Chapter 7 Solutions

Chapter 7 Solutions - MIME 310 ENGINEERING ECONOMY...

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M I M E 3 1 0 E N G I N E E R I N G E C O N O M Y SOLUTIONS TO PROBLEM SET #7 – INCOME TAX CONSIDERATIONS I NTRODUCTORY COMMENT – Most problems involving taxation can be solved by either one of two approaches, i.e., using a period-by-period approach, or with tax factors. In the period-by- period approach, after-tax cash flows are determined for every period of the project's life, using revenues, operating expenses, tax payments and capital expenditures. Appropriate tax regula- tions are applied for the purpose of determining tax payments. Then, the project's profitability and/or whatever other required indicators are determined from the profile of cash flows. Spreadsheet software is most suited to this approach. In the second approach, tax factors are applied to convert the project's before-tax estimates to after-tax values. The desired indicators can then be determined from these after-tax values in combination with appropriate time value factors. In particular circumstances, tax factors often provide a quicker and much simpler approach to solving a problem. However, caution should taken with this approach, because tax factors contain particular built-in assumptions regarding the timing of tax savings. Therefore, they should only be used when these assumptions are correct and/or reasonable given the situa- tion. In cases when the assumptions are inappropriate, the longer period-by-period approach becomes necessary. Only one approach should be used at a time, otherwise, double-counting may occur. For instance, tax payments or savings should be based on the before-tax components of a project, and not on the after-tax components derived from the application of tax factors. As well, the period-by-period approach may still necessitate the use of tax factors under particular circum- stances. In the Canadian tax system for instance, the capital tax factor is a convenient way of handling tax credits that extend beyond a project's life when assets are depreciated by the declining-balance method. With practice, the problem-solver will learn to recognize the more suitable approach. 1. i) Using the estimates as given, i.e. on a before-tax basis, the rate of return is the discount rate (r) that yields a net present value of zero. NPV = -56 000 + 13 500 (P/A,r,7) = 0 Thus, (P/A,r,7) = 56 000 / 13 500 = 4.1481 From the compound interest factor tables, (P/A,15%,7) = 4.1604 and (P/A,16%,7) = 4.0386 By linear interpolation, r = 15 + (4.1604 - 4.1481) / (4.1604 - 4.0386) = 15.1% A financial calculator yields a value of 15.10%. 50
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The before-tax rate of return is 15.1%. ii) The tax factor approach is used here. The assumption that any tax allowances exceeding the annual savings can be applied against other corporate income is compatible with the use of the Capital Tax Factor. OTF = 1 - t = 1 - 0.45 = 0.55
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This note was uploaded on 04/25/2010 for the course MIME 310 taught by Professor Bilido during the Winter '08 term at McGill.

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Chapter 7 Solutions - MIME 310 ENGINEERING ECONOMY...

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