571 Consider the following three alternatives There is also

5.71 Consider the following three alternatives. There is also a \"do nothing\" alternative. Cost Net annual benefit Useful life, in years $50 $30 $40 12 4.5 6 5 10 10 At the end of the 5-year useful life of A, a replace- ment is made. If a 10-year analysis period and a 8 % interest rate are selected, which is the preferred alternative?

Solution

Time = 10 years

R = 8%

Net present worth = present worth of all the benefits – present worth of all the cost

Net present worth of alternative A = 12*(1-1/1.08^10)/.08 - 50 - 50/1.08^5

Net present worth of alternative A = -$3.51

Net present worth of alternative B = 4.5*(1-1/1.08^10)/.08 - 30 = $.20

Net present worth of alternative C = 6*(1-1/1.08^10)/.08 - 40 = $.26

There is a do nothing alternative also whose present worth is $0.

Since the alternative C has the highest and positive net present worth that is $.26 among all the alternatives, then alternative C should be selected.