Ross et al.: Fundamentals
of Corporate Finance, Sixth
Edition, Alternate EditionVIII. Topics in Corporate
Finance(^856) 24. Option Valuation © The McGraw−Hill
Companies, 2002
Options and Capital Budgeting
In our earlier chapter on options, we discussed the many options embedded in capital
budgeting decisions, including the option to wait, the option to abandon, and others. To
add to these option-related issues, we now consider two additional issues. What we will
show is that, for a leveraged firm, the shareholders might prefer a lower NPV project to
a higher one. We then show that they might even prefer a negativeNPV project to a pos-
itive NPV project.
As usual, we will illustrate these points first with an example. Here is the basic back-
ground information on the firm:
The risk-free rate is 4 percent. As we have now done many times, we can calculate eq-
uity and debt values:
This firm has a fairly high degree of leverage; the debt/equity ratio based on market val-
ues is $14.276/5.724 2.5, or 250 percent. This is high, but not unheard-of. Notice also
that the option here is out of the money; as a result, the delta is .546.
The firm has two mutually exclusive investments under consideration. They both
must be taken now or never, so there is no timing issue. The projects affect both the mar-
ket value of the firm’s assets and the firm’s asset return standard deviation as follows:
Which project is better? It is obvious that Project A has the higher NPV, but by now you
are wary of the change in the firm’s asset return standard deviation. One project reduces
it, the other increases it. To see which project the stockholders like better, we have to go
through our by now very familiar calculations:
There is a dramatic difference between the two projects. Project A benefits both the
stockholders and the bondholders, but most of the gain goes to the bondholders. Proj-
ect B has a huge impact on the value of the equity plus it reduces the value of the debt.
Clearly, the stockholders prefer B.
What are the implications of our analysis? Basically, what we have discovered is two
things. First, when the equity has a delta significantly smaller than 1.0, any value created
Project A Project B
Market value of equity $ 5.938 $8.730
Market value of debt $18.062 $13.27
Project A Project B
NPV $4 $2
Market value of firm’s assets ($20 NPV) $24 $22
Firm’s asset return standard deviation 40 percent 60 percent
Market value of equity $5.724 million
Market value of debt $14.276 million
Market value of assets $20 million
Face value of pure discount debt $40 million
Debt maturity 5 years
Asset return standard deviation 50 percent
CHAPTER 24 Option Valuation 831