Question

Your firm is considering leasing a new computer. The lease lasts for 4 years. The lease calls for 5 payments of $450 per year with the first payment occurring immediately. The computer would cost $5,900 to buy and would be depreciated using the straight-line method to zero salvage over 4 years. The firm can borrow at a rate of 5%. The corporate tax rate is 20%. What is the NPV of the lease?

Answer 1

Your firm is considering leasing a new computer. The lease lasts for 4 years. The lease calls for 5 payments of $450 per year with the first payment occurring immediately. The computer would cost $5,900 to buy and would be depreciated using the straight-line method to zero salvage over 4 years. The firm can borrow at a rate of 5%. The corporate tax rate is 20%.

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What is the NPV of the lease?

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Net Present value of lease payment calculation

For calculating Net present value use the formula of present value of annuity due.

*Here we use the PV annuity due formula, because the payment are made beginning of each month.

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PV of annuity due = The present value of an annuity due is the current worth of a series of cash flows from an annuity due that begins immediately. The payments from the annuity are distributed at the beginning of each period

The formula for finding the net present value of future lease payments on a contract is same as PV of annuity formula:

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PV of annuity = C * ( ( ( 1 - (1 / (1 + r))^n) ) / r ) * ( 1 + r )

Where,

PV of annuity = Present value of lease payment

C = Annual due payment = $450

R = discount rate = 5%

N = number of period in payment = 5

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Net Present value of lease payment = 450 * ( ( 1 - (1 / (1 + 5%))^5) / 5% ) * ( 1 + 5% )

Net Present value of lease payment = 450 * (( 1 - 0.7835) / 5% ) * 1.05

Net Present value of lease payment = 450 * (0.2164738 / 5%) * 1.05

Net Present value of lease payment = 450 * 4.327 * 1.05

Net Present value of lease payment = 2045.68