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33#
发表于 2012-3-29 11:13
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Two projects being considered by a firm are mutually exclusive and have the following projected cash flows:
Year | Project 1 Cash Flow | Project 2 Cash Flow | 0 | −$4.0 | ? | 1 | $3.0 | $1.7 | 2 | $5.0 | $3.2 | 3 | $2.0 | $5.8 | [/table]
The crossover rate of the two projects’ NPV profiles is 9%. What is the initial cash flow for Project 2? [table]
A)
−$4.51.
The crossover rate is the rate at which the NPV for two projects is the same. That is, it is the rate at which the two NPV profiles cross. At a discount rate of 9%, the NPV of Project 1 is: CF0 = –4; CF1 = 3; CF2 = 5; CF3 = 2; I = 9%; CPT → NPV = $4.51. Now perform the same calculations except that we need to set the unknown CF0 = 0. The remaining entries are: CF1 = 1.7; CF2 = 3.2; CF3 = 5.8; I = 9%; CPT → NPV = $8.73. Since by definition the crossover rate produces the same NPV for both projects, we know that both projects should have an NPV = $4.51. Since the NPV of Project 2 (with CF0 = 0) is $8.73, the unknown cash flow must be a large enough negative amount to reduce the NPV for Project 2 from $8.73 to $4.51. Thus the unknown initial cash flow for Project 2 is determined as $4.51 = $8.73 + CF0, or CF0 = −$4.22. |
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