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# NPV, Opportunity Cost of Capital and Payoffs

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In real life the future health of the economy cannot be reduced to three equally probable states like slump, normal, and boom. But we'll keep that simplification for one more example.

Your company has identified to more projects, B and C. Each will require a \$5 million outlay immediately. The possible payoffs at year 1, are in millions:

Slump Normal Boom
B 4 6 8
C 5 5.5 6

You have identified the possible payoffs to investors in three stocks, X, Y, and Z:
Price Per Share PAYOFF AT YR 1
Current/ Slump/ Normal/ Boom
X 95.65/ 80/ 110/ 140
Y 40/ 40/ 44/ 48
Z 10/ 8/ 12/ 16

a. What are the expected cash inflows of projects B and C?
b. What are the expected rates of return offered by stocks, X, Y, and Z?
c. What are the opportunity costs of capital for projects B and C? Hint: Calculate the percentage differences, slump versus normal and boom versus normal, for stocks X, Y, and Z. match up to the percentage differences in B's and C's payoffs.
d. What are the NPVs of projects B and C?
e. Suppose B and C are launched and \$5 million are invested in each. How much will they add to the total market value of your company's shares?

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