Question

Growth Option: Decision-Tree 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 $26,000 per year for 2 years. If demand is bad (60% probability), then the net cash flows will be $6,000 per year for 2 years. Fethe's cost of capital is 11%. Do not round intermediate calculations.

1. What is the expected NPV of the project? Negative value, if any, should be indicated by a minus sign. 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). Write out the decision tree.  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 7%.

   Select the correct decision tree.

     

   The correct graph is -Select-ABCDItem 2 .

   Use decision-tree analysis to calculate the expected NPV of this project, including the option to continue for an additional 2 years. Negative values, if any, should be indicated by a minus sign. Round your answer to the nearest dollar.
   $  

Answer 1

Part (a)

Expected annual cash flows, C = p1 x C1 + p2 x C2 = 40% x 26,000 + 60% x 6,000 =  14,000

Hence, expected NPV = - C0 + C/(1 + r) + C / (1 + r)² = -20,000 + 14,000 / (1 + 11%) + 14,000 / (1 + 11%)² = 3,975

Part (b)

The decision trees should be as shown below:

NPV of first path = -20,000 + 26,000 / 1.11 + 26,000 / 1.11² - 20,000 / (1 + 7%)² + 26,000 / 1.11³ + 26,000 / 1.11⁴ = 43,195 = NPV1

NPV of second path = -20,000 + 6,000 / 1.11 + 6,000 / 1.11² = -9,725 = NPV 2

Hence, the expected NPV = p1 x NPV1 + p2 x NPV2 = 40% x 43,195 + 60% x (-9,725) = 11,443