Question

Suppose a project is dependent on whether there is a good economy and whether a competitor enters the market. If there is no competitor, the project will produce $50 million in a good economy and $15 million in a poor economy. If there is a competitor, the project will produce $30 million in a good economy and $10 million in a poor economy. The probability of a good economy is 60%, versus 40% for a poor economy; and the probability for a competitor to enter the market is 30%, versus 70% for no competitor.

a. Find the expected value of the cash flow from the project.

b. Assume the project cannot begin for three years and has a risk-adjusted discount rate of 18%. Calculate the present value of the project’s expected cash flow.

c. Using the calculation from part b, calculate the expected three-year holdingperiod return, the variance of the three-year holding-period return, and the standard deviation of the three-year holding-period return.

d. Adjust the variance and the standard deviation in part c to annual terms

Part a.

Expected value of the cash flow $ ___ million (round your answer to one decimal place in millions)

Part b.

The present value of the cash flow is $ ___ million (round your answer to four decimal places in millions)

Part c.

Expected three-year holding period return is ___ % (round your answer to two decimal places)

Expected three-year variance in returns is ___ (round your answer to two decimal places)

Expected three-year standard deviation of returns is ___ % (round your answer to two decimal places)

Part d.

Annual Variance: ___ (round your answer to two decimal places)

Annual Standard Deviation: ___ % (round your answer to two decimal places)

Answer 1

a.Expected cash flow=

(70%*((50%*50)+(50%*15)))+(30%*((50%*30)+(50%*10)))

28.75

Millions

b.

PV of the project’s expected cash flow

28.75/1.18^3=

17.50

Millions

c.

3 Year holding period return=

17.5/28.75=

60.87%

Variance of the 3 Year holding period return

(1-0.6087)^2=

0.1531

Std.devn. Of the 3 Year return

Sq.rt.of 0.1531

0.3913

d.

Annual Variance=0.1531/3=

0.0510

Annual std. Deviation

0.3913/3=

13.04%