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12model 10/6/2009 8:15 1/13/2003 Chapter 12. Spreadsheet Model for Analyzing Unequal Lives and Real Options PROJECTS WITH UNEQUAL LIVES If two mutually exclusive projects have different lives, and if the projects can be repeated, then it is necessary to deal explicitly with those unequal lives. We use the replacement chain (or common life) approach. This procedure compares projects of unequal lives by equalizing their lives by assuming that each project can be repeated as many times as necessary to reach a common life span. The NPVs over this life span are then compared, and the project with the higher common life NPV is chosen. To illustrate, suppose a firm is considering two mutually exclusive projects, either a conveyor system (Project C) or a fleet of forklift trucks (Project F) for moving materials. The firm's cost of capital is 12%. The cash flow time lines are shown below, along with the NPV and IRR for each project. Project C WACC: 12% End of Period: 0 1 2 3 4 5 6 (\$40,000) \$8,000 \$14,000 \$13,000 \$12,000 \$11,000 \$10,000 NPV \$6,491 IRR 17.47% Project F End of Period: 0 1 2 3 (\$20,000) \$7,000 \$13,000 \$12,000 NPV \$5,155 IRR 25.20% Initially, it would appear that Project C is the better investment, based upon its higher NPV. However, if the firm chooses Projec F, it would have the opportunity to make the same investment three years from now. Therefore, we must reevaluate Project F using an extended common life of 6 years. The time lines are shown below. Note that only F's is changed. Project C End of Period: 0 1 2 3 4 5 6 (\$40,000) \$8,000 \$14,000 \$13,000 \$12,000 \$11,000 \$10,000 NPV \$6,491 Use function wizard, IRR 17.47% Financial, NPV and IRR. Recall that the cost must Project F be input separately for NPV because Excel 0 1 2 3 4 5 6 assumes that CFs occur at (\$20,000) \$7,000 \$13,000 \$12,000 end of periods. (\$20,000) \$7,000 \$13,000 \$12,000 (\$20,000) \$7,000 \$13,000 (\$8,000) \$7,000 \$13,000 \$12,000 NPV \$8,824 IRR 25.20% A B C D E F G H I 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

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On the basis of this extended analysis, it is clear that Project F is the better of the two investments (with either the NPV and IRR methods). In earlier editions of the book we used another method to deal with unequal lives, the Equivalent Annual Annuity method. We no longer discuss it for four reasons: (1) It leads to the same decisions as the replacement chain method, (2) the replacement chain method is easier to understand and explain, (3) the availability of spreadsheets makes it easy to implement the replacement chain approach, and (4) setting up the replacement chain model in a spreadsheet makes it easy to build in inflation. INTRODUCTION TO REAL OPTIONS Traditionally, capital budgeting has been handled in a straightforward, but in some cases incomplete and inaccurate, manner. Its NPV under the most likely set of conditions is calculated, and then a project is accepted. However, larger, more complex projects, often contain one or more "embedded options" whose existence can have a dramatic effect on a project's true value. In the following sections, we examine four types of real options: abandonment, timing, growth, and flexibility.
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