26. Real Options

A project will cost $45 million to implement. The cost of capital is 14%. The expected annual operating cash flows for each of 2 years are $28.25 million. What is the traditional NPV for the project? Based on this DCF analysis, should the project be accepted?

$1.51 million; accept −$45.00 + $28.25/(1 + 0.14)1 + $28.25/(1 + 0.14)2 = $1.51.

Using decision tree analysis, the probabilities and expected NPVs of 3 scenarios for a timing option are as follows: The cost of capital is 14%. The expected NPV of the project if proceeding today is $1.93 million. What is the expected NPV of the timing option? Should the project be delayed?

$14.03 million; delay $35.00(0.25) + $10.56(0.50) + $0.00(0.25) = $14.03. Yes, waiting adds value to the project.

A project will cost $45 million to implement. The cost of capital is 14%. The probabilities and expected cash flows of three scenarios for the project are as follows: What are the expected annual operating cash flows for the project?

$25.80 million $51(0.25) + $30(0.50) + $2(0.25) = $28.25.

Using decision tree analysis, the probabilities and expected NPVs of 3 scenarios for a growth option are as follows: What is the expected NPV of the growth option?

$7.07 million $63.56(0.25) + $2.36(0.50) + −$40.00(0.25) = $7.07.

Which of the following statements regarding the use of real options techniques is accurate?

Today, 26% of companies use real option techniques when evaluating projects, and that number is expected to grow rapidly. Twenty years ago very few companies used real options, but a survey of CFOs reported that more than 26% of companies now use real option techniques when evaluating projects. Just as with NPV, it's only a matter of time before virtually all companies use real option techniques.

Many real options can be analyzed using a standard model for an existing financial option.

True Given the large number of standard models for existing financial options, it is often possible to find a financial option that resembles the real option being analyzed.

Finance theory has not yet provided a way to estimate the cost of capital for options in a decision tree?

True Since the decisions change the risk of a project, the original project's cost of capital is probably not the correct cost to use in the decision tree. However, finance theory has not yet provided a way to estimate the appropriate cost of capital for a decision tree in situations like this so sensitivity analysis should be used to identify the effect that different costs of capital have on the project's value.

If 14% is the appropriate cost of capital in the "proceed immediately" case, then some lower rate would be appropriate in the "delay decision" case.

True The company may proceed with better information and more certainty after delaying, therefore the project will be less risky and the cost of capital should be adjusted to reflect the reduced risk.

All models for valuing a real option are wrong and yet useful.

True We might not be able to find the exact value of a real option, but the value we find can be helpful in deciding whether or not to accept the project. Equally important, the process of looking for and then valuing real options often identifies critical issues that might otherwise go unnoticed.

Of the five possible procedures for dealing with real options, which is the simplest?

Use discounted cash flow (DCF) valuation and assume real option values are zero. The simplest way to deal with real options is to ignore them (assume their values are zero) when using DCF valuation.

Which of the following does NOT describe a growth option?

developing a new product under a new brand name Growth options are an extension of an existing project or a second-generation product. A new product under a different brand name would be a completely new stand-alone project.

Risk-neutral valuation, which uses simulation, is a type of which of the following techniques for valuing timing options?

financial engineering Risk-neutral valuation is a financial engineering technique that uses simulation.

To use the Black-Scholes model to value a timing option, five inputs are needed, which include all EXCEPT the:

future value of the project's expected cash flows For a real option, the underlying asset is the project itself, and its current "price" is the present value of its expected future cash flows. Therefore, as a proxy for the stock price we can use the present value of the project's future cash flows.

To use the Black-Scholes model to value a growth option, which of the following is substituted as the input for the stock price?

present value of the second-generation project's expected cash flows The input for stock price in the Black-Scholes model is the current value of the underlying asset. For the growth option, the underlying asset is the second-generation project, and its current value is the present value of its cash flows.

All of the following are examples of real options EXCEPT:

trade options. Four examples of real options are investment timing options, growth options, abandonment options, and flexibility options.

Which of the following characterizes investment timing options?

waiting to make a better-informed decision By waiting, a better-informed decision can be made, and this investment timing option adds value to the project and reduces its risk.