A land surveyor just starting in private practice needs a van to carry crew and

Question

A land surveyor just starting in private practice needs a van to carry crew and equipment. He can lease a used van for $3,000 per year, paid at the beginning of each year, in which case maintenance is provided. Alternatively, he can buy a used van for $7,000 and pay for maintenance himself. He expects to keep the van three years at which time he could sell it for $1,500. What is the most he should pay for uniform annual maintenance to make it worthwhile buying the van instead of leasing it. if his pre-tax MARR is 20%?

Explanation / Answer

when he lease:

he has to pay $3000 at the beginning of each year

so for 3 years PV(cash outflows) =PV(0.2,3,-3000,0,1) = $7,583.33 = his total costs

when he buys the van:

cost = 7,000

salvage value(at the end of three years) = 1500

let he pays annualy $p as his mantenance costs:

then PV(salvage value) =PV(0.2,3,0,1500) = $868.06

let PV(maintenance cost) = x

then his total costs are 7000+x-868.06 = 6131.94 + x

now both the costs should be equal:

hence 7583.33=6131.94+x

hence x = 1451.40

hence annual maintenance cost P =PMT(0.2,3,1451.4) = $689.02

at most he should pay $689.02 as his uniform annual costs

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