Question

You work for a nuclear research laboratory that is contemplating leasing a diagnostic scanner (leasing is a common practice with expensive, high-tech equipment). The scanner costs $7,200,000, Because of radiation contamination, it will actually be completely valueless in four years. You can lease it for $2,115,000 per year for four years. Assume that the tax rate is 24 percent. You can borrow at 8 percent before taxes. Assume that the scanner will be depreciated as three-year property under the MACRS depreciation. What is the NAL of the lease? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) NAL

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 * 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) = $2,115,000 * (1 - 24%) = $1,607,400

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) = 8% * (1 - 24%) = 6.08%.

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

NPV of the lease relative to the purchase = $99,368.36

NAL = $99,368.36

A B C D E F Discount Factor @ 1 Year Buying Leasing Advantage 6.08% NAL 2 0 ($7,200,000) $7,200,000 1.0000 $7,200,000 1 $575,942 ($1,607,400) ($2,183,342) 0.9427 ($2,058,204) 2 $768,096 ($1,607,400) ($2,375,496) 0.8887 ($2,110,995) 3 $255,917 ($1,607,400) ($1,863,317) 0.8377 ($1,560,940) 4 $128,045 ($1,607,400) ($1,735,445) 0.7897 ($1,370,493) TOTAL $99,368.36

3 1 1 Year Buying 20 -7200000 =7200000*33.33%*24% =7200000*44.45%*24% =7200000*14.81%*24% =7200000*7.41%*24% Leasing Advantage Discount Factor @ 6.08% NAL =C2-B2 =1/1.0608^A2 =D2*E2 =-2115000*(1-24%) =C3-B3 =1/1.0608^A3 =D3*E3 =-2115000*(1-24%) =C4-B4 =1/1.0608^44 =D4*E4 --2115000*(1-24%) =C5-B5 =1/1.0608^A5 =D5*E5 =-2115000*(1-24%) =C6-B6 =1/1.0608^A6 =D6*E6 TOTAL =SUM(F2:F6) N w