Real OptionsQuestion $4-$Real Options $[25$ points$]$

AMC Corp. is considering launching a new product but there is some uncertainty about how the

product will be received by consumers. Your junior analyst has provided you with three scenarios

of possible market conditions and estimated the probability of each scenario. Starting the project

today $(t=0)$ would incur costs of $$12,000,000,$ the cost of capital is $11\%,$ you can ignore taxes.

The three scenarios are as follows:

"Good": The product is very popular and operating profits are estimated to start at

$$1,100,000$ in year $1(t=1)$ and afterwards will grow at $7\%$ forever. The probability of this

scenario is $30\%.$

"Average": Year $1$ operating profits $($cash flow at $t=1)$ are $$1,100,000$ and grow at $4\%$ in

perpetuity. The probability of this scenario is $55\%.$

"Poor": Year $1$ operating profits are $$800,000$ but decline by $10\%$ each year. The probability

of this scenario is $15\%.$

a$)$ What is the NPV of this project?

Hint:

i$.$ First, calculate the NPV of the project for each scenario individually $($i$.$e$.,$ good, average, poor$).$

ii$.$ Then, calculate a weighted average of the three scenarios using the probabilities provided in the

question.

b$)$ Suppose AMC can hire consultants to do additional market research to determine how

consumers will receive the product. The research will take one year $($i$.$e$.$ the project cash

flows would start one year later$).$ With this research, AMC will know exactly which of the

three scenarios is accurate and there would be no uncertainty about the project's outcome

before investing at the end of the first year. What is the project's NPV today in this case?

$($Hint: Think about in which scenarios AMC would decide to go forward with the project.$)$

c$)$ What is the maximum AMC Corp. would be willing to pay for conducting this additional

market research? $($Hint: find the value of the "option to wait" for one year.$)$

d$)$ Without doing any calculations, if the probabilities of the "good", "average", and "poor"

scenario were $40\%,35\%,$ and $25\%$ instead, respectively, would you expect the value of the

option to conduct additional research to be higher, lower, or unchanged? Explain.