Introduction to Corporate Finance

5: Valuing Shares

But what do we mean by ‘an appropriate discount rate’? This is a subtle issue that we discuss

in much greater detail in Chapter 11. To understand the main idea, recall that FCF represents the

total cash available for all investors. We suspect that debt is not as risky as preferred shares, and that

preferred shares are not as risky as ordinary shares. This means that bondholders, preferred shareholders

and ordinary shareholders each have a different required return in mind when they buy a company’s

securities. Somehow, we have to capture these varying required rates of return to come up with a single

discount rate to apply to free cash flow, the aggregate amount available for all three types of investors.

The solution to this problem is known as the weighted average cost of capital (WACC).^9 The WACC is the

after-tax, weighted average required return on all types of securities issued by the company, where the

weights equal the percentage of each type of financing in the company’s overall capital structure. For

example, suppose a company finances its operation with 50% debt and 50% equity. Further suppose the

company pays an after-tax return of 8% on its outstanding debt, and that investors require a 16% return

on the company’s shares. The WACC for this company would be calculated as follows:

WAC C = (0.50 × 8%) + (0.50 × 16%) = 12%

If we obtain forecasts of the FCFs, and if we discount those cash flows at a 12% rate, the resulting

present value is an estimate of the total value of the company, which we denote Vcompany.

When analysts value free cash flows, they use some of the same types of models that we have used

to value other kinds of cash flow. We could assume that a company’s free cash flows will experience zero,

constant or variable growth. In each instance the procedures and equations would be the same as those

introduced earlier for dividends, except we would now substitute FCF for dividends.

Remember, our goal in using the free cash flow approach is to develop a method for valuing a

company’s shares without making assumptions about its dividends. The free cash flow approach begins

by estimating the total value of the company. To find out what the company’s shares, Vshare, are worth, we

subtract from the total enterprise value, Vcompany, the value of the company’s debt, Vdebt, and the value of

the company’s preferred shares, Vpreferred. Equation 5.7 depicts this relationship:

Eq. 5.7 Vshares = Vcompany – Vdebt – Vpreferred

We already know how to value bonds and preferred shares, so this step is relatively straightforward.

Once we subtract the value of debt and preferred shares from the total enterprise value, the remainder

9 We provide only a brief sketch of the WACC concept at this point, deferring a deeper analysis until Chapter 11.

weighted average cost of

capital (WACC)

The after-tax, weighted

average required return on

all types of securities issued

by a company, where the

weights equal the percentage

of each type of financing in

a company’s overall capital

structure

LO5.3

> >

Then we calculate the PV 3 (at the end of year 3)

of the FCFs from year 4 to ∞.

PV $41, 010 (0.200.05)

$41, 010

0.15

$273, 400

3 =÷−

=

=

Discounting the end-of-year-3 cash flow above

back to time 0, we get:

PV

$273, 400

120

$158,218

0 = 3

=

Adding the PV 0 s for the first three years to those

for year 4 to ∞, we get:

1 Current value of the business = $72,766 +

$158,218 = $230,984

Taking 25% of the current value of the business, we

get:

2 Value of a 25% interest in the business =

0.25 × $230,984 = $57,746

Assuming your estimates are correct, you should pay

$50,000 for a 25% interest in Sawft Pty Ltd, given that

it is in fact worth $57,746.