Changes in Input Conditions for Breaking Even in a Given Time As markets fluctuate more widely and as the product lifetimes become shorter, financial officers become
Changes in Input Conditions for Breaking Even in a Given Time As markets fluctuate more widely and as the product lifetimes become shorter, financial officers become
more concerned with their investments’ breaking even in shorter times. They may therefore limit invest- ments to values that will be returned in a reasonably short time. The following example shows how to use Excel’s Goal Seek or Solver tool to determine the maximum investment that will be returned in a given time.
376 ❧ Corporate Financial Analysis with Microsoft Excel ®
Example 12.2: Given the year-end annual benefits and other conditions in Example 12.1, determine the maximum investment in equipment that Consolidated can afford to make that will paid back in three years.
Solution: Figure 12-5 shows that for the given values of projected cash flows, discount rate, reinvestment rate, and depreciation conditions, the investment must be limited to not more than $84,599 in order to break even in three years.
Figure12-5
Maximum Equipment Cost for Breaking Even in Three Years
1 Example 12-2: CONSOLIDATED ENTERPRISES
2 Equipment cost
Depreciation Method: Straight Line
3 Salvage value
4 Life, years
5 Maximum equipment cost
5 Discount rate
for breaking even in 3 years
6 Reinvest rate
7 Income tax rate
0 1 2 3 4 5 9 Year-end annual benefit
10 Before-tax cash flow
14,920 $ 14,920 12 Taxable income
11 Annual depreciation
14 After-tax cash flow
32,968 $ 33,968 15 Net present value
19,520 $ 37,162 16 Internal rate of return
30.79% 17 Modified internal rate of return
22.61% 18 Break-even point, years
To create this spreadsheet, copy the spreadsheet of Figure 12-3. Select Goal Seek from the Tools menu to open the dialog box shown in Figure 12-6. Enter Cell E15 (the NPV at the end of three years) and a target value of 0. Enter Cell B2 (the equipment cost) as the changing cell. Click on the OK button or press Enter. The result is Figure 12-5. (The break-even chart at the bottom has been omitted.)
Figure12-6
Goal Seek Dialog Box with Entries for Solving Example 12.2
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Capital Budgeting: The Basics ❧ 377
You can also solve this example with Excel’s Solver tool. Figure 12-7 shows the Solver settings with an alternate target of setting Cell B18 (the break-even point in years) equal to 3. The result is the same, because the break-even point is the time for the NPV to equal zero. However, the goal of setting the NPV equal to zero requires fewer calculations and is computationally more efficient and faster.
Figure12-7
Solver Settings to Solve Example 12.3
Satisfying Financial Goals by Increasing Sales There are countless variations of Example 12.3 that might be of interest. For example, a CFO might want
to know the sales level needed to satisfy his or her goal for a specified net present value or rate of return at the end of a given number of years.
Increasing sales is an alternative to reducing investment costs that might be tried in order to reach higher financial goals than possible under the given conditions. The following example shows how to evaluate the increase needed to attain a specific goal.
Example 12.3: Consolidated’s CFO (see preceding example) is concerned about a $100,000 investment’s taking more than three years to break even. If the investment cannot be reduced below $100,000, she wants to know how much the annual benefits would have to increase in order to break even at the end of three years. She plans to use this information to discuss strategies for accomplishing her goal with the company’s marketing division.
Solution: Figure 12-8 is a spreadsheet solution. To create this spreadsheet, copy the previous spreadsheet and insert two new rows, Rows 9 and 10, in Figure 12-8. This will move everything below Row 8 in the previous spreadsheet down two rows.
