Question

Growth Option: Option Analysis

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%.

1. What is the expected NPV of the project? Round your answer to the nearest dollar.

   $ ________

2. 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). Use the Black-Scholes model to estimate the value of the option. Assume the variance of the project's rate of return is 0.2756 and that the risk-free rate is 7%. Do not round intermediate calculations. Round your answers to the nearest dollar.

   Use computer software packages, such as Minitab or Excel, to solve this problem.

   Value of the growth option: $ _______

   Value of the entire project: $ ________

Answer 1

Part (a)

Cash Flow = $ 20,000

Annual cash inflow = (Good demand probability *Cash Flow) + (Bad demand probability *Cash Flow)

= (40% * $25,000) + (60% * $5,000)

= (0.4* $25,000) + (0.6 * $5,000)

= $10,000 + $3,000

= $ 13,000

Therefore, Annual Cash inflow is $13,000

PV factor at year 0 = 1

PV factor at year 1 = 1 / (1+r)n

where, n = 1

r = 10%

Thus, PV factor at year 1 = 1 / (1+10%)1  

= 1 / (1+0.10)1  

= 1 / (1.10)1

= 0.9091

  

Thus, PV factor at year 2 = 1 / (1+10%)2

= 1 / (1+0.10)2  

= 1 / (1.10)2

= 0.8264

Now, Present Values =

Year	PV of Cash Flow
0	- $20,000 (outflow)
1	$13,000* 0.9091 = $11,818.3
2	$13,000 * 0.8264 = $ 10,743.8

Thus, NPV = -20000 + 11,818.3 + 10743.8

Net Present Value  = $2,562.102

  

Part (b)

Cash Outflow (Y0) = -$20,000

Risk Free Rate (Rf) = 7%

PV of outflow at the end of year 2 = 1/ (1+7%)2 * (-20,000)

= $ - 17,468.8

PV of total cash outflow = -20,000 + (- 17,468.8)

= - $ 37,468.8

Year	Prob. of good demand	Cash flow of good demad	Cashflow [(2)*(3)]	Pv factor 1 / (1+r)n	PV of cash inflow [(4)*(5)]
(1)	(2)	(3)	(4)	(5)	(6)
0	-	-	- $ 37,468.8	1	- $ 37,468.8
1	40% i.e 0.4	$25,000	$10,000	1 / (1.10)1  = 0.9091	$ 9,091
2	40% i.e 0.4	$25,000	$10,000	1 / (1.10)2 = 0.8264	$ 8,264
3	40% i.e 0.4	$25,000	$10,000	1 / (1.10)3 ​​​​​​​​​​​​​​ = 0.7513	$ 7,513
4	40% i.e 0.4	$25,000	$10,000	1 / (1.10)4 ​​​​​​​​ = 0.6830	$ 6,830

Net Present Value = Sum of column no. (6)

= - $ 5,770.8