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Unformatted text preview: Question on Calculating NPV and IRR for a Replacement: A firm is considering an investment in a new machine with a price of $12 million to replace its existing machine. The current machine has a book value of $4 million and a market value of $3 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$4.5 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 current market rate for a similar project (same risk) is 10%, and the tax rate is 39%. What are the Net Present Value (NPV) and Internal Rate of Return (IRR) of the decision to replace the old machine? Solution: Replacement decision analysis is the same as the analysis of two competing projects, in this case, keep the current equipment, or purchase the new equipment. We will consider the purchase of the new machine first. Purchase new machine: The initial cash outlay for the new machine is the cost of the new machine, plus the increased net working capital. So, the initial cash outlay will be: Purchase new machine Net working capital Total –$12,000,000 –250,000 –$12,250,000 Next, we can calculate the operating cash flow created if the company purchases the new machine. The saved operating expense is an incremental cash flow. Additionally, the reduced operating expense is a cash inflow, so it should be treated as such in the income statement. The savings resulted in using the new machine is $4.5 million that we get to keep. This is one way our cash flow is going to be affected. Another way the cash flow is going to be affected each year during the life of the new machine is going to be working through the depreciation of the new machine. Assuming straight line depreciation, we get to deduct $12/4=$3 million from our Net Income, which will provide us with some savings in our tax obligation. The pro forma income statement, and adding depreciation to net income, the operating cash flow created by purchasing the new machine each year will be: Operating expense $4,500,000 Depreciation EBT $1,500,000 Taxes 585,000 Net income $915,000 OCF 3,000,000 $3,915,000 So in each year for the coming four years this will be the incremental cash flow of the company. This is the same thing as saying “the cash flow of the project of buying a new machine is $3,915,000 for four years.” Just like with most projects we assume the recovery of the net working capital at the end of the four years. So, the cash outflow of $250,000 in the initial year of the project will be an inflow in the last year of the project. Then, considering all these ingredients, the NPV of purchasing the new machine, including the recovery of the net working capital, is: NPV=–$12,250,000+ $3,915,000/(1+.10)+ $3,915,000/(1+.10)2 + $3,915,000/(1+.10)3 + $3,915,000/(1+.10)4 + $250,000 / 1.104 NPV = $330,776.59 **Note that we would have added the salvage value (after taking care of its tax obligation) to the last term of the NPV calculation, if the machine had any salvage value at the end of its lifetime. Now we can calculate the IRR is: 0 =–$12,250,000+ $3,915,000/(1+IRR)+ $3,915,000/(1+IRR)2 + $3,915,000/(1+IRR)3 + $3,915,000/(1+IRR)4 + $250,000 / (1+IRR)4 Using a spreadsheet or a calculator, we find the IRR (rounded) is: IRR = 11.23% Now we can calculate the decision to keep the old machine: Keep old machine: The initial cash outlay for the old machine is the market value of the old machine, including any potential tax consequence. The decision to keep the old machine has an opportunity cost, namely, the company could sell the old machine. Also, if the company sells the old machine at its current value, it will receive a tax benefit. Both of these cash flows need to be included in the analysis. So, the initial cash flow of keeping the old machine will be: Keep machine –$3,000,000 Taxes –390,000 Total –$3,390,000 $3,000,000 is the opportunity cost of forgone sale price of the old machine. Since the market value is less than the book value of the old machine we would incur a loss of $1,000,000. Therefore our tax obligation would be reduced by $390,000 if we sold the machine now. Next, we can calculate the operating cash flow created if the company keeps the old machine. There are no incremental cash flows from keeping the old machine, but we need to account for the cash flow effects of depreciation. The book value of the old machine is $4,000,000. It will be given as $0 at the end of the 4 years. Then using a straight line depreciaton, there is a $1,000,000 depreciation entering our books every year when we keep the old machine. The income statement, adding depreciation to net income to calculate the operating cash flow will be: Depreciation $1,000,000 EBT Taxes –390,000 Net income –$610,000 OCF –$1,000,000 $390,000 So, the NPV of the decision to keep the old machine will be: NPV = –$3,390,000 + $390,000/(1+.10)+ $390,000/(1+.10)2 + $390,000/(1+.10)3 + $390,000/(1+.10)4 + NPV = –$2,153,752.48 That is, by keeping the old machine we forego an initial cash flow of $3,390,000. This is the opportunity cost of keeping the old machine. But by keeping it we are able to enter it as a depreciation item in our books which helps us reduce our tax obligation by $390,000 each of the four years in which it is still operational. And the IRR is: 0 = –$3,390,000 + $390,000/(1+IRR)+ $390,000/(1+IRR)2 + $390,000/(1+IRR)3 + $390,000/(1+IRR)4 + Using a spreadsheet or calculator, we find the IRR (rounded) is: IRR = –25.15% There is another way to analyze a replacement decision that is often used. It is an incremental cash flow analysis of the change in cash flows from the existing machine to the new machine, assuming the new machine is purchased. In this type of analysis, the initial cash outlay would be the cost of the new machine, the increased NWC, and the cash inflow (including any applicable taxes) of selling the old machine. In this case, the initial cash flow under this method would be: Purchase new machine –$12,000,000 Net working capital –250,000 Sell old machine 3,000,000 Taxes on old machine Total 390,000 –$8,860,000 The cash flows from purchasing the new machine would be the saved operating expenses. We would also need to include the change in depreciation. The old machine has a depreciation of $1 million per year, and the new machine has a depreciation of $3 million per year, so the increased depreciation will be $2 million per year. The pro forma income statement and operating cash flow under this approach will be: Operating expense savings $4,500,000 Depreciation 2,000,000 EBT $2,500,000 Taxes Net income $1,525,000 OCF $3,525,000 975,000 The NPV under this method is: NPV = –$8,860,000 + $3,525,000(1/1.10+1/1.102+1/1.103+ 1/1.104 )+$250,000 / 1.104 NPV = $2,484,529.06 And the IRR is: 0 = –$8,860,000 + $3,525,000(1/IRR+1/IRR2+1/IRR3+ 1/IRR4) + $250,000 / (1 + IRR)4 Using a spreadsheet or calculator, we find the IRR is: IRR = 22.26% So, this analysis still tells us the company should purchase the new machine. This is really the same type of analysis we originally did. Consider this: Subtract the NPV of the decision to keep the old machine from the NPV of the decision to purchase the new machine. You will get: Differential NPV = $330,776.59 – (–$2,153,752.48) = $2,484,529.06 This is the exact same NPV we calculated when using the second analysis method. ...
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This note was uploaded on 12/05/2011 for the course ENGINEERIN 111 taught by Professor Melihabulu-taciroglu during the Fall '11 term at UCLA.
- Fall '11