Corporate Finance (Book 1)(1).pdf

The initial working capital is 20000 and will remain

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The initial working capital is €20,000 and will remain unchanged over the life of the project. If tax rate is 34%, initial investment is €90,000 and cost of capital is 20%, is this project worth undertaking? Problem 160
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Copyright © 2018 Terence Tse Topic 6: Free Cash Flows Equivalent Annual Cost 161
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Copyright © 2018 Terence Tse When comparing two projects with unequal lifespan, you can use equivalent annual cost Use of equivalent annual cost Aspect Description Suppose a firm must choose between 2 machines, A and B. Both machines can do the same job, but they have different operating costs. They also have different operating lives A simple PV calculation suggests taking the machine with the costs that have lowest PV. However, this might be a mistake because machine A, which has a lower cost, may need to be replaced before machine B So, how do you solve this problem? The answer is to transform an investment today into an equivalent stream from cash flows hence the name equivalent annual cost Equivalent annual cost is therefore the cost per year of owning and operating an asset over its entire lifespan The formula for calculating equivalent annual cost: ?𝑉 ?? ?? ????𝑖?𝑦 = ? × 1 ? 1 ?(1 + ?) ? ???𝑖?????? ?????? ???? = ?𝑉 ?? ????? ????𝑖?𝑦 ?????? 162
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Copyright © 2018 Terence Tse When comparing two projects with unequal lifespan, you can use equivalent annual cost (cont’d) Costs (£) Machine Year 0 Year 1 Year 2 Year 3 PV at 10% A +15,000 +4,000 +4,000 +4,000 24,947 B +10,000 +6,000 +6,000 20,413 Example Consider the following two machines that can do exactly the same job. Which one is the cheapest to own? It is important to remember that the investment in year 0 is positive because you are dealing with cost only We cannot simply compare these 2 figures because they have different longevity 163
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Copyright © 2018 Terence Tse When comparing two projects with unequal lifespan, you can use equivalent annual cost (cont’d) Costs (£) Machine Year 0 Year 1 Year 2 Year 3 PV at 10% Machine A 15,000 4,000 4,000 4,000 24,947 Equivalent annual cost 10,800 10,800 10,800 24,947 Machine A is better than machine B because it costs less on a per year basis to own and operate Costs (£) Machine Year 0 Year 1 Year 2 Year 3 PV at 10% Machine B 10,000 6,000 6,000 20,413 Equivalent annual cost 12,223 12,223 20,413 *The annuity factor in this case is 2.49 *The annuity factor in this case is 1.67 164
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