Question

An energy efficiency project with a first cost of $150,000, life of 10 years, and with no salvage value has a most likely value of $30,000. The high estimate of 40,000 has a probability of 0.2, and the low estimate of $20,000 has a probability of 0.3.

Assume that interest rates are 8%. What is the present worth based on the probabilities given?

Answer 1

PW of Most likely = - 150,000 + 30,000*(P/A,8%,10) = - 150,000 + 30,000 * 6.7101 = $51,303

PW of High estimate = - 150,000 + 40,000*(P/A,8%,10) = - 150,000 + 40,000 * 6.7101 = $118,404

PW of Low estimate = - 150,000 + 20,000*(P/A,8%,10) = - 150,000 + 20,000 * 6.7101 =  -$15,798

Expected value of PW ($) = (1 - 0.3 - 0.2)*51,303 + 0.2*118,404 - 0.3*15,798 = 25,651.50 + 23,680.80 - 4,739.40 = $44,592.90

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