What is the equivalent uniform annual cost of two hydraulic systems with expecte

Question

What is the equivalent uniform annual cost of two hydraulic systems with expected 30-year life with the following features? The first hydraulic system requires annual operating, maintenance and repair cost of $1,000 and it has a useful life of 15 years. Its initial cost is $35,000 and it has a salvage value of $6,000 at the end of its useful life. The second hydraulic system has an initial cost or $18,000 and is expected to be unserviceable after ten years. It requires $500 annual operating, maintenance and repair cost and has a zero salvage value after its 10-year useful life. Assume the interest rate is 8%.

Explanation / Answer

First Hydraulic system Cash Flows Cash Flows Y0=35000 Y1 to Y15 = 1000 per year Y15=-6000 salvage value PV of the cash flow=35000+PVA(A=1000,n=15,i=7%)-6000/(1.07^15) =35000+1000*9.1079-6000/(1.07^15)=41933.22 UAC=41933.22/PVA(n=15,i=7%)=41933.22/9.1079=4604.05 Second hydraulic system Cash Flows Y0=18000 Y1 to Y10= 500 per year PV of the cash flow=18000+PVA(A=500,n=10,i=7%) =18000+500*7.0236=21511.8 UAC=21511.8/PVA(n=10,i=7%)=21511.8/7.0236=3062.79 In the cited case the expected life of 30 years is irrelevant as we have to consider only the actual useful life.

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