Question

1 pts A land surveyor just starting in private practice needs a van to carry crew and equipment. He can lease a used van for $8000 per year, paid at the beginning of each year, in which case maintenance is provided. Alternatively, he can buy a used van for $16,000 and pay for maintenance himself. He expects to keep the van for 3 years, at which time he would sell it for an anticipated $3500. Given a MARR of 6%, what is the most the surveyor should pay for uniform annual maintenance to make it worthwhile to buy the van instead of leasing it? $3500 $2003 $5574 $6500

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Answer 1

Option (1).

PV of lease payments = 8,000 x P/A(6%, 3) x 1.06** = 8,480 x 2.6730 = 22,667

Of annual maintenance cost be M, then

PV of costs for buy option = 16,000 + M x P/A(6%, 3) - 3,500 x P/F(6%, 3) = 16,000 + M x 2.673 - 3,500 x 0.8396

= 16,000 + M x 2.673 - 2,939

= 13,061 + M x 2.673

For equivalence, PV of lease = PV of buy

13,061 + M x 2.673 = 22,667

M x 2.673 = 9,606

M = 3,594 (slight difference in value is due to rounding off)

**Since payments are at beginning of year, a multiplicative factor of (1 + MARR) is used