Problem 1 (25pts) Your company is planning on investing in a new piece of machin

Question

Problem 1 (25pts) Your company is planning on investing in a new piece of machinery, but there is a bit of uncertainty in the proposed costs involved with it. The machinery requires a capital investment (with a standard deviation of $0) of $10,000, and will last for four years. Annual '"revenues less expenses" are normally distributed, with an expected net income of $4000 per year, and a standard deviation of $1500. Salvage value at the end of four years is expected to be negligible. Assuming normal distribution and a MARR 7%, what is the probability that the PW ofthis investment will be unprofitable for the company (i.e., w is Pr(PW(790) 0))?

Explanation / Answer

0 1 2 3 4 Cost of machinery $10,000 depreciation per year $2,500 Value of the machinery $7,500 $5,000 $2,500 $0 Income per year $4,000 Standard deviation $1,500 MARR 0.07 Income per year($) - positive case $4,000 5500 5500 5500 5500 Income per year($) - Neutral case 4000 4000 4000 4000 Income Per year($) - negative case 2500 2500 2500 2500 Cumulative income - Positive case 5500 11000 16500 22000 Cumulative income - Neutral case 4000 8000 12000 16000 Cumulative income - Negative case 2500 5000 7500 10000 PW of the investment - Posiitve case 5140.19 9607.83 13468.91 16783.69 45000.62 PW of the investment - neutral case 3738.32 6987.51 9795.57 12206.32 32727.73 PW of the investment - negative case 2336.45 4367.19 6122.23 7628.95 20454.83 Probability is 0 % (as all cases NPW is above 10000

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