A firm is considering an investment in a new machine with a price of $18 million

Question

A firm is considering an investment in a new machine with a price of $18 million to replace its existing machine. The current machine has a book value of $6 million and a market value of $4.5 million. The new machine is expected to have a four-year life, and the old machine has four years left in which it can be used. If the firm replaces the old machine with the new machine, it expects to save $6.7 million in operating costs each year over the next four years. Both machines will have no salvage value in four years. If the firm purchases the new machine, it will also need an investment of $250,000 in net working capital. The required return on the investment is 10 percent, and the tax rate is 39 percent. What is the NPV and the IRR of the decision to replace the old machine.

Explanation / Answer

Initial Investment = 18000000 - 4500000 + 250000 = 13750000

Tax savng on old machine sold = (6-4.5)*39% = 0.585 Million = 585000

Annual after tax Operating cost saving = Operating cost saving*(1-tax rate) + Increase in Depreciation*tax rate

Annual after tax Operating cost saving = 6.7*(1-39%) + (18-6)/4 *39%

Annual after tax Operating cost saving = 5.257 Million

Annual after tax Operating cost saving = $ 5,257,000

Working capital realised at the end = 250000

Cash Flow:

Year 0 = - 13750000

Year1 = 5,257,000 + 585000 = $ 5,842,000

Year 2 = 5,257,000

Year 3 = 5,257,000

Year 4 = 5,257,000 + 250000 = $ 5,507,000

NPV = - 13750000 + 5842000/1.1 + 5257000/1.1^2 + 5257000/1.1^3 + 5507000/1.1^4

NPV = $ 3,616,554.20

At IRR NPV = 0

0 = - 13750000 + 5842000/(1+r) + 5257000/(1+r)^2 + 5257000/(1+r)^3 + 5507000/(1+r)^4

13750000 = 5842000/(1+r) + 5257000/(1+r)^2 + 5257000/(1+r)^3 + 5507000/(1+r)^4

By solving above equation we get

IRR = 21.81%

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