Your firm is considering leasing a new radiographic device. The lease lasts for

Question

Your firm is considering leasing a new radiographic device. The lease lasts for three years. The lease calls for four payments of $25,000 per year with the first payment occurring immediately. The computer would cost $140,000 to buy and would be straight-line depreciated to a zero salvage value over three years. The actual salvage value is negligible because of technological obsolescence. The firm can borrow at a rate of 12%. The corporate tax rate is 40%.
a. What is the NPV of the lease relative to the purchase?
b. What would the after-tax cash flow in year three be if the asset had a residual value of $1,000 (ignoring any possible risk differences)?

Explanation / Answer

a) After Cash flow Leasing = -25000(1-0.40) = -15000

NPV = (– initial investment + Cash flow /(1+r)^n)

NPV(Leasing) = - 25000 + 15000(1.12)^1 +15000(1.12)^2 +15000(1.12)^3 = 31690

NPV = (– initial investment + Cash flow /(1+r)^n)

After Cash flow Purchasing

Depreciation = cost / no of years = 140000/3 = 46667

Tax 40 % = 46667 (1-.40) = 28000

So Depreciation ( Add back after tax) = 46667 +28000 = 74667

NPV(Purchasing ) = - 140000 + 74667(1.12)^1 +74667(1.12)^2 + 74667(1.12)^3 = 142191

b) Depreciation = (cost – salvage value) / no of years

= (140000-1000)/3 = 43333

So after tax cash flow = 53333(1-.40) +43333 = 75333

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