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Real Options

								2/1/12
Chapter 14. Real Options
Assume that you have just been hired as a financial analyst by Tropical Sweets Inc., a mid-sized California company that specializes in creating exotic candies from tropical fruits such as mangoes, papayas, and dates. The firm's CEO, George Yamaguchi, recently returned from an industry corporate executive conference in San Francisco, and one of the sessions he attended was on real options. Since no one at Tropical Sweets is familiar with the basics of real options, Yamaguchi has asked you to prepare a brief report that the firm's executives could use to gain at least a cursory understanding of the topics.
a. What are some types of real options?
b. What are the five steps for analyzing a real option?
c. Tropical Sweets is considering a project that will cost $70 million and will generate expected cash flows of $30 per year for three years. The cost of capital for this type of project is 10 percent and the risk-free rate is 6 percent. After discussions with the marketing department, you learn that there is a 30 percent chance of high demand, with future cash flows of $45 million per year. There is a 40 percent chance of average demand, with cash flows of $30 million per year. If demand is low (a 30 percent chance), cash flows will be only $15 per year. What is the expected NPV?
REAL OPTIONS: THE INVESTMENT TIMING OPTION
Cost=		($70)
WACC=		10%
Risk-free rate=		6%
	Demand	Prob.	Annual Cash Flow	Prob. x (CF)
	High	0.3	$45	$13.50
	Average	0.4	$30	$12.00
	Low	0.3	$15	$4.50
			Expected CF=	$30.00
Procedure 1: DCF Only
	Year		1	2	3
	Expected CF		$30.00	$30.00	$30.00
	NPV=	$4.61
d. Now suppose this project has an investment timing option, since it can be delayed for a year. The cost will still be $70 million at the end of the year, and the cash flows for the scenarios will still last three years. However, Tropical Sweets will know the level of demand, and will implement the project only if it adds value to the company. Perform a qualitative assessment of the investment timing option’s value.
e. Use decision tree analysis to calculate the NPV of the project with the investment timing option.
Procedure 3: Decision Tree Analysis
a. Scenario Analysis: Proceed with Project Today
Cost		Future Cash Flows			NPV this	Prob.	Data for
Year 0	Prob.	1	2	3	Scenario	x NPV	Std Deviation
		$45	$45	$45	$41.91	$12.57	417
	30%
-$70	40%	$30	$30	$30	$4.61	$1.84	0
	30%
		$15	$15	$15	-$32.70	-$9.81	417
					Expected NPV of Future CFs =	$4.61	835	=Variance of PV
					Standard Deviation=	$28.89
					Coefficient of Variation =	6.27
b. Decision Tree Analysis: Implement in One Year Only if Optimal
		Cost	Future Cash Flows			NPV this	Prob.	Data for
Year 0	Prob.	1	2	3	4	Scenarioa	x NPV	Std Deviation
		-$70	$45	$45	$45	$35.70	$10.71	177
	30%
$0	40%	-$70	$30	$30	$30	$1.79	$0.71	37
	30%
		$0	$0	$0	$0	$0.00	$0.00	39
						Expected NPV of Future CFs =	$11.42	253		=Variance of PV
						Standard Deviation=	$15.91
						Coefficient of Variation =	1.39
Notes:	a Discount the cost of the project at the risk-free rate, since the cost is known. Discount the operating cash flows at the WACC.
f. Use a financial option pricing model to estimate the value of the investment timing option.
Procedure 4: Analysis with a Financial Option
The option to defer the project is like a call option. The company has until Year 1 to decide whether or not to implement the project, so the time to maturity of the option is one year. If the company exercises the option, it must pay a strike price equal to the cost of implementing the project. If the company does implement the project, it gains the value of the project. If you exercise a call option, you will own a stock that is worth whatever its price is. If the company implements the project, it will gain a project, whose value is equal to the present value of its cash flows. Therefore, the present value of a project's future cash flows is analogous to the current value of a stock. The rate of return on the project is equal to its cost of capital. To find the value of a call option, we need the standard deviation of its rate of return; to find the value of this real option, we need the standard deviation of the projects expected rate of return.
The first step is to find the value of the project's future cash flows, as of the time the option must be exercised. We also need the standard deviation of the project's value as of the date it must be exercised. Finally, we need the present value of the project's future cash flows.
