Principles of Corporate Finance_ 12th Edition

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Chapter 22 Real Options 589


bre44380_ch22_573-596.indd 589 09/30/15 12:08 PM


In this chapter we have presented several examples of important real options. In each case we
used the option-pricing methods developed in Chapter 21, as if the real options were traded
calls or puts. Was it right to value the real options as if they were traded? Also we said next
to nothing about taxes. Shouldn’t the risk-free rate be after-tax? What about the practical
problems that managers face when they try to value real options in real life? We now address
these questions.


A Conceptual Problem?


When we introduced option pricing models in Chapter 21, we showed that the trick is to
construct a package of the underlying asset and a loan that would give exactly the same pay-
offs as the option. If the two investments do not sell for the same price, then there are arbitrage
possibilities. But most real assets are not freely traded. This means that we can no longer
rely on arbitrage arguments to justify the use of Black-Scholes or binomial option valuation
methods.
The risk-neutral method still makes practical sense for real options, however. It’s really just an
application of the certainty-equivalent method introduced in Chapter 9.^18 The key assumption—
implicit until now—is that the company’s shareholders have access to assets with the same risk
characteristics (e.g., the same beta) as the capital investments being evaluated by the firm.
Think of each real investment opportunity as having a “double,” a security or portfolio
with identical risk. Then the expected rate of return offered by the double is also the cost of
capital for the real investment and the discount rate for a DCF valuation of the investment
project. Now what would investors pay for a real option based on the project? The same
as for an identical traded option written on the double. This traded option does not have to
exist; it is enough to know how it would be valued by investors, who could employ either
the arbitrage or the risk-neutral method. The two methods give the same answer, of course.
When we value a real option by the risk-neutral method, we are calculating the option’s value
if it could be traded. This exactly parallels standard capital budgeting. Share holders would vote
unanimously to accept any capital investment whose market value if traded exceeds its cost, as
long as they can buy traded securities with the same risk characteristics as the project. This key
assumption supports the use of both DCF and real-option valuation methods.


What about Taxes?


So far this chapter has mostly ignored taxes, but just for simplicity. Taxes have to be accounted
for when valuing real options. Take the Mark II microcomputer in Table 22.2 as an example.
The Mark II’s forecasted PV of $807 million should be calculated from after-tax cash flows
generated by the product. The required investment of $900 million should likewise be calcu-
lated after-tax.^19
What about the risk-free discount rate used in the risk-neutral method? It should also be
after-tax. Look back to the Chapter 19 Appendix, which demonstrates that the proper discount
rate for safe cash flows is the after-tax interest rate. The same logic applies here because pro-
jected cash flows in the risk-neutral method are valued as if they were safe.


(^18) Use of risk-neutral probabilities converts future cash flows to certainty equivalents, which are then discounted to present value at a
risk-free rate.
(^19) Capital investments are not usually an immediately tax-deductible expense, but they do generate depreciation tax shields. These tax
shields may be taken account of in calculating after-tax operating cash flows. If not, you should subtract the PV of the tax shields from
the pre-tax capital investment, thus converting the investment to a net after-tax outlay.
22-6 Valuing Real Options

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