An Example The following example shows how to create a spreadsheet for evaluating the various financial measures
An Example The following example shows how to create a spreadsheet for evaluating the various financial measures
of success for given cash flows, discount rates, and depreciation conditions.
Example 12.1: Consolidated Enterprises is a large manufacturing firm. It plans to invest $100,000 in new factory equipment to increase the production efficiency for one of its many products. The equipment will
be depreciated by the straight-line method, and its salvage value at the end of five years is expected to be $10,000. The firm’s industrial engineers and market analysts estimate that the increases in the firm’s annual net operating income before depreciation and taxes due to the equipment will vary as follows:
Years after Investment
Year-End Annual Benefit
Considering the risks involved and the other investment opportunities, Consolidated’s chief financial offi- cer decides on using a discount rate of 14 percent for evaluating the investment. The value of 14 percent will also be used for the rate at which future cash inflows can be reinvested.
Consolidated’s income tax rate is 40 percent. What is the net present value of the investment, its internal rate of return, its modified internal rate of
return, and its break-even point? Solution: Figure 12-3 shows a spreadsheet solution. Data values are entered in Rows 1 to 9, and calculated
or transferred values are in Rows 10 to 18. The before-tax cash flow (BTCF) for Year 0 in Cell B10 is the negative value of the investment in Cell B2. The year-end BTCFs for the following years, except the last, are the same as the year-end annual benefits; that is, the entry in C10 is =C9 and is copied to D9:F9. The year-end BTCF for the fifth (final) year is the sum of the year-end annual benefit plus the salvage value; that is, the entry in G10 is =G9+B3.
The annual depreciation is calculated by entering =SLN($B2,$B3,$B4) in Cell C11 and copying the entry to D11:G11. Except for the final year, taxable income is calculated as the difference between the BTCF and the depreciation; that is, enter =C10-C11 in Cell C12 and copy the entry to D12:F12. The taxable income for the final year requires an adjustment for salvage value, since the salvage value income is not taxable when the income equals the projected salvage value. The entry for taxable income for the final year is =G10-G11-B3 in Cell G12.
(Continued)
Capital Budgeting: The Basics ❧ 373
Figure12-3
Capital Budgeting Analysis for Consolidated Enterprises
1 Example 12-1: 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 Year-end annual benefit
10 Before-tax cash flow
18,000 $ 18,000 12 Taxable income
11 Annual depreciation
34,200 $ 35,200 15 Net present value
14 After-tax cash flow
7,709 $ 25,991 16 Internal rate of return
24.21% 17 Modified internal rate of return
19.39% 18 Break-even point, years
22 BREAK-EVEN POINT = 3.62 YEARS
26 $– 27 ALUE V 28 $(20,000) 29 30
31 $(40,000) 32 33 NET PRESENT
Key Cell Entries
B10 =–B2 (Investment at Year 0 is a cash outflow.) C10 = C9, copy to D10:F10 (Year-end cash flows for years 1 to 4 are the annual benefits.) G10 =G9+B3 (Year-end cash flow year 5 is the annual benefit plus salvage value.) C11 =SLN($B2,$B3,$B4), copy to D11:G11 (Computes annual depreciation by straight-line method.) C12 = C10–C11, copy to D12:F12 (Taxable income for years 1 to 4 is before-tax cash flow less depreciation.) G12 = G10–G11–B3 (Taxable income for year 5 is before-tax cash flow less depreciation and salvage value.) C13 =C12*$B7, copy to D13:G13 (Tax is taxable income multiplied by tax rate.) B14 =B10–B13, copy to C14:G14 (After-tax cash flow is before-tax cash flow less tax.) B15 =B14 (Net present value at time zero is the cash outflow for the investment.) C15 =NPV($B5,$C14:C14)+$B14, copy to D15:G15 (Computes net present value at ends of years 1 to 5.) B16 =–100% C16 =IRR($B14:C14,guess), copy to D16:G16 (Computes internal rate of return at ends of years 1 to 5.) B17 =–100% C17 =MIRR($B14:C14,$B5,$B6), copy to D16:G16 (Computes modified internal rate of return at ends of years 1 to 5.) B18 =IF(C15>0,B8–B15/(C15–B15), IF(D15>0,C8–C15/(D15–C15), IF(E15>0,D8–D15/(E15–D15),
IF(F15>0,E8–E15/(F15–E15), IF(G15>0,F8–F15/(G15–F15), “failed”))))) (Computes years to break even.)