Find the Year 1 Value and Risk of Future Cash Flows If Project is Deferred
			Future Cash Flows			PV at	Prob.	Data for
Year 0	Prob.	1	2	3	4	Year 1	x Value	Std Deviation
			$45	$45	$45	$111.91	$33.57	417
	30%
	40%		$30	$30	$30	$74.61	$29.84	0
	30%
			$15	$15	$15	$37.30	$11.19	417
						Expected Year 1 Value of Future CFs =	$74.61	835		=Variance of PV
						Standard Deviation of value at Year 1=	$28.89
						Coefficient of Variation at Year 1 =	0.39
Find the current value of future cash flows if project is deferred (note: this is the estimate of P).
	Current Value =	Year 1 Value	=	$74.61	=	$67.82
		(1+WACC)		1.10
	P =	$67.82
Use the direct approach to estimate the variance of the project's rate of return.
						Probability		Data for
PVYear 0		PVYear 1	Return		Probability	x ReturnYear 1		Std Deviation
		$111.91	65.00%		0.30	19.5%		9.1%
	High
$67.82	Average	$74.61	10.0%		0.40	4.0%		0.0%
	Low
		$37.30	-45.0%		0.30	-13.5%		9.1%
					1.00
					Expected return =	10.0%		18.2%	=Variance of PV
					Standard deviation of return =	42.6%
					Direct estimate of s2 = Variance of return =	18.2%
Use the indirect approach to estimate the variance of the project's rate of return. Start by estimating the coefficient of variation, CV, of the project's value at the time the option expires. This was done in an earlier step.
			CV =Coefficient of Variation =	0.39 Michael C. Ehrhardt: Note: we rounded this to make it consistent with the PowerPoint Show.
Now use the following formula to estimate the variance of the project's rate of return.
			t = time until the option expires =	1
			Indirect estimate of s2 =	14.2%
Find the Value of a Call Option Using the Black-Scholes Model
	Financial Option				Real Option
rRF =	Risk-free interest rate			=	Risk-free interest rate
t =	Time until the option expires			=	Time until the option expires
X =	Strike price			=	Cost to implement the project
P =	Current price of the underlying stock			=	Current value of the project
s2 =	Variance of the stock's rate of return			=	Variance of the project's rate of return
	rRF =	6%
	t =	1
	X =	$70.00
	P =	$67.82
	s2 =	14.2%
	d1 =	{ ln (P/X) + rRF + s2 /2) ] t } / (s t1/2 )				=	0.2637
	d2 =	d1 - s (t 1 / 2)				=	-0.1131
	N(d1)=					=	0.6040		Note: use the NORMSDIST function.
	N(d2)=					=	0.4550
	V =	P[ N (d1) ] - Xe-rRF t [ N (d2) ]				=	$ 10.97
REAL OPTIONS: THE GROWTH OPTION
g. Now suppose the cost of the project is $75 million and the project cannot be delayed. But if Tropical Sweets implements the project, then Tropical Sweets will have a growth option. It will have the opportunity to replicate the original project at the end of its life. What is total expected NPV of the two projects if both are implemented?
	Cost=	$75
	WACC=	10%
	Risk-free rate =	6%
Original Project
Cost		Future Cash Flows			NPV this		Prob.	Data for
Year 0	Prob.	1	2	3	Scenario		x NPV	Std Deviation
		$45	$45	$45	$36.91		$11.07	417.45
	30%
-$75	40%	$30	$30	$30	-$0.39		-$0.16	0.00
	30%
		$15	$15	$15	-$37.70		-$11.31	417.45
						Expected NPV =	-$0.39	834.90		=Variance of PV
						Standard Deviation=	$28.89
						Coefficient of Variation =	(73.25)
NPV without growth option:
	NPV =	-$0.39
Expected NPV is you simply repeat project at time 3:
	NPV =	NPV of project 1 + PV of repeated project
	NPV =	NPV1	+	NPV1 / (1+WACC)3
	NPV =	-$0.39	+	-$0.30 Michael C. Ehrhardt: The NPV would be even lower if we separately discounted the $75 million cost of Replication at the risk-free rate.
	NPV =	-$0.69
h. Tropical Sweets will replicate the original project only if demand is high. Using decision tree analysis, estimate the value of the project with the growth option.
