Sensitivity to Input Conditions
Sensitivity to Input Conditions
Because it deals with the future, capital budgeting is based on many assumptions or expectations that may prove wrong. Analysts should therefore ask themselves what might possibly go wrong—and then perform
a sensitivity analysis to evaluate its impacts on the expected payoffs.
A great advantage of spreadsheets is that once they have been created, the effects of variations in input variables can be studied by editing the spreadsheet or by creating auxiliary tables. The examples that follow illustrate how to perform sensitivity analysis with one- and two-variable input tables.
Effect of Changes in the Year-End Benefits on Financial Payoffs The year-end benefits are forecasts, and even the best forecasts are wrong. The following example exam-
ines the sensitivity of the financial payoffs to changes in the year-end benefits.
Example 12.5: Use the spreadsheet of Figure 12-9 to evaluate the impacts of changes in the annual year-end benefits from –20% to +20%. Show the results as a one-variable input table with values for the NPV, IRR, and MIRR at the end of five years and the years to break even for the changes in annual benefits.
Solution: Figure 12-10 shows the solution. Charts have been added that show how the changes in annual benefits affect the net present value and years to break even.
The one-variable input table in Figure 12-10 is created by the following entries in Row 23. (The height of Row 23 has been reduced, and the entries hidden by custom formatting them with three semicolons.)
Cell B23: =B10 Cell C23: =G17 Cell D23: =G18 Cell E23: =G19 Cell F23: =B20 These entries link the table in Rows 21 to 32 with the spreadsheet model above. The next step is to high-
light the Range B23:F32 and access the Table dialog box shown in Figure 12-11 from the Data drop-down menu. After making the entries shown in Figure 12-11, click OK or press Enter to create the table of results. Format the values as shown in Figure 12-10.
Example 12.6: Use the spreadsheet of Figure 12-9 to create two-variable input tables for showing sensitivity of the NPV at the end of five years and the years to break even to changes in the annual benefits from –20% to +20% and values for the discount rate from 10 percent to 18 percent.
Solution: Figure 12-12 shows the solution. The entry in Cell B23 is =G17, and the entry in Cell B31is =B20. These entries link the first table to the NPV at the end of five years and to the years to break even in the body of the spreadsheet. To create the first table, highlight the Range B23:G28 and make the entries shown in Figure 12-13 in the “Table” dialog box. Repeat the procedure to create the second table.
(Continued)
Capital Budgeting: The Basics ❧ 381
Figure12-10
Impacts of Changes in Annual Year-End Benefits on Financial Measures of Success
1 Example 12-5: CONSOLIDATED ENTERPRISES
2 Equipment cost
Depreciation Method: Straight Line
3 Salvage value
4 Life, years
5 Discount rate
6 Reinvest rate
7 Income tax rate
8 Year 0 1 2 3 4 5 9 Projected year-end annual benefits
45,000 $ 30,000 10 Increase in projected benefits
11 Year-end annual benefit
49,500 $ 43,000 13 Annual depreciation
12 Before-tax cash flow
18,000 $ 18,000 14 Taxable income
16 After-tax cash flow
17 Net present value
$ 35,599 18 Internal rate of return
27.82% 19 Modified internal rate of return
21.16% 20 Break-even point, years
3.25 SENSITIVITY OF FINANCIAL PAYOFFS TO CHANGE IN THE
21 YEAR-END ANNUAL BENEFITS
Change in
NPV at
IRR at End
MIRR at
Annual
End of Five
of Five
End of Five
Years to
Break Even
O BREAK EVEN T 3.6
T END OF 5 $15,000 43
45 NPV A $5,000
10% 20% 48 CHANGE IN ANNUAL BENEFITS
CHANGE IN ANNUAL BENEFITS 49
(Continued)
382 ❧ Corporate Financial Analysis with Microsoft Excel ®
Figure12-11
“Table” Dialog Box with Entry for the One-Variable Input Table of Figure 12-10
Figure12-12
Sensitivity of NPV and Years to Break Even to Changes in Annual Benefits and the Discount Rate
1 Example 12-6: CONSOLIDATED ENTERPRISES
2 Equipment cost
Depreciation Method: Straight Line
3 Salvage value
4 Life, years
5 Discount rate
6 Reinvest rate
7 Income tax rate
0 1 2 3 4 5 9 Projected year-end annual benefits
8 Year
45,000 $ 30,000 10 Increase in projected benefits
11 Year-end annual benefit
12 Before-tax cash flow
45,000 $ 40,000 13 Annual depreciation
18,000 $ 18,000 14 Taxable income
16 After-tax cash flow
17 Net present value
7,709 $ 25,991 18 Internal rate of return
24.21% 19 Modified internal rate of return
19.39% 20 Break-even point, years
SENSITIVITY OF NET PRESENT VALUE AT END OF 5 YEARS TO 21 CHANGES IN THE YEAR-END ANNUAL BENEFITS AND DISCOUNT RATE
Change in Annual 22 Benefits
Discount Rate
SENSITIVITY OF THE NUMBER OF YEARS TO BREAK EVEN TO 29 CHANGES IN THE YEAR-END ANNUAL BENEFITS AND DISCOUNT RATE
Change in Annual 30 Benefits
Discount Rate
4.08 4.32 4.59 4.88 Failed
Capital Budgeting: The Basics ❧ 383
Figure12-13
“Table” Dialog Box with Entries for Creating the First of the Two-Variable Input Tables of Figure 12-12