Question

Fethe’s Funny Hats is considering selling trademarked, orange-haired curly wigs for University of Tennessee football games. The purchase cost for a 2-year franchise to sell the wigs is $20,000. If demand is good (40% probability), then the net cash flows will be $25,000 per year for 2 years. If demand is bad (60% probability), then the net cash flows will be $5,000 per year for 2 years. Fethe’s cost of capital is 10%. Explain your work. a. What is the expected NPV of the project? b. If Fethe makes the investment today, then it will have the option to renew the franchise fee for 2 more years at the end of Year 2 for an additional payment of $20,000. In this case, the cash flows that occurred in Years 1 and 2 will be repeated (so if demand was good in Years 1 and 2, it will continue to be good in Years 3 and 4). Write out the decision tree and use decision-tree analysis to calculate the expected NPV of this project, including the option to continue for an additional 2 years. Note: The franchise fee payment at the end of Year 2 is known, so it should be discounted at the risk-free rate, which is 6%.

Answer 1

	EXPECTED NPV for TWO YEARS
	Present Value of Cash flow
	(Cash Flow)/((1+i)^N)
	i=discount rate=cost of capital=10%	0.1
	N=Year of Cash Flow
	If Demand is Good
	N	CF	PV=CF/(1.1^N)
	Year	Cash flow	Present Value
	0	($20,000)	($20,000)
	1	$25,000	$22,727
	2	$25,000	$20,661
		SUM	$23,388
	NPV =Sum of PV of cash flows	$23,388
	Probability	0.4
	If Demand is Bad
	N	CF	PV=CF/(1.1^N)
	Year	Cash flow	Present Value
	0	($20,000)	($20,000)
	1	$5,000	$4,545
	2	$5,000	$4,132
		SUM	($11,322)
	NPV =Sum of PV of cash flows	($11,322)
	Probability	0.6
		Probability	NPV	NPV* Probability
		0.4	$23,388	$9,355
		0.6	($11,322)	-$6,793
			SUM	$2,562
	EXPECTED NPV =SUM (NPV*Probability)
	EXPECTED NPV =	$2,562
	EXPECTED NPV WITH OPTION TO CONTINUE FOR ANOTHER 2 YEARS
	If Demand is good
	N	CF	PV=CF/(1.1^N)
	Year	Cash flow	Present Value
	0	($20,000)	($20,000)
	1	$25,000	$22,727
	2	$25,000	$20,661
	2	($20,000)	($17,800)	(-20000/(1.06^2)		(discounted at 6%)
	3	$25,000	$18,783
	4	$25,000	$17,075
		SUM	$41,447
	NPV =Sum of PV of cash flows	$41,447
	Probability	0.4
	If Demand is Bad
	NPV =Sum of PV of cash flows	($11,322)
	Probability	0.6
		Probability	NPV	NPV* Probability
		0.4	$41,447	$16,579
		0.6	($11,322)	-$6,793
			SUM	$9,785
	EXPECTED NPV =SUM (NPV*Probability)
	EXPECTED NPV =	$9,785