Question

Your firm needs to invest in a new delivery truck. The life expectancy of the delivery truck is five years. You can purchase a new delivery truck for an upfront cost of $200,000, or you can lease a truck from the manufacturer for five years for a monthly lease payment of $4,000 (paid at the beginning of each month). Your firm can borrow at 7% APR with quarterly compounding.

a. Calculate the effective annual rate on your firm's borrowings.

b. Calculate the effective monthly discount rate that you should use to evaluate the truck lease.

c. What is the present value of the lease payments for the delivery truck?

d. Calculate the lease rate for which you would be indifferent between leasing and buying the truck.

e. Should you lease or buy?

(Hint: Do not round intermediate results from a. to d.)

a. The effective annual rate is %. (round to two decimals)

b. The effective monthly rate is %. (round to three decimals)

c. The PV of the lease is $. (round to full $)

d. The indifference lease rate is $. (round to full $)

e. (fill in "lease" or "buy")

Answer 1

a.

EAR = (1 + 0.07/4)4 - 1

EAR = 7.186%

b.

APR(monthly) = 12[(1 + 0.07/4)1/3 - 1]

APR(monthly) = 6.96%

c.

Monthly Lease Payment = $4,000

Time Period = 60 months

Calculating Present Value of Lease Payment,

Using TVM Calculation,

PV [FV = 0, PMT = 4,000, N = 60, I = 0.0696/12]

PV = $202,200.63

d.

Calculating Lease rate,

Using TVM Calculation,

I = [PV = -200,000, FV = 0, PMT = 4,000, N = 60]

I = 7.42%