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 $24,000 per year for 2 years. If demand is bad (60% probability), then the net cash flows will be $7,000 per year for 2 years. Fethe's cost of capital is 13%. Do not round intermediate calculations. 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. $ 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 5%. Select the correct decision tree. The correct graph is -Select- . 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

1). NPV if demand is good: PMT = 24,000; N = 2; rate = 13%, solve for PV.

PV = 40,034

NPV = -initial investment + PV = -20,000 + 40,034 = 20,034

NPV if demand is bad: PMT = 7,000; N = 2; rate = 13%, solve for PV.

PV =11,677

NPV = -20,000+11,677 = -8,323

Expected NPV = sum of (probability*NPV) = (40%*20,034) + (60%*-8,323) = 3,020 (Answer)

2). Decision tree:

Note: Since graph options are not provided in the question posted, please pick the correct option using the above decision tree.

NPV if demand is good:

PV of investment (at Time T = 0) = 20,000 + 20,000/(1+5%)^2 = 38,141

PV of cash inflows: PMT = 24,000; N = 4; rate = 13%, solve for PV.

PV = 71,387

NPV = -38,141+71,387 = 33,247

NPV if demand is bad: NPV = -8,323 (as calculated in part (1))

Expected NPV = (40%*33,247) + (60%*-8,323) = 8,305 (Answer)