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%?
4
Answer in dollars, without dollar sign or other symbols

Answer 1

It can pay up to $ 689.012 annual maintenance cost for the van at the MARR of 20%

Step-by-step explanation:

Present value of the lease:

`C * (1-(1+r)^(-time) )/(rate)(1+r) = PV\\`

C 3,000.00

time 3 years

rate 0.2

`3000 * (1-(1+0.2)^(-3) )/(0.2)(+.20) = PV\\`

PV $7,583.3333

Now, present value of the van:

7,000 - salvage value + maintenance cost

`(Salvage)/((1 + rate)^(time) ) = PV`

Salvage: 1,500.00

time 3 years

rate 0.20000

`(1500)/((1 + 0.2)^(3) ) = PV`

PV 868.0556

7,000 - 868.06 = 6.131,94‬

the maximum maintenance cost should match the lease:

lease Present worth 7,583.3333

purhcase Present worth (6.131,94)

PV of maintenance: 1,451.39

We know calculate the quota which matches this PV:

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV 1,451

time 3

rate 0.2

`1451.39 / (1-(1+0.2)^(-3) )/(0.2) = C\\`

C $ 689.012