Question

Super Sonics Entertainment is considering buying a machine that costs $435,000. The machine will be depreciated over five years by the straight-line method and will be worthless at that time. The company can lease the machine with year-end payments of $107,500. The company can issue bonds at a 9 percent interest rate. If the corporate tax rate is 35 percent, should the company buy or lease?

Please Show Calculations

Answer 1

All financials below are in $.

Case I: Buy

Initial cost, C₀ = Machine Cost = 435,000

Annual depreciation, D = Machine Cost / Life = 435,000/5 =  87,000

Tax rate, T = 35%

Annual Depreciation tax shield = DTS = D x T = 87,000 x 35% =  30,450

DTS will occur as annuity over N = 5 years

Discount rate, R = 9%

Hence, NPV_Buy = - C₀ + Sum of PV of DTS as annuity = - C₀ + DTS / R x [1 - (1 + R)^-N] = - 435,000 + 30,450 / 9% x [1 - (1 + 9%)^-5] =  - 316,560.12

Case II: Lease

Post tax cash flows, L = Pre tax annual lease payments x ( 1- T) = - 107,500 x (1 - 35%) = -69,875

Hence, NPV_Lease = Sum of PV of L = L / R x [1 - (1 + R)^-N] = - 69,875 / 9% x [1 - (1 + 9%)^-5] = - 271,789.38

Since, NPV_Lease = - 271,789.38 > NPV_Buy = - 316,560.12, the company should lease the machine.