Question

Sparrow Corporation is considering the acquisition of an asset for use in its business over the next five years. However, Sparrow must decide whether it would be better served by leasing the asset or buying it. An appropriate asset could be purchased for $15,000, and it would qualify as a three-year asset under the MACRS classification. Assume that the election to expense assets under § 179 is not available, that any available additional first-year depreciation is not claimed, and that the asset is not expected to have a salvage value at the end of its use by Sparrow. Alternatively, Sparrow could lease the asset for a $3,625 annual cost over the five-year period. If Sparrow is in the 21% tax bracket, would you recommend that Sparrow buy or lease the asset? In your calculations, assume that 10% is an appropriate discount factor.

Answer 1

Net advantage of leasing is the NPV of the lease relative to the purchase.

This is calculated by calculating the present value of the advantage each year.

Advantage each year = Cash flow with leasing - cash flow with buying.

Buying :

Cash outflow in year 0 = cost of equipment.

Cash inflow in each year = depreciation for the year * tax rate (The depreciation is a tax-deductible expense, and hence provides a depreciation tax shield. This is treated as a cash inflow).

Leasing :

Net cash outflow with leasing = lease payment * (1 - tax rate) = $3,625 * (1 - 21%) = $2,863.75

NPV of leasing vs buying

Advantage each year = Cash flow with leasing - cash flow with buying.

Present value factor (discount factor) each year = 1 / (1 + discount rate)^year.

Discount rate = after-tax cost of borrowing = interest rate on borrowing * (1 - tax rate) = 10% * (1 - 21%) = 7.9%.

Net Advantage of leasing each year = advantage amount * discount factor.

NPV of the lease relative to the purchase = -$9,413.11

As the net advantage of leasing is negative, it is recommended to buy the asset

| А в Discount Factor @ 1 Year Buying Leasing Advantage 7.9% NAL 2 0 $ (15,000.00) $ 15,000.00 $ 1.00 $ 15,000.00 3 1 $ 4,999.50 $ (2,863.75) $ (7,863.25) $ 0.93 $ (7,287.53) 2 $ 6,667.50 $ (2,863.75) $ (9,531.25) $ 0.86 $ (8,186.66) 3 $ 2,221.50 $ (2,863.75) $ (5,085.25) $ 0.80 $ (4,048.07) 4 $ 1,111.50 $ (2,863.75) $ (3,975.25) $ 0.74 $ (2,932.77) 5 $ - $ (2,863.75) $ (2,863.75) $ 0.68 $ (1,958.07) TOTAL ($9,413.11)

A B 1 Year Leasing 20 Buying - 15000 =15000*33.33% =15000*44.45% =15000*14.81% =15000*7.41% =-3625*(1-21%) =-3625*(1-21%) =-3625*(1-21%) =-3625*(1-21%) =-3625*(1-21%) Advantage =C2-B2 =C3-B3 =C4-B4 =C5-B5 =C6-B6 =C7-B7 Discount Factor @ 7.9% =1/(1+7.9%)^A2 =1/(1+7.9%)^A3 =1/(1+7.9%)^A4 =1/(1+7.9%)^A5 =1/(1+7.9%)^A6 =1/(1+7.9%)^A7 TOTAL NAL =D2*E2 =D3*E3 =D4*E4 =D5*E5 =D6*E6 =D7*E7 =SUM(F2:F7)