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^193

Companies, 2002

CHAPTER 6 Discounted Cash Flow Valuation 163

If you can earn 12 percent on your money, then you can duplicate this investment’s cash

flows for $1,432.93, so this is the most you should be willing to pay.

How Much Is It Worth? Part 2

You are offered an investment that will make three $5,000 payments. The first payment will

occur four years from today. The second will occur in five years, and the third will follow in six

years. If you can earn 11 percent, what is the most this investment is worth today? What is the

future value of the cash flows?

We will answer the questions in reverse order to illustrate a point. The future value of the

cash flows in six years is:

($5,000 1.11^2 ) (5,000 1.11) 5,000 $6,160.50 5,550 5,000

$16,710.50

The present value must be:

$16,710.50/1.11^6 $8,934.12

Let’s check this. Taking them one at a time, the PVs of the cash flows are:

$5,000 1/1.11^6 $5,000/1.8704 $2,673.20

$5,000 1/1.11^5 $5,000/1.6851  2,967.26

$5,000 1/1.11^4 $5,000/1.5181  3,293.65

Total present value $8,934.12

This is as we previously calculated. The point we want to make is that we can calculate pres-

ent and future values in any order and convert between them using whatever way seems

most convenient. The answers will always be the same as long as we stick with the same dis-

count rate and are careful to keep track of the right number of periods.

EXAMPLE 6.4

CALCULATOR HINTS

How to Calculate Present Values with Multiple

Future Cash Flows Using a Financial Calculator

To calculate the present value of multiple cash flows with a financial calculator, we will

simply discount the individual cash flows one at a time using the same technique we used

in our previous chapter, so this is not really new. There is a shortcut, however, that we can

show you. We will use the numbers in Example 6.3 to illustrate.

To begin, of course we first remember to clear out the calculator! Next, from Example

6.3, the first cash flow is $200 to be received in one year and the discount rate is 12 per-

cent, so we do the following:

N %i PMT PV FV

Enter 1 12 200

Solve for 
178.57