Principles of Corporate Finance_ 12th Edition

588 Part Six Options

bre44380_ch22_573-596.indd 588 09/30/15 12:08 PM

To value the real option, we need a risk-free rate (assume 4%) and a volatility of the value

of the drug once launched (assume 20%). With these inputs, the Black–Scholes value of

a two-year call on an asset worth $177 million with an exercise price of $130 million

is $58.4 million. (Refer to Table 22.2 if you need a refresher on how to use the Black–

Scholes formula.)

But there’s only a 44% chance that the drug will pass phase II trials. So the company must

compare an initial investment of $18 million with a 44% chance of receiving an option worth

$58.4 million. The NPV of the drug at year 0 is

NPV = −18 + (.44 × 58.4) = $7.7 million

This NPV is less than the $19 million NPV computed from Figure 10.6.^15 Nevertheless, the

R&D project is still a “go.”

Of course Figure 22.8 assumes only one decision point, and only one real option, between

the start of phase II and the product launch. In practice there would be other decision points,

including a Go/No Go decision after phase III trials but before prelaunch investment. In this

case, the payoff to the first option at the end of phase II is the value at that date of the second

option. This is an example of a compound call.

With two sequential options, you could look up the formula for a compound call in an

option pricing manual or you could build a binomial tree for the R&D project. Suppose you

take the binomial route. Once you set up the tree, using risk-neutral probabilities for changes

in the value of the underlying asset, you solve the tree as you would solve any decision tree.

You work back from the end of the tree, always choosing the decision that gives the highest

value at each decision point. NPV is positive if the PV at the start of the tree is higher than the

$18 million initial investment.

Despite its simplifying assumptions, our example explains why investors demand higher

expected returns from R&D investments than from the products that the R&D may gener-

ate. R&D invests in real call options.^16 A call option is always riskier (higher beta) than

the underlying asset that is acquired when the option is exercised. Thus the opportunity

cost of capital for R&D is higher than for a new product after the product is launched

successfully.^17

R&D is also risky because it may fail. But the risk of failure is not usually a market or

macroeconomic risk. The drug’s beta or cost of capital does not depend on the probabilities

that a drug will fail in phase II or III. If the drug fails, it will be because of medical or clinical

problems, not because the stock market is down. We take account of medical or clinical risks

by multiplying future outcomes by the probability of success, not by adding a fudge factor to

the discount rate.

(^15) Note that the Black–Scholes formula treats the exercise price of $130 million as a fixed amount and calculates its PV at a risk-free
rate. In Chapter 10, we assumed this investment was just as risky as the drug’s postlaunch cash flows. We discounted the investment at
the 9.6% overall cost of capital, reducing its PV and thus increasing NPV overall. This is one reason why the Black–Scholes formula
gives a lower NPV than we calculated in Chapter 10. Of course the $130 million is only an estimate, so discounting at the risk-free rate
may not be correct. You could move from Black–Scholes to the valuation formula for an exchange option, which allows for uncertain
exercise prices (see footnote 3). On the other hand, the R&D investment is probably close to a fixed cost, because it is not exposed to
the risks of the drug’s operating cash flows postlaunch. There is a good case for discounting R&D investment at a low rate, even in a
decision tree analysis.
(^16) You could also value the R&D example as (1) the PV of making all future investments, given success in clinical trials, plus (2) the
value of an abandonment put, which will be exercised if clinical trials are successful but the PV of postlaunch cash flows is suffi-
ciently low. NPV is identical because of put–call parity.
(^17) The higher cost of capital for R&D is not revealed by the Black–Scholes formula, which discounts certainty-equivalent payoffs at
the risk-free interest rate.