The Kellogg Company is considering the following investment project and has estimated all cost and revenues in constant dollars. The project requires the purchase of a $9,000 asset, which will be used for only two years (the project life).
€¢ The salvage value of this asset at the end of two years is expected to be $4,000.
€¢ The project requires an investment of $2,000 in working capital, and this amount will be fully recovered at the end of the project year.
€¢ The annual revenue, as well as general inflation, are discrete random variables but can be described by the probability distributions in Table P12.20 (both random variables are statistically independent).
€¢ The investment will be classified as a three-year MACRS property (tax life).
€¢ It is assumed that the revenues, salvage value, and working capital are responsive to the general inflation rate.
€¢ The revenue and inflation rate dictated during the first year will prevail over the remainder of the project period.
€¢ The marginal income tax rate for the firm is 40%. The firm's inflation-free interest rate (/') is 10%.
(a) Determine the NPW as a function of X and Y.
(b) In part (a), compute the expected NPW of this investment.
(c) In part (a), compute the variance of the NPW of the investment.
Table P12.20

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Probability General Inflation Probability Annual Revenue (A) $10,000 20,000 30,000 0.30 0.40 0.30 Rate () 3% 5% 7% 0.25 0.50 0.25