11.2The Risk-Adjusted Discount Rate Method

This section discusses what is perhaps the most popular method for obtaining the pres-

ent value of the future cash flows of a real asset. The method discounts the expected

future cash flows at a rate known as the project’s cost of capital.The cost of capital

of a project is the expected return that investors require for holding an investment with

the same risk as the project. To employ this method, one has to estimate the expected

cash flow, the expected return of the market (or factor portfolios), and the CAPM beta

(or factor betas) of the project return.⁶

Defining and Implementing the Risk-Adjusted Discount Rate Method with Given Betas

The method of discounting expected cash flows at a risk-adjusted discount rate, the

risk-adjusted discount rate method,is primarily used in cases where there is a com-

parison firm or set of firms in the same line of business as the project. Managers who

use this valuation method are assuming that the returns of the traded equity of the com-

parison firm or set of firms have the same beta as the returns of the project. As shown

below, using the risk-adjusted discount rate method generally provides present values

that are consistent with the tracking portfolio approach.

⁶Also, as noted in an earlier footnote, the expected cash flow and present value have to be either both

positive or both negative.

Grinblatt768Titman: Financial	III. Valuing Real Assets	11. Investing in Risky	© The McGraw768Hill
Markets and Corporate		Projects	Companies, 2002
Strategy, Second Edition

378Part IIIValuing Real Assets

For simplicity, we begin our analysis by assuming a single cash flow which is

generated in the next period. The following result describes how to calculate present

values with the risk-adjusted discount rate method.

Result 11.2

To find the present value of next period’s cash flow using the risk-adjusted discount ratemethod:

1.compute the expected future cash flow next period, E˜);

(C

2.compute the beta of the return of the project, ;

3.compute the expected return of the project by substituting the beta calculated in

step 2 into the tangency portfolio risk-expected return equation;

4.divide the expected future cash flow in step 1 by one plus the expected return from

step 3.

In	algebraic	terms
			E˜ (C) PV 1r (R r) fTf	(11.1)

Example 11.1 illustrates how to implement the risk-adjusted discount rate method.⁷

Example 11.1:Using the Cost of Capital to Value a Non-Traded Subsidiary

Hot Shot Computer Corp (HSCC), a wholly owned subsidiary of Novel, Inc., has a of 1.2

when computed against the tangency portfolio.One year from now, this subsidiary has a .9

probability of being worth $10 per share and a .1 probability of being worth $20 per share.

The risk-free rate is 9 percent per year.The tangency portfolio has an expected return of 19

percent per year.What is the present value of a share of HSCC, assuming no dividend pay-

ments to the parent firm in the coming year?

Answer:The expected value per share of HSCC one year from now is

$11 .9($10) .1($20)

According to the tangency portfolio risk-expected return equation, the appropriate discount

rate is

21% per year .09 1.2(.19 .09)

The subsidiary’s present value per share is the share’s expected future value divided by one

plus the appropriate discount rate, or approximately

$11 per share

$9.09 per share

1.21

The in Example 11.1 was given to us. In general, the hallmark of the risk-adjusted

discount rate method is that it is implemented with a comparison approach, which

provides an estimate of the appropriate beta for the project by analyzing the betas of

traded comparison securities. In Example 11.1, the comparison approach would have

identified the project of 1.2 by estimating the betas of the traded stocks of compar-

ison firms in the computer industry and using some average of their betas as a proxy

for HSCC’s . Implicitly, this comparison approach assumes that the present value is

not negative or zero.

⁷Example 11.1 is used to value an entire subsidiary, which is a collection of projects. The risk-

adjusted discount rate method also can be used to value a single project.

Grinblatt770Titman: Financial	III. Valuing Real Assets	11. Investing in Risky	© The McGraw770Hill
Markets and Corporate		Projects	Companies, 2002
Strategy, Second Edition

Chapter 11

Investing in Risky Projects

379

The Tracking Portfolio Method Is Implicit in the Risk-Adjusted Discount Rate Method

To understand the relation between the risk-adjusted discount rate method and track-

ing, assume that the CAPM is applied to value the Hilton casino cash flow considered

in the last section. To do this, we discount the expected cash flow, assumed to be $11.3

million, at the discount rate implied by the CAPM.

The average of the betas of the traded equity of a group of comparison casinos is

estimated to be .5. Thus, the Hilton casino cash flow is tracked by a portfolio that is

invested

50 percent in the market portfolio and

50 percent in the risk-free asset.

If the expected return on the market is 20 percent and the risk-free rate is 6 percent,

the appropriate discount rate is

.06 .5(.20 .06) .13.

Hence, the present value of the expected future cash flow is

$11.3 million/1.13 $10 million.

The 13 percent used to discount the $11.3 million expected future cash flow

from the Hilton casino is the expected return of the tracking portfolio. Hence, if one

buys enough of the tracking portfolio to have an expected future value of $11.3 mil-

lion, the tracking portfolio will cost $10 million today. This tracking portfolio con-

sists of $5 million in the market portfolio (50 percent) and $5 million in the risk-

free asset (50 percent). Thus, the discounted (or present) value of the expected future

cash flow is nothing more than the cost of acquiring the tracking portfolio’s cash

flows ($10 million) while the CAPM beta (.5) represents the proportion of the track-

ing portfolio allocated to the market portfolio, which is assumed to be the tangency

portfolio.