A Conceptual Real-Options Decision Framework When You Can Resolve Uncertainty by Waiting Consider a project that requires a $200 million investment and expects to last three years with the following cash flows: Demand Probability Annual Cash Flow Good 0.25 $250 million Moderate 0.30 $100 million

Question

A Conceptual Real-Options Decision Framework When You Can Resolve Uncertainty by Waiting

Consider a project that requires a $200 million investment and expects to last three years with the following cash flows:

Annual Cash Flow	Probability	Demand
$250 million	0.25	Good
$100 million	0.30	Moderate
$ 35 million	0.45	Poor

The cost of capital that accounts for the market risk, known as the risk-adjusted discount rate, is 10%, and a risk-free interest rate is known to be 6%. Can we defer the project by one year and then implement it only if demand is either moderate or good?

Accepted Answer

Given: Three demand scenarios, required investment = $200 million, risk-free rate = 6%, risk-adjusted discount rate = 10%, and T = 1 year.
Find: Option value for deferring the investment for one year.

Conventional Approach: We will determine the acceptability of the project on the
basis of the expected NPW as

[latex]E\left[A_{n} \right][/latex] = 0.25($250) + (0.30)($100) + 0.45($35)

= $108.25

[latex]E\left[PW\left(10\%\right) \right]_{Benefits}[/latex] = $108.25(P/A, 10%, 3)

= $269.20

E[PW(10%)] = $269.20 - $200

= $69.20 [latex]\gt[/latex] 0

Since the expected NPW is positive, the project would be considered for immediate action. Note that we need to use the risk-adjusted discount rate, which reflects the risk inherent in estimating the project cash flows. If we proceed immediately with the project, its expected NPW is $69.20 million. However, the project is very risky. If demand is good, NPW = $421.72 million; if demand is moderate, NPW = $48.69 million; and if demand is poor, NPW = -$112.96 million. (See Figure 13.21.) Certainly, we are uneasy about the prospect of realizing a poor demand, even though its expected NPW is positive.

Real-Options Approach: Suppose we have an option to defer the investment decision by one year, and then we will gain additional information regarding demand.

If demand is low, we will not implement the project. If we wait, the up-front cost and cash flows will stay the same, except they will be shifted ahead by a year. The following table depicts the demand scenarios:

		Future Cash Flows
Probability	NPW at n = 0	4	3	2	1	0	Demand Scenarios
25%	$376.51	$250	$250	$250	-$200	[latex]\blacktriangleright[/latex]	Good
30%	$37.40	$100	$100	$100	-$200	[latex]\blacktriangleright[/latex]	Moderate
45%	$0	0	0	0	0	[latex]\blacktriangleright[/latex]	Poor

Note that our assumption here is that there is no cost of delaying the investment in terms of the initial investment of $200 million. If there is, we simply increase the initial investment by the amount of cost of delaying. In finding the NPW, we will use two different discount rates. We will use 6% to discount the cost of the project at the risk-free rate, since the cost is known. Then we will discount the operating cash flows at the cost of capital. Under the various scenarios, we have

[latex]PW_{Good}[/latex] = -$200(P/F, 6%, 1) + $250(P/A, 10%, 3)(P/F, 10%, 1)
= $376.51

[latex]PW_{Moderate}[/latex] = -$200(P/F, 6%, 1) + $100(P/A, 10%, 3)(P/F, 10%, 1)
= $37.40

[latex]PW_{Poor}[/latex] = $0

Next, we calculate the project’s expected NPW if we wait by using the preceding three scenarios with their given probabilities:

[latex]E\left[NPW\right] _{wait}[/latex] = (0.25)($376.51) + 0.30($37.40) + 0.45($0)
= $105.35

This is exactly what we call the expanded NPW (ENPW). Now we can compare the option to wait against the conventional NPW analysis. Note that the option to wait is higher ($105.35 million versus $69.20 million):

Value of real-option = $105.35 - $69.20 = $36.15

In other words, the waiting option is worth $36.15 million. If we implement the project today, we gain $69.20 million but could lose the future project, worth $105.35 million for a net loss of $36.15 million on the differential project. Therefore, we should wait and decide next year whether to implement the project based on the observed demand. Note also that the cash flows are less risky under the option to wait, since we can avoid the low cash flows. Also, the cost of implementing the project may not be risk free. Given the change in risk, perhaps we should use different rates to discount the cash flows. Another important observation is that the ENPW is equivalent to the EVPI concept we discussed in Chapter 12, as this is the value that we can attain if we have the perfect information about the future.

Comments: The option to wait resembles a financial call option: We get to “buy” the project for $200 million in one year if the projected value is greater than $200 million after one year. This is like a call option with an exercise price of $200 million and an expiration date of one year. If we use the Black–Scholes model to value the option to wait, the required inputs are

K = I, which is the exercise price = cost to implement the project = $200 million

r = risk-free rate = 6%

T = time to maturity = 1 year

[latex]S_{0}[/latex] = V = current stock price = estimated current value of the project

[latex]\sigma ^{2}[/latex] = variance of stock return = estimated variance on project return

In general, we need to estimate two unknown parameters: V and [latex]\sigma ^{2}[/latex] . Estimating V is equivalent to matching the current stock price in a financial option. In a real option, V is the value of the project today, which is found by computing the present value of all of the project’s future expected cash flows at its cost of capital (or risk-adjusted discount rate). Estimating [latex]\sigma ^{2}[/latex] will be more difficult, but the procedures will be discussed in Section 13.6.

Question 13.8: A Conceptual Real-Options Decision Framework When You Can Re...

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