Question

Your landscaping company can lease a truck for $8,700 a year (paid at year-end) for 7 years. It can instead buy the truck for $46,000. The truck will be valueless after 7 years. The interest rate your company can earn on its funds is 8%. a. What is the present value of the cost of leasing? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. Is it cheaper to buy or lease? c. What is the present value of the cost of leasing if the lease payments are an annuity due, so the first payment comes immediately? (Do not round intermediate calculations. Round your answer to 2 decimal places.) d. Is it now cheaper to buy or lease?

Answer 1

A. $45,295.419

B.Cheaper to LEASE

C.$48,919.0525

D. Cheaper to BUY

Step-by-step explanation:

a. Calculation for the present value of the cost of leasing

Present value=8,700/8%*(1-1/1.08^7)

Present value=8,700/0.08*0.41650960

Present value=108,750*0.41650960

Present value=$45,295.419

Therefore the present value of the cost of leasing will be $45,295.419.

b. Based on the above calculation it cheaper to LEASE than to buy

c. Calculation for the present value of the cost of leasing if the lease payments are an annuity

Present value =8,700/8%*(1-1/1.08^7)*1.08

Present value=8,700/0.08%*(1-1/1.08^7)*1.08

Present value=8,700/0.08%*0.41650960*1.08

Present value=108,750*0.41650960*1.08

Present value=$48,919.0525

Therefore the present value of the cost of leasing if the lease payments are an annuity due will be $48,919.0525.

D. Based on the above calculation it is Cheaper to BUY than to lease.