Copy the values for the projected annual benefits, which will now be in Cells C11:G11, to Cells C9:G9 and label these the projected year-end annual benefits. Use Paste Special/Values to paste the values from Cells C11:G11 rather than paste the entries. Enter a trial value, such as 0.10 (i.e., 10%) in Cell B10 for the
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378 ❧ ® Corporate Financial Analysis with Microsoft Excel
Figure12-8
Increase in Projected Year-End Annual Benefits for Breaking Even by the End of Three Years
1 Example 12-3: CONSOLIDATED ENTERPRISES
2 Equipment cost
Depreciation Method: Straight Line
3 Salvage value
4 Life, years
5 Increase in year-end annual benefits
5 Discount rate
to break even in 3 years
6 Reinvest rate
7 Income tax rate
8 Year 0 1 2 3 4 5 9 Projected year-end annual benefits
10 Yearly increase
52,977 $ 35,318 12 Before-tax cash flow
11 Year-end annual benefit
18,000 $ 18,000 14 Taxable income
13 Annual depreciation
16 After-tax cash flow
38,986 $ 38,391 17 Net present value
23,083 $ 43,022 18 Internal rate of return
30.55% 19 Modified internal rate of return
22.46% 20 Break-even point, years
Key Cell Entry: Cell C11: =C9*(1+$B10), copy to D11:G11 Goal Seek or Solver Settings: Target Cell is E17, to be set equal to 0 by changing Cell B10.
benefit increase. Enter =C9*(1+$B10) in Cell C11 and copy it to D11:G11. Label these the year-end annual benefit. They are the original projected values in Cells C9:G9 increased by the percentage in Cell B10.
Use Excel’s Solver (or Goal Seek) tool with a target of setting Cell E17 (i.e., the NPV at the end of year 3), equal to 0 by changing the percentage value in Cell B10 (i.e., the increase needed in the projected annual benefits).
The results show that the annual benefits must be increased 17.73 percent from their projected values in order for the investment to break even by the end of the third year.
Should You Use Goal Seek or Solver? Although either the Goal Seek or Solver tool can be used interchangeably to solve the examples in this chapter,
Solver is a better choice because it provides a higher degree of precision. For example, Goal Seek gives the value 42.46 percent for Cell B10 of Example 12.5 (Figure 12-9), while Solver gives the value 42.48 percent. The relative difference between the two values is only 0.05 percent and either result suffices for the purpose of the example. However, the result provided by Solver and other values that depend on it is more accurate.
Both tools use an iterative procedure that refines a starting value for the changing cell until successive results agree within a prescribed level of accuracy. The default level for Solver is more precise than for Goal Seek. Solver also provides an option for increasing the precision further.
Goal Seek is a simpler tool to use and explain. However, Solver is more powerful, versatile, and accurate. Solver can do everything Goal Seek can—and more, and better.
Capital Budgeting: The Basics ❧ 379 Rather than setting a goal for the years to break even, a CFO’s goals might be to reach a given net
present value or rate of return by a specified time, as illustrated by the following example.
Example 12.4: Not satisfied with the results from Example 12.3, Consolidated’s CFO now wants to know how much the annual benefits would have to increase in order to provide an MIRR of 25 percent by the end of the fourth year.
Solution: Figure 12-9 is a spreadsheet solution. The spreadsheet is produced by copying the spreadsheet of Figure 12-8 to a new spreadsheet and changing the Solver setting of the Solver tool to a goal of 0.25 (i.e., 25%) in Cell F19 by changing the value in Cell B10. The results show that the annual benefits must increase by
42.48 percent from their projected values in order for the investment’s MIRR to equal 25 percent by the end of the fourth year. Note that the time to break even has been reduced to 2.56 years, and the investment’s NPV has increased to $66,804.
Figure12-9
Increase in Projected Year-End Annual Benefits to Achieve a 25% Modified Internal Rate of Return at the End of Four Years
1 Example 12-4: CONSOLIDATED ENTERPRISES
2 Equipment cost
Depreciation Method: Straight Line
3 Salvage value
4 Life, years
5 Increase in year-end annual benefits to
5 Discount rate
achieve a 25% MIRR at the end of 4 years
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
64,116 $ 42,744 12 Before-tax cash flow
11 Year-end annual benefit
18,000 $ 18,000 14 Taxable income
13 Annual depreciation
16 After-tax cash flow
45,669 $ 42,846 17 Net present value
$ 66,804 18 Internal rate of return
39.07% 19 Modified internal rate of return
25.00% 26.28% 20 Break-even point, years
Key Cell Entry: Cell C11: =C9*(1+$B10), copy to D11:G11 Goal Seek or Solver Settings: Target Cell is F19, to be set equal to 25% by changing Cell B10.
380 ❧ Corporate Financial Analysis with Microsoft Excel ®