Corporate Finance

Risk Analysis in Capital Investments 
 227

Return expected by equity investors = Risk free rate + Risk premium

= Rf + β [E (Rm) – Rf]

But investors may demand a premium for other risks like country and currency risk, project risk. So the
discount rate may have to be adjusted upwards/downwards to reflect these as well. The net present value of
the project:

∑

= +

=

N

t

t

t

k

E

1 )1(

NPV

where

k= risk adjusted discount rate

= I + Q (i.e., risk free rate + premium),

Et= risky cash flow in period t, and

N= life of the project.

To calculate NPV we used the firm’s WACC as the discount rate. The underlying assumption is that the
project has the same business and financial risk as that of the parent company. Stated in another fashion,
WACC can be applied only when the project is a carbon copy of the firm’s assets. At times, the project may
have a different operating risk profile and more or less leveraged than the parent. So it is improper to apply
the firm’s WACC as the discount rate. To arrive at the project discount rate:

a) Estimate the project beta
b) Plug it into the capital asset pricing model (CAPM) to arrive at cost of equity
c) Estimate cost of debt
d) Calculate the WACC for the project

Since the beta for the project is unobservable in the marketplace, a proxy beta derived from a publicly
traded firm whose operations are as similar as possible to the project in question is used as the measure of the
project’s systematic risk. The pure play approach attempts to identify firms with publicly traded securities
that are engaged solely in the same line of business as the division. This comparable firm is called a ‘Pure play’
firm. The characteristics of a pure play firm are:

• The firm should have only one business line and no miscellaneous revenues.


• The pure play should be in the same industry or business line as the division in question.


• The revenues of the pure play should be roughly the same as those of the division in question.


• When more than one firm could be identified as a potential pure play, the firm with the median beta could
  be chosen as the pure play.

After obtaining the proxy betas, estimate the asset betas for each of these firms. The idea is to remove the
effect of capital structure on beta. The asset beta reflects only operating risk.

βA = βE (E/V)

The average of these serves as an estimate of asset beta for the project. Re-lever the project beta to reflect
the project’s financing mix using the same equation. Assume that a company is setting up an engineering
services company. The project will have a D/V ratio of 0.3. The company has identified four pure plays: