Question

1. Your firm has just sold non-strategic assets to raise cash for capital investment while avoiding the use of debt. The firm may buy a piece of machinery for $140,000 [with a useful or depreciable life of 4 years]. Your pretax cost of capital is 8% [and your tax rate is 20%]. You can lease the machine for $43,500 per year and the estimated salvage/recovery value at the end of four years [based on actual market data] is $20,000. Should you lease or buy? Please show work.

Answer 1

Post tax cost of capital, r = 8% x (1 - T) = 8% x (1 - 20%) = 6.4%

On leasing:

Post tax lease payment = - L x (1 - T) = 43,500 x (1 - 20%) =  - 34,800

PV of lease payments = - 34,800 x PVAF (6.4%, 4) = -34,800 x  3.4336 = - $ 119,489.34

On buying:

Annual depreciation = Cost / n = 140,000 / 4 = 35,000

Depreciation tax shield per year, DTS = D x T = 35,000 x 20% = 7,000

Hence, NPV = -C0 + DTS x PVAF (6.4%, 4) + Post tax salvage value x PVIF (6.4%, 4) = -140,000 + 7,000 x 3.4336 + 20,000 x (1 - 20%) x (1 + 6.4%)^-4 = - $ 103,480.80

NPV of buying is less negative than NPV of leasing

Or, NPV of buying > NPV of leasing

Hence, you should buy the piece of machinery.