Please provide step by step problem soliving as well as formula used to arrive a
ID: 2732484 • Letter: P
Question
Please provide step by step problem soliving as well as formula used to arrive at answer.
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
Answer to Part a)
After tax cost of debt: 0.12 * ( 1 - 0.40) = 0.072, or 7.2%
"Value" of the lease:
NPV of the lease pmts = 25,000 + (25,000 / 1.072) + (25,000 / 1.072^2) + (25,000 / 1.072^3)
= $90,368.90< PV of the lease pmts., e.g. today's value of the future cash Outflows
change to a negative number to reflect Outflow
($90,368.90)
NPV of purchase...
depreciation per year: 140,000 / 3 = 46,666.67
tax shield arising from depreciation expense: 46,666.67 * 0.40 = $18,666.67
NPV: (140,000) + (18,666.67 / 1.072) + (18,666.67 / .072^2) + (18,666.67^3)
= (140,000) + 48,808.79
= ($91,191.20)
Answer to Part b.
The after-tax cash flow from leasing relative to the after-tax cash flow from purchasing in year 3 will be $14,000.
Cash flow from leasing in year 3 $25,000
Less: Tax @ 40% $10,000
After-tax cash flow from leasing in year 3 $15,000
After-tax cash flow from purchasing in year 3 $ 1000
Less: After-tax cash flow from leasing in year 3 $15,000
Net after-tax cash flow from leasing relative to purchasing in year 3 ($ 14,000)
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