Question

Your firm is considering leasing a new computer. The lease lasts for 8 years. The lease calls for 8 payments of $8,000 per year with the first payment occurring immediately. The computer would cost $50,000 to buy and would be straight-line depreciated to a zero salvage value over 8 years. The actual salvage value is negligible because of technological obsolescence. The firm can borrow at a rate of 5%. The corporate tax rate is 34%. What is the NPV of the lease relative to the purchase?

-$2,325

$1,639

-$1,742

-$2,537

-$1,492

Answer 1

Tax Rate	34%
Rate of Interest for Borrowing	5%
Effective Discounting rate	3.3%
Year	0	1	2	3	4	5	6	7	8
Lease Payments (at Start of Year)	8000	8000	8000	8000	8000	8000	8000	8000
Tax Savings on Lease Payments	2720	2720	2720	2720	2720	2720	2720	2720
Effective Lease Cash Outflows	5280	5280	5280	5280	5280	5280	5280	5280
Present Value of Lease Outflows	5280	5111	4948	4790	4637	4489	4345	4207
Total PV for Lease Outflows	37807
Loan Book Value	50000	44764	39266	33493	27432	21067	14385	7368	0
Loan repayment amount (at year end)		7736	7736	7736	7736	7736	7736	7736	7736
Depreciation for the year		6250	6250	6250	6250	6250	6250	6250	6250
Interest expense		2500	2238	1963	1675	1372	1053	719	368
Tax Savings on Depreciation and Interest Expense		2975	2886	2793	2694	2591	2483	2370	2250
Net Cash Outflows		4761	4850	4944	5042	5145	5253	5367	5486
PV of Net Cash Outflows		4609	4545	4485	4428	4374	4323	4276	4231
Total PV of Net Cash Outflows for Buy	35270
NPV of Lease relative to Purchase	-2537

Formulae Used:

Effective Discounting rate = Rate of Borrowing*(1-tax rate)

Tax Savings on Lease Payments = Lease payments*(tax rate)

Effective Lease Outflows = Lease payments*(1-tax rate)

Present Value of Lease Outflows = Effective Lease Outflows / (1+ Effective Discounting rate)^(n) ; n = 0 to 7

Loan repayment amount = (50000×(5%)×(1 + 5%)^(8))/((1 + 5%)^(8) - 1)

Depreciation = 50000/8

Interest expense at Year 'n' = (Loan book value at year 'n-1' )* 5% ; n = 1 to 8

Loan Book Value at year 'n' = (Loan book value at year 'n-1' ) - (Loan repayment amount at Year 'n' + Interest expense at Year 'n') ; n = 1 to 8

Tax Savings on Depreciation and Interest Expense = (Depreciation for the year + Interest Expense)*(34%)

Net Cash Out Flows = Loan repayment amount - Tax Savings on Depreciation and Interest Expense

PV of Net Cash Flows = (Net Cash Out Flows)/(1+ Effective Discounting rate)^(n) ; n = 1 to 8

NPV of Lease relative to Purchase = Total PV of Net Cash Outflows for Buy - Total PV for Lease Outflows