Helvetica Corporation is interested in leasing a piece of machinery that has a fair value of $150,000. The market rate for financing is 8% and Helvetica plans to lease the machinery for the next five years. Calculate the quarterly lease payments.

Question

Quizplus · Accepted Answer

To calculate the quarterly lease payments, we use the formula for the present value of an annuity because lease payments are essentially an annuity. The formula is: $PMT = \frac{PV}{\frac{1 - (1 + r)^{-n}}{r}}$, where PMT is the payment per period, PV is the present value (or initial amount) of the loan/lease, r is the interest rate per period, and n is the total number of payments.Given:- PV = $150,000 (fair value of the machinery)- Annual interest rate = 8%, but since payments are quarterly, we divide this by 4 to get the quarterly rate: $r = \frac{8\%}{4} = 2\%$- The lease is for 5 years, with quarterly payments, so there are $5 \times 4 = 20$ payments in total.First, convert the interest rate to decimal form: $r = 2\% = 0.02$.Now, plug the values into the formula:$$PMT = \frac{150,000}{\frac{1 - (1 + 0.02)^{-20}}{0.02}}$$$$PMT = \frac{150,000}{\frac{1 - (1 + 0.02)^{-20}}{0.02}}$$$$PMT = \frac{150,000}{7.53608}$$$$PMT ≈ 9,174$$Therefore, the quarterly lease payments are approximately $9,174.

Helvetica Corporation Is Interested in Leasing a Piece of Machinery