Using the Correct Financial Criteria to Select Investments
Using the Correct Financial Criteria to Select Investments
The preceding discussions have used four measures of an investment’s financial success: (1) the net pres- ent value, (2) the internal rate of return, (3) the modified internal rate of return, and (4) the time to break even. Different financial criteria can lead to different choices among alternate investments. The best
384 ❧ Corporate Financial Analysis with Microsoft Excel ® Figure12-14
Early Sale, with Sale Price Less Than Book Value
1 Example 12-7: CONSOLIDATED ENTERPRISES
2 Equipment cost
Depreciation Method: Straight Line 3 Salvage value
Selling price of equipment at end
4 Life, years
5 of year 4 $7,500
5 Discount rate
Tax rate for long-term capital gains
6 Reinvest rate
or losses 30.0%
7 Tax rate on regular income
0 1 2 3 4 9 Year-end annual benefit
8 Year
10 Before-tax cash flow from operations $ (100,000) $ 40,000 $ 55,000 $ 60,000 $ 45,000
11 Annual depreciation $ 18,000 $ 18,000 $ 18,000 $ 18,000 12 Taxable income
$ 22,000 $ 37,000 $ 42,000 $ 27,000 13 Tax @ 40%
14 After-tax cash flow from operations $ (100,000) $ 31,200 $ 40,200 $ 43,200 $ 34,200 15 Before-tax cash flow from sale of equipment
16 Book value of equipment $28,000 17 Capital gain (loss) on sale of equipment
($20,500) 18 Tax benefit from sale of equipment
19 After-tax cash flow from sale of equipment
$13,650 20 Net after-tax cash flow
21 Net present value
20.98% 23 Modified internal rate of return
22 Internal rate of return
18.26% 24 Break-even point, years
Given two options with large positive NPVs, for example, should an investor select the one with the higher NPV, the higher IRR, the higher MIRR, or the shorter time to break even? The choice depends on the amounts invested, the cost of capital, the timing of the future cash flows, and the volatility of market demand for a product. It is important to recognize when one choice is correct, and the others are wrong.
Check the Amount Invested The correct choice may depend on the amount invested. Would you choose an investment of $100,000
with an NPV of $10,000 at the end of one year over an investment of $20,000 with an NPV of $5,000 at the end of one year? If you selected the first alternative because it provides a higher NPV, you would
be making a costly mistake. You should recognize that the first investment has a rate of return of only 10 percent on the investment, whereas the second has an return of 25 percent, which is more than twice the first. The difference of $80,000 in the first investment has added only $5,000 to the NPV. This is a return of only 6.25 percent on the incremental investment, which may be