Emma runs a small factory that needs a vacuum oven for brazing small fittings. She can purchase the model she needs for $180 000 up front, or she can lease it for five years for $3 500 per month. She can borrow at 5% APR, compounded monthly. Assuming that the oven will be used for five years, should she purchase the oven or should she lease it?
A)Buy, since the present value (PV)of the lease is $5 468 more than the cost of the oven.
B)Lease, since the present value (PV)of the lease is $8 642 less than the cost of the oven.
C)Lease, since the present value (PV)of the lease is $2 212 less than the cost of the oven.
D)Lease, since the present value (PV)of the lease is $12 224 less than the cost of the oven.

Question

Quizplus · Accepted Answer

To determine whether to buy or lease, we calculate the present value (PV) of the lease payments and compare it to the purchase price. The lease involves 60 payments of $3,500 each, with a 5% APR compounded monthly. The formula for the present value of an annuity is PV = P * [(1 - (1 + r)^-n) / r], where P is the payment amount, r is the monthly interest rate, and n is the total number of payments. Here, r = 0.05/12 and n = 60. Plugging in the values, we find the PV of the lease payments. If the PV of leasing is higher than the purchase price, it's better to buy. The correct choice indicates that buying is advantageous because the PV of leasing exceeds the purchase cost by $5,468, making buying the more cost-effective option.

Emma Runs a Small Factory That Needs a Vacuum Oven