9. A heat exchanger is being installed as part of a plant modernization program.

Question

9. A heat exchanger is being installed as part of a plant modernization program. It costs $80,000, including installation, and is expected to reduce the overall plant fuel cost by $20,000 per year. Estimates of the useful life of the heat exchanger range from: an optimistic (with probability 15%) 12 years to a pessimistic (with probability 5%) 4 years with probability 15%. The most likely (with probability 80%) value is 5 years. Assume the heat exchanger has no salvage value at the end of its useful life.

a) Determine the pessimistic, most likely, and optimistic rates of return.

b) Use the range of estimates to compute the mean life and determine the estimated before-tax rate of return.

c) What is the expected value of the rate of return?

Explanation / Answer

a)

pesismistic rate of return

probability = .05

we have to calculate IRR

80,000 = 20,000*PVIFA(IRR,4)

using ccalculator

IRR = 0%

optimistic

probability = .15

80,000 = 20,000PVIFA(IRR,12)

IRR = 22.89%

most likely

80,000 = 20,000*PVIFA(IRR,5)

IRR = 7.93%

mean life = .8*5+.05*4+.15*12 = 6 years

estimated before tax rate of return for 6 years,

80,000 = 20,000*PVIFA(IRR,6)

IRR = 12.98% (estimated before tax rate of return)

expected value of rate of return = .15*22.89+.05*0+.8*7.93 = 9.7775%

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