Problem 1. Myers Business Systems is evaluating the introduction of a new product. The possible levels of unit sales and the probabilities of their occurrence are given below:
Possible Sales
Market Reaction in Units Probabilities
Low response . . . . . . . . . . . . . 20 .10
Moderate response . . . . . . . . . 40 .30
High response . . . . . . . . . . . . . 55 .40
Very high response . . . . . . . . . 70 .20
A) What is the expected value of unit sales for the new product?
B) What is the standard deviation of unit sales?
Problem 2: Possible outcomes for three investment alternatives and their probabilities of occurrence are given below.
Alternative 1 Alternative 2 Alternative 3
Outcomes Probability Outcomes Probability Outcomes Probability
Failure 50 .2 90 .3 80 .4
Acceptable 80 .4 160 .5 200 .5
Successful 120 .4 200 .2 400 .1
Rank the three alternatives in terms of risk (compute the coefficient of variation).
Problem 3: Silverado Mining Company is analyzing the purchase of two silver mines. Only one investment will be made. The Alaska mine will cost $2,000,000 and will produce $400,000 per year in years 5 through 15 and $800,000 per year in years 16 through 25. The Montana mine will cost $2,400,000 and will produce $300,000 per year for the next 25 years. The cost of capital is 10 percent.
a) Which investment should be made? (Note: In looking up present value factors for this problem, you need to work with the concept of a deferred annuity for the Alaska mine. The returns in years 5 through 15 actually represent 11 years; the returns in years 16 through 25 represent 10 years.)
b) If the Alaska mine justifies an extra 5 percent premium over the normal cost of capital because of its riskiness and relative uncertainty of flows, does the investment decision change?