Question

Hudson Bay Corporation is considering leasing a new equipment. The lease lasts for 5 years. The lease calls for 5 payments of $42,000 per year with the first payment occurring immediately. The equipment would cost $195,000 to buy and would be straight-line depreciated to a zero salvage value over 5 years. The actual salvage value is negligible because of technological obsolescence. The firm can borrow at a rate of 6%. The corporate tax rate is 25%. What is the NPV of the lease relative to the purchase? $7,690.67 -$12,815.60 $23,546.73 -$18,944.26 $15,840.42

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 = annual depreciation * tax rate (The depreciation is a tax-deductible expense, and hence provides a depreciation tax shield. This is treated as a cash inflow).

Annual depreciation tax shield = (cost of equipment / depreciable life) * tax rate = ($195,000 / 5) * 25% = $9,750.

Leasing :

Net cash outflow with leasing = lease payment * (1 - tax rate) = $42,000 * (1 - 25%) = $31,500.

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) = 6% * (1 - 25%) = 4.5%.

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

NPV of the lease relative to the purchase = $7,690.67.

fx =SUM(F2:F7) A B C D Ε F. Discount Factor @ 1 Year Buying Leasing Advantage 4.5% NAL 0 ($195,000) ($31,500) $163,500 1.0000 $163,500 3 1 $9,750 ($31,500) ($41,250) 0.9569 ($39,474) 2 $9,750 ($31,500) ($41,250) 0.9157 ($37,774) 5 3 $9,750 ($31,500) ($41,250) 0.8763 ($36,147) $9,750 ($31,500) ($41,250) 0.8386 ($34,591) $9,750 ($9,750) 0.8025 $7,824) TOTAL $7,690.67

А в F 1 Year Buying Leasing Advantage Discount Factor @ 4.5% NAL 20 -195000 =-42000*(1-25%) =C2-B2 =1/1.045^A2 =D2*E2 3 1 =(195000/5)*25% --42000*(1-25%) =C3-B3 =1/1.045^A3 =D3*E3 42 =(195000/5)*25% =-42000*(1-25%) =C4-B4 =1/1.045^A4 =D4*14 =(195000/5)*25% --42000*(1-25%) =C5-B5 =1/1.0454A5 =D5 E5 64 =(195000/5) *25% --42000*(1-25%) =C6-B6 =1/1.0454A6 =D6*E6 75 =(195000/5)*25% =C7-B7 =1/1.045^A7 =D7*E7 TOTAL =SUM(F2:F7)