Valuing Cash Flow to Equity Holders

To calculate the net present value of a project to equity holders,the analyst must deter-

mine the appropriate discount rate for the cash flow to equity holders. Since these cash

flows are often highly levered, they probably have betas that are substantially larger

than those used to discount unlevered cash flows. In addition, given the option-like

payoffs of these equity holder claims, it is very cumbersome to use a CAPM- or APT-

based risk-adjusted discount rate approach to value these payoffs. In our view, the real

options approach would be the preferred valuation approach whenever these options

are likely to affect the valuation to a significant degree.

Example 13.17 illustrates how the real options approach can be used for this

application.

Example 13.17:Valuing Cash Flow to Equity Holders with Real Options

In a two-date binomial model, assume that Unitron, from Example 13.16, has existing proj-

ects that generate a firm worth $110 million at date 1 if the up state occurs and $71.5 mil-

lion if the down state occurs.Assuming no taxes, a risk-free rate of 10 percent, and risk-

¹2attached to each of the two states, Unitron’s date 0 value is $82.5

neutral probabilities of

million ([.5($110 million) .5($71.5 million)]/1.1).Unitron currently has debt maturing at

date 1 with a face value of $77 million and a date 0 market value of $67.5 million ([.5($77

million) .5($71.5 million)]/1.1) and equity with a date 0 market value of $15 million

( [.5($110 million$77 million) .5($0)]/1.1).

Anna Kramer identifies a riskless project that will cost Unitron $28.23 million and will pro-

duce a cash flow of $31.62 million at date 1, providing a 12 percent return.The project will

be entirely financed with debt that is equal in seniority to Unitron’s existing debt.Compute

the effect of the adoption of this project on the value of Unitron’s existing debt and on the

value of its equity.

Answer:After adopting the project, Unitron’s date 1 cash flows will be $141.62 million

($110 million $31.62 million) in the up state and $103.12 million ($71.5 mil-

lion $31.62 million) in the down state.This generates a new firm value of $111.25 million

([.5($141.62 million) .5($103.12 million)]/1.1).Since the new debt holders’payment of

$28.23 million is a fair market price for their debt, the existing debt and equity holders now

have claims worth $83.02 million.The additional $0.52 million in value for the existing debt

and equity holders ($83.02 million versus $82.5 million) is simply the net present value of

the project ($28.23 million $31.62 million/1.1).

For $28.23 million to be the fair market price of the new debt, the promised payments on

the new debt, F, which capture the fraction F/(F $77 million) of the firm’s assets in

F

default, must satisfy $28.23 million .5F.5 ($103.12 million)1.1

F $77 million

implying F$31.90 million, and a debt yield (for both old and new debt of 13 percent

([$31.90 million$28.23 million]/$28.23 million).

Grinblatt995Titman: Financial	III. Valuing Real Assets	13. Corporate Taxes and	© The McGraw995Hill
Markets and Corporate		the Impact of Financing on	Companies, 2002
Strategy, Second Edition		Real Asset Valuation

Chapter 13

Corporate Taxes and the Impact of Financing on Real Asset Valuation

491

However, with promised payments to debt holders at $108.90 million ($77 mil-

lion $31.90 million) if the project is adopted, the value of the shares of the equity holders

is only $14.87 million ([.5($141.62 million$108.90 million) .5($0)]/1.1).

Thus, the adoption of the project destroys $.13 million in equity value.This $.13 million

is transferred to the existing debt holders along with the $.52 million positive NPV.

The loss in equity value, seen in Example 13.17, occurs whether the project is

financed with debt or equity or any mix of the two. The NPVto equity holders crite-

rion rejects the project whereas the NPVto the firm criterion says adopt the project

because it accounts for the fact that the project enhances the value of the firm’s

existingdebt.

Real Options versus the Risk-Adjusted Discount Rate Method

Example 13.17 illustrates the importance of using the real options approach when

wealth transfers, generated by debt default, are significant considerations in project

evaluation. It is true that traditional approaches, like the risk-adjusted discount rate

method, can be easily applied to value cash flows to equity holders when the options

arising because of default play a negligible role in valuation. However, as the next result

points out, project present values computed with the WACC method and those com-

puted by discounting cash flows to equity holders are identical in the absence of such

default considerations.

Result	13.5	In the absence of default, the present value of a project’s future unlevered cash flows, dis-
		counted at the WACC, is identical to the present value of cash flows to equity holders dis-
		counted at the cost of equity. Hence, in the absence of default, the NPVs generated with
		both present value calculations select and reject the same projects. When debt default is a
		significant consideration, projects that increase firm value may not increase the values of
		the shares held by equity holders and vice versa. However, in these cases, it is more appro-
		priate to analyze the values of cash flows with the real options approach.