Should I lease or purchase a machine?

Question

A machine can be leased for 36 months at a rate of $2,800/month, or purchased outright for $88,000. (If purchased outright, the machine is assumed to have zero value at the end of the 36 months). Using your company's internal interest rate (sometimes known as a hurdle rate) of 18% yr, do you recommend leasing or purchasing the machine?

Answer 1

The question becomes whether the present value of the lease payments is Greater or less than the purchase price The Present value of a constant steam of Payments is PV=PMT*K(i,t) where PV = Present Value, PMT = Payment and k is the multiplier which is a decreasing function of i and an increasing function of t (the higher the interest rate the lower the PV and the more payments the higher the PV.

K is given as K=(1/i)(1 -(1/(1+i))^t) Here we have 3 years of monthly payments (t=36) and the periodic or monthly interest rate is 18%/3 = 1.5%) so K = (1/0.015)(1 - ((1/(1.015))³⁶) = 27.66

The monthly lease payment is 2,800 so the PV = 27.66*2,800=77,449.91. So it is more than $10,000 cheaper to lease.

Hope this helps. If you need help studying for finals please reach out.

Answer 2

The lease price of the machine is 100,800 (2,800 x 36 months) plus the interest of 18,144 (2,800 x 18% x 36 months). So the total lease price would be 118,944. Therefore, purchasing the machine is the better option.