Chapter 9

Chapter 9 - Chapter 9 Project Analysis 1 Plan of the...

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1 Chapter 9 Project Analysis

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2 Plan of the lecture Sensitivity analysis Scenario analysis Simulation analysis Break even analysis Operating leverage analysis Real options and the value of flexibility
3 Some “what if” questions Chapter 9 extends the ideas and techniques in Chapters 7 and 8 to a more realistic business setting In particular, since the future is risky , our estimates of a project’s future cash flows will be uncertain and are subject to errors . As a result, we need methods to deal with project uncertainty

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4 Sensitivity analysis This method analyzes the effects of changes in variables (e.g. sales, variable costs etc.), one at a time , on the NPV of a project This approach will reveal to you the most and least critical variables in your NPV analysis. Consider the following example
5 Sensitivity analysis Example : Year 0 Year 1-3 Investment \$2,400 Sales \$6,000 - Variable costs 4,200 ( 70% of sales ) - Depreciation ( straight line ) 800 Pretax profit 1,000 Taxes @ 35% 350 Net profit 650 Cash flow from operations (CFO) \$1,450 800 \$ 3 400 , 2 \$ Years Investment = = Method 2 = depreciation + net profit

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6 Sensitivity analysis Example (continued) : The NPV of this project is: 206 , 1 \$ 400 , 2 \$ 4869 . 2 450 , 1 \$ 400 , 2 \$ ] ) 1 . 1 ( 1 . 0 1 1 . 0 1 [ 450 , 1 \$ NPV 3 = - × = - - × = An annual opportunity cost of capital of 10%
7 Sensitivity analysis Example (continued) : Given the changes of variables below, one at a time , we recalculate the NPV of the project Variable: Normal Good Bad Investment \$2,400 \$1,800 \$3,000 Sales \$6,000 \$9,000 \$3,000 Variable costs as a % of sales 70% 60% 80%

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8 Sensitivity analysis Example (continued) : For instance, if sales were \$3,000, instead of \$6,000, the NPV would be 83 . 248 \$ 400 , 2 \$ 4869 . 2 865 \$ 400 , 2 \$ ] ) 1 . 1 ( 1 . 0 1 1 . 0 1 [ 865 \$ NPV \$865, \$800 \$65 CFO \$65, profit net \$35, 35% @ taxes , 100 \$ 800 \$ 100 , \$2 \$3,000 profit pretax , 800 \$ 3 \$2,400 on depreciati , 100 , 2 \$ % 70 000 , 3 \$ costs Variable 3 - = - × = - - × = = + = = = = - - = = = = × =
9 Sensitivity analysis Example (continued) : After all the recalculations, we will have the following table of recalculated NPV Variable: Normal Good Bad Investment \$1,206 \$1,632 \$780 Sales \$1,206 \$2,661 (\$249) Variable costs as a % of sales \$1,206 \$2,176 \$236 NPV Be careful: when investment changes, depreciation also changes!

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10 Sensitivity analysis Example (continued) : We then measure the range of NPV changes for each of the variables Range = maximum NPV - minimum NPV Investment : range = \$1,632 - \$780 = \$852 Sales : range = \$2,661 - (-\$249) = \$2,910 Variable costs : range = \$2,176 - \$236 = \$1,940
11 Sensitivity analysis Example (continued) : The larger the range, the more critical this variable is; and vice versa In this example, sales is the most critical variable, whereas investment is the least critical variable So you might want to collect more information on sales in order to resolve some of the uncertainty regarding this variable

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12 Sensitivity analysis Drawbacks of the sensitivity analysis Variables are often related , so it may be very hard to separate the effects of one variable from the effects of another For example, if the number of trucks ( investment ) goes up, you need to hire more drivers, so the pay checks ( variable costs ) also increase Conclusion: you can NOT push the one at a time sensitivity analysis too far
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