Harrowfield Deliveries has decided to lease a delivery van for the next 5 years using a fixed price lease that allows them to buy the van for $18,000.The purchase price of the van is $67,000,and there is no risk that Harrowfield will default on the lease.If the risk-free rate is a 8% APR with monthly compounding,what would be the monthly lease payment for a 5-year lease in a perfect capital market?

Question

Quizplus · Accepted Answer

We need to find the monthly payment for a 5-year lease with a fixed price of $18,000 to be paid at the end of the lease term. This is equivalent to finding the present value of this fixed payment.

First, we need to calculate the present value of the purchase price, which is the future value of the lease payments over 5 years at 8% APR monthly compounding:

PV = 67000/(1+0.08/12)^60 = $39,839.68

The present value of the lease payments can be calculated by adding the present value of the purchase price and the fixed payment:

PV = 39839.68 + 18000 = $57,839.68

The monthly lease payment can be found by dividing this present value by the present value of an annuity due of 60 months at 8% APR monthly compounding:

PMT = 57839.68/((1-(1+0.08/12)^-60)/(0.08/12)*(1+0.08/12)) = $1,106.01

Therefore, the monthly lease payment is $1,106, which corresponds to choice (A).

Harrowfield Deliveries Has Decided to Lease a Delivery Van for the Next