(Continued)
374 ® ❧ Corporate Financial Analysis with Microsoft Excel
Tax is calculated as the product of the taxable income multiplied by the tax rate; that is, the entry in Cell C13 is C12*$B7 and is copied to D13:G13. After-tax cash flows (ATCFs) are calculated as what is left of the BTCFs after paying taxes; that is, the entry in cell B14 is =B10-B13 and is copied to C14:G14. (An alternate method for calculating the ATCFs is discussed later.)
Enter =B14 in Cell B15 for the net present value of the investment at year 0. To calculate the investment’s net present value at the ends of other years, enter =NPV($B5,$C14:C14)+$B14 in Cell C15 and copy it to D15:G15. Note that because the value in Cell B14 is already a present value, it is not included in the range for the NPV function. The NPV function discounts only future values to their present equivalents at the given discount rate.
Enter =-100% in Cell B16 for the investment’s internal rate of return at year 0. To calculate the invest- ment’s internal rate of return at the ends of other years, enter =IRR($B14:C14,-0.40) in Cell C16 and copy it to D16:G16. The guess of -0.40 is close enough for the result in Cell C16. In whatever cells the guess of -0.40 (or any other guess) is not close enough for the IRR function to converge in 20 iterations to a value, the result will
be the error message #NUM!. If this occurs, simply change the guess to a value that is closer to the expected result. Enter =-100% in Cell B17 for the investment’s modified internal rate of return at year 0. To calculate the investment’s modified internal rate of return at the ends of other years, enter =MIRR($B14:C14,$B5,$B6) in Cell C17 and copy it to D17:G17.
Figure12-4
Capital Budgeting Analysis for Consolidated Enterprises (Alternate Calculation of After-Tax Cash Flow)
1 Example 12-1: CONSOLIDATED ENTERPRISES (ALTERNATE CALCULATION OF ATCF)
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 Year-end annual benefit
10 Before-tax cash flow
11 Annual depreciation
12 After-tax cash flow
34,200 $ 35,200 13 Net present value
7,709 $ 25,991 14 Internal rate of return
24.21% 15 Modified internal rate of return
19.39% 16 Break-even point, years
3.62 Change in Key Cell Entries from Figure 12-3
B12 =B10 C12 =(C9–C11)*(1–$B7)+C11, copy to D12:F12 G12 =(G9–G11)*(1–B7)+G11+B3
(Continued)
Capital Budgeting: The Basics ❧ 375
To calculate the number of years for the investment to break even, we need an entry that instructs the computer to move across the values for NPV in Row 15 and, when it encounters the first positive value, to back up one year and add a fraction of the next year, as shown in Figure 12-2. The entry to do this is a succession of IFs that check successive cells in the Range C15:G15 to see if the NPV is positive (i.e., the NPV>0). When the first Cell with a positive NPV is found, the cell value of the preceding year in the range C8:G8 is identified and the fractional part of a year is added to it. The entry in Cell B18 to do this is the following:
=IF(C15>0,B8-B15/(C15-B15),IF(D15>0,C8-C15/(D15-C15),IF(E15>0,D8-D15/(E15-D15), IF(F15>0,E8-E15/(F15-E15),IF(G15>0,F8-F15/(G15-F15),”failed”)))))
Note that if none of the NPVs is greater than 0, the investment fails to break even during the analysis horizon. The results give the investment’s NPV at the end of 5 years as $25,991, its IRR as 24.21 percent, its MIRR as 19.39 percent, and its break-even point as 3.62 years. The chart in the center of Figure 12-3 shows how the NPV increases from the negative value of -$100,000 at the time of the investment, reaches zero NPV after 3.62 years, and increases further to a positive value of $25,991 at the end of 5 years. (To make the Y-axis line at zero heavy, as shown in Figure 12-3, double-click on the axis to open the Format Axis dialog box, select the Patterns tab, and scroll down the Weight box to the second entry from the bottom.)
Figure 12-4 shows a solution with the ATCFs calculated by an alternate method. This method omits the calculations of taxable income and tax in Rows 12 and 13 of Figure 12-3. The after-tax cash flows at the ends of years 1 and 4 are calculated by the entry =(C9-C11)*(1-$B7)+C11 in Cell C12 and copying the entry to D12:F12. The entry in G12 for year 5 is =(G9-G11)*(1-B7)+G11+B3, where B3 is the salvage value.