Decision Tree: Implement the repeated project only if demand is high.												Data for
Cost		Future Cash Flows						NPV this		Prob.		Std Deviation
Year 0	Prob.	1	2	3	4	5	6	Scenario Michael C. Ehrhardt: The operating cash flows are discounted at the project cost of capital. The cost to implement the repeated project is discounted at the risk-free rate, since the cost is known.		x NPV
		$45	$45	-$30	$45	$45	$45	$58.02		$17.40		1,010
	30%
-$75	40%	$30	$30	$30	$0	$0	$0	-$0.39		-$0.16		0
	30%
		$15	$15	$15	$0	$0	$0	-$37.70		-$11.31		- 0
								Expected NPV =		$5.94
												1,010	=Variance of PV
								Standard Deviation=		$31.78
								Coefficient of Variation =		5.35
Notes:	1. The CF in Year 3 includes the cost to implement the second project if it is optimal to do so.
	2. When finding the NPV, the cost to implement the second project is discounted at the risk-free rate; other cash flows are discounted at the cost of capital.
i. Use a financial option model to estimate the value of the growth option.
Financial Option Approach
Find the value and risk of the future cash flows as of the time the option expires.
												Data for
Cost		Future Cash Flows						PV at		Prob.		Std Deviation
Year 0	Prob.	1	2	3	4	5	6	Year 3		x NPV
					$45	$45	$45	$111.91		$33.57		417
	30%
	40%				$30	$30	$30	$74.61		$29.84		- 0
	30%
					$15	$15	$15	$37.30		$11.19		417
								Expected value at Year 3 =		$74.61
												835	=Variance of PV
								Standard Deviation of value at Year 3=		$28.89
								Coefficient of Variation at Year 3=		0.39
Find the current value of future cash flows if project is deferred (note: this is the estimate of P).
	Current Value =	Year 3 Value	=	$74.61	=	$56.05
		(1+WACC)3		1.33
	P =	$56.05
Use the direct approach to estimate the variance of the project's rate of return.
					Annual			Data for
PVYear 0		1	2	PVYear 3	Return	Probability	x Return2005				Std Deviation
				$111.91	25.9%	0.30	7.8%				1.0%
	High
$56.05	Average			$74.61	10.0%	0.40	4.0%				0.0%
	Low
				$37.30	-12.7%	0.30	-3.8%				1.3%
						1.00
						Expected return =	7.968%				2.3%	=Variance of PV
						Standard deviation of return =	15.0%
						Direct estimate of s2 = Variance of return =	2.3%
Use the indirect approach to estimate the variance of the project's rate of return. Start by estimating the coefficient of variation, CV, of the project's value at the time the option expires. This was done in an earlier step.
			CV =Coefficient of Variation =	0.39 Michael C. Ehrhardt: Note: we rounded this to make it consistent with the PowerPoint Show.
				Michael C. Ehrhardt: The NPV would be even lower if we separately discounted the $75 million cost of Replication at the risk-free rate.	Now use the following formula to estimate the variance of the project's rate of return.
			t = time until the option expires =	3
			Indirect estimate of s2 =	4.7% Michael C. Ehrhardt: Note: we rounded to make it consistent with PowerPoint show.
j. What happens to the value of the growth option if the variance of the project’s return is 14.2 percent? What if it is 50 percent? How might this explain the high valuations of many dot.com companies?
Find the Value of a Call Option Using the Black-Scholes Model
							Sensitivity Analysis
						Base Case	Case 1	Case 2
	rRF =					6%	6%	6%
	t =					3	3	3
	X =					$75.00	$75.00	$75.00
	P =					$56.05	$56.05	$56.05
	s2 =					4.70%	14.20%	50.00%
	d1 =	{ ln (P/X) + [rRF + s2 /2) ] t } (s t1/2 )			=	-0.1085	0.1559	0.5215
	d2 =	d1 - s (t 1 / 2)			=	-0.4840	-0.4968	-0.7032
	N(d1)=				=	0.4568	0.5619	0.6990		Note: we used the NORMSDIST function.
	N(d2)=				=	0.3142	0.3097	0.2410
	V =	P[ N (d1) ] - Xe-rRF t [ N (d2) ]			=	$ 5.92	$ 12.10	$ 24.08
Total Value =		Value of Project 1 + Value of growth option
Total Value =		-$0.39	+	$5.92
Total Value =		$ 5.53

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