Question

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. The firm's CEO has asked you to prepare a brief on possible outcomes of the project the company is planning. Tropical Sweets is considering a project that will cost $100 million. This project will run for 8 years. The cost of capital for this type of project is 10%. After discussions with the marketing department, you learn that there is a 60% chance of high demand, with future cash flows of $35 million per year. There is a 40% chance of low demand, with cash flows of only $15 million per year. Use the information provided above on Tropical Sweets Inc. to answer questions 2(a), 2(b) and 2(c).

2a) What are the expected NPV and Coefficient of variation (CV) of this project if the firm has no real option?  

2b) Now suppose the project cannot be delayed. But if the firm implements the project there will exist an opportunity to rerun the project if the outcomes are favorable, thus there exists a growth option. The firm will have an opportunity to replicate the original project at the end of its life if it adds value. What is total expected NPV, the value of the growth option, and CV of the project? Discount all cash flows at the WACC.  

2c) Now suppose the firm decides to wait for 3 years before implementing this project, what is total expected NPV, the value of the wait option, and CV of the project? Discount all cash flows at the WACC

Answer 1

		SECENARIO A: HIGH DEMAND
	Rate	Discount Rate=Cost of Capital=	10%
	Nper	Number of years of cash inflows	8
	Pmt	Annual Cash inflows	$35	Million
	PV	Present Value of Cash inflows	$186.72	Million
		(Using PV function of excel)
		SECENARIO B: LOW DEMAND
	Rate	Discount Rate=Cost of Capital=	10%
	Nper	Number of years of cash inflows	8
	Pmt	Annual Cash inflows	$15	Million
	PV	Present Value of Cash inflows	$80.02	Million
		(Using PV function of excel)
			p	PV	NPV=PV-100	p*NPV
		Scenario	Probability	PV($ million)	NPV	Probability*NPV
		High Demand	0.6	$186.72	$86.72	$52.03
		Low Demand	0.4	$80.02	($19.98)	($7.99)
					SUM	$44.04
		Expected NPV=144.04-100=	$44.04	Million
		Scenario	p	NPV	D=NPV-44.04	E=D^2	F=E*p
			Probability	Net Present Value	Deviation from expected	Deviation Squared	Deviation squared*Probability
		High Demand	0.6	$86.72	$42.68	$1,821.53	$1,092.92
		Low Demand	0.4	($19.98)	($64.02)	$4,098.45	$1,639.38
						SUM	$2,732.30
		Variance of NPV	$2,732.30
		Standard Deviation of NPV=Square Root of Variance	$52.27	Million	SQRT(2732.30)
		Coefficient of Variation=Standard Deviation /Expected NPV
		Coefficient of Variation=52.27/44.04	1.18682604
	2b	If The Project is successful, it will be rerun
		Probability of success=0.6
		NPV of the rerun =86.72/(1.1^8)	$33.44	million
		Total NPV if successful=86.72+33.44	$120.16	million
		Scenario	p	NPV	D=NPV-64.10	E=D^2	F=E*p
			Probability	Net Present Value	Deviation from expected	Deviation Squared	Deviation squared*Probability
		High Demand	0.6	$120.16	$56.05	$3,142.00	$1,885.20
		Low Demand	0.4	($19.98)	($84.08)	$7,069.49	$2,827.80
		Expected NPV=120.16*0.6-19.98*0.4=	$64.10			SUM	$4,712.99
		Variance of NPV	$4,712.99
		Standard Deviation of NPV=Square Root of Variance	$68.65	Million	SQRT(4712.99)
		Coefficient of Variation=Standard Deviation /Expected NPV
		Coefficient of Variation=68.65/64.10	1.07093287
	2c	Weight for 3 years
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