Question

A firm can lease a truck for 4 years at a cost of $30,000 annually. It can instead buy a truck at a cost of $80,000, with annual maintenance expenses of $10,000. The truck will be sold at the end of 4 years for $20,000. What is the better option if the discount rate is 10%?

Answer 1

Answer:

Leasing.

Explanation:

Find the present value of each and compare and choose the one with the lowest cost in present value terms.

LEASE;

Payments are in form of an annuity ;done using financial calculator (TI BA II plus)

PMT = -30,000

N ;duration = 4

I/Y = 10%

FV = 0

then CPT PV = -$95,095.96

BUY

Initial cost; (already in present value terms) = -$80,000

Annual maintenance(is an annuity); done using financial calculator (TI BA II plus)

PMT = -10,000

N ;duration = 4

I/Y = 10%

FV = 0

then CPT PV = -$31,698.65

Add PV of salvage value;

PV = FV/ (1+r)^4

PV = 20,000 /(1.10^4)

= 20,000/ 1.4641

= $13,660.26911

Overall PV of BUYING = (-80,000 -31,698.65 + 13,660.26911) = -$98,038.38

Therefore, leasing is a better option since the overall present value of costs  is lower at $95,095.96 compared to that of buying at 98,038.38.