Using Probabilities to Define Risks
Using Probabilities to Define Risks
Of all the future values that are uncertain in capital budgeting, the least certain are usually future sales. These directly affect year-end benefits and the calculations of an investment’s profitability.
As we learned in Chapter 3, statistical projections of past sales have margins of error. In addition, changes from past trends occur because of changes in the general economy, demographics, and other factors that are largely outside the control of a company. These all translate into risks.
Our goal in this section is to create a downside risk chart, such as the one shown in Figure 14-1. This figure shows the risk level for the investment’s payoff in terms of the probability for failing to achieve different net present values. The chart is based on the variability of a single factor the annual year- end benefits. In the next chapter, we will extend the discussion to the variability of more than a single factor.
We have used the Albertus Enterprises case study in Chapter 13 to prepare Figure 14-1. To use the results from Chapter 13 to prepare the downside risk chart, copy Figure 13-1 and clear the information on
Capital Budgeting: Risk Analysis with Scenarios ❧ 437 Figure14-1
Downside Risk Curve for Net Present Value (Albertus Enterprises Case Study from Chapter 13)
There’s a 90% probability the NPV
will be less than $300,000 and a 10% chance it will be more.
70% WILL BE LESS)
60% There’s a 50% probability the NPV will be less than $204,426 and a 50% chance it will be more.
50% OBABILITY NPV
WNSIDE RISK (PR 20% DO
There’s a 10% probability the NPV will be less than $105,000 and a 90% chance it will be more.
NET PRESENT VALUE
key cell entries and the charts below Row 29. To provide for entries that will be made later, insert a new column B and change the widths of Columns A and B. This provides the upper portion of Figure 14-2.
To create the downside risk chart shown as Figure 14-1, we need to plot a series of probabilities on the Y-axis against the series of net present values (NPV) on the X-axis. The range of X-values should cover
a range from the lowermost value, at which there is very little probability of doing worse, to the highest value, at which there is very little probability for doing better. These correspond to the smallest annual demand that we might expect to the highest.
The expected annual year-end benefit is the forecast of $350,000 in Cell F31 of Figure 14-2. The forecast has a standard error of forecast of 10 percent, or $35,000. Enter the series of values from $240,000 to $460,000 in increments of $10,000 in Cells A36:A58 for the annual year-end benefits. This range covers slightly more than three standard forecast errors above and below the forecast annual values; that is, there is less than a 0.3 percent chance that the future year-end benefits will be outside the range from $240,000 to $460,000. That pretty well covers all likely values.
438 ® ❧ Corporate Financial Analysis with Microsoft Excel Figure14-2
Risk Analysis Based on Forecast Annual Benefits and Their Standard Forecast Error
1 ALBERTUS, INC. — CAPITAL BUDGETING SPREADSHEET
2 Equipment cost, including installation
3 Salvage value, as percent of cost
4 Market value, end of Year 5
5 Discount and reinvestment rate
6 Tax rate
7 Year 0 1 2 3 4 5
8 Depreciation and Book Value Schedule
9 Depreciation base
10 Annual depreciation, per MACRS
10.93% 8.75% 11 Annual depreciation, dollars
122,480 $ 87,440 $ 70,000 12 Year-end book value
13 Year-End Cash Flow Analysis
14 Regular income
15 Annual year-end benefit
350,000 $ 350,000 $ 350,000 16 Taxable regular income
227,520 $ 262,560 $ 280,000 17 Tax on regular income
91,008 $ 105,024 $ 112,000 18 ATCF for regular income
19 Sale of equipment
20 Income from sale of equipment $ 80,000 21 Capital gain(loss)
$ (68,640) 22 Capital gain tax (benefit)
$ (27,456) 23 ATCF from sale of equipment
24 After-Tax Cash Flow Analysis
25 After-tax cash flow (ACTF)
258,992 $ 244,976 $ 345,456 26 Net present value
27 Internal rate of return (IRR)
28 Modified internal rate of return (MIRR)
29 Discounted break-even point, years
3.92 30 ALBERTUS,INC - DOWNSIDE PROBABILITY (RISK) ANALYSIS
31 Forecast annual year-end benefits
$350,000 Risks are based on the
32 Standard error of forecast, percent
forecast annual year-end
33 Standard error of forecast, dollars
benefits (Cell F31) and
Annual year-end
NPV at end of 5
IRR at end of MIRR at end of Years to break
the standard error of
Downside risk forecast (Cell F32 or F33).
59 Key Cell Entries
60 A35: =D15
B35: =H26
C35: =H27
D35: =H28
E35: =C29
Capital Budgeting: Risk Analysis with Scenarios ❧ 439 For each value of annual year-end benefits in Cells A36:A58, we next calculate the investment’s
NPV, IRR, and MIRR at the end of five years and the number of years to break even. We will use a one- variable input table to do this. Make the following entries in Row 35:
In Cell A35, enter =D15 (This connects the table to the annual benefits in the main program.) In Cell B35, enter =H26 (This connects the table to the NPV in the main program.) In Cell C35, enter =H27 (This connects the table to the IRR in the main program.) In Cell D35, enter =H28 (This connects the table to the MIRR in the main program.) In Cell E35, enter =C29 (This connects the table to the years to break even in the main program.)
As each of the above entries is made, the value in the referenced cell will appear. For example, the value $350,000 will appear in Cell A35 when =D15 is entered there. To hide these values, format the cells with the custom format ;;; (i.e., three semicolons).
(N.B. Make sure the values in Cells E15:H15 depend on and are the same as the value in Cell D15. You should set up your spreadsheet with the value 350,000 entered in Cell D15, and with the entry =$D$15 in Cells E15:H15. Alternatively, you can enter =D15 in Cell E15 and copy it to F15:H15.)
Drag the mouse to select the Range A35:E58. From the Data menu on the toolbar, click on Table to open the dialog box shown in Figure 14-3. Enter D15 as the column input cell and click OK or press Enter. Format the results in Cells B36:E58 as shown in Figure 14-2. We now have values that tell us what the NPV, IRR, MIRR, and payback period will be for each of the assumed values for the year-end annual benefits. For example, if we ask, “What happens if the annual benefits are $300,000?” we can read the resulting values for the NPV, IRR, MIRR, and years to break even in Cells B42:E42.
Our next step is to express the probabilities associated with each of the assumed values for annual year-end benefits. To do this, we use the forecast of $350,000, the standard forecast error of 10 percent (or $35,000), and Excel’s NORMDIST function. The syntax for the NORMDIST function is