentals

of Corporate Finance, Sixth

Edition, Alternate Edition

III. Valuation of Future

Cash Flows

6. Discounted Cash Flow
   Valuation

© The McGraw−Hill^197

Companies, 2002

To calculate the annuity present value factor, we just plug this in:

Annuity present value factor (1 
Present value factor)/r

(1 
.75131)/.10

.248685/.10 2.48685

Just as we calculated before, the present value of our $500 annuity is then:

Annuity present value $500 2.48685 $1,243.43

Annuity Tables Just as there are tables for ordinary present value factors, there are ta-
bles for annuity factors as well. Table 6.1 contains a few such factors; Table A.3 in the
appendix to the book contains a larger set. To find the annuity present value factor we
calculated just before Example 6.5, look for the row corresponding to three periods and
then find the column for 10 percent. The number you see at that intersection should be
2.4869(rounded to four decimal places), as we calculated. Once again, try calculating a
few of these factors yourself and compare your answers to the ones in the table to make
sure you know how to do it. If you are using a financial calculator, just enter $1 as the
payment and calculate the present value; the result should be the annuity present value
factor.

CHAPTER 6 Discounted Cash Flow Valuation 167

How Much Can You Afford?

After carefully going over your budget, you have determined you can afford to pay $632 per

month towards a new sports car. You call up your local bank and find out that the going rate

is 1 percent per month for 48 months. How much can you borrow?

To determine how much you can borrow, we need to calculate the present value of $632

per month for 48 months at 1 percent per month. The loan payments are in ordinary annuity

form, so the annuity present value factor is:

Annuity PV factor (1 
Present value factor)/r

[1 
(1/1.01^48 )]/.01

(1 
.6203)/.01 37.9740

With this factor, we can calculate the present value of the 48 payments of $632 each as:

Present value $632 37.9740 $24,000

Therefore, $24,000 is what you can afford to borrow and repay.

EXAMPLE 6.5

TABLE 6.1

Annuity Present Value

Interest Factors

Interest Rate

Number of Periods 5% 10% 15% 20%

1 .9524 .9091 .8696 .8333

2 1.8594 1.7355 1.6257 1.5278

3 2.7232 2.4869 2.2832 2.1065

4 3.5460 3.1699 2.8550 2.5887

5 4.3295 3.7908 3.3522 2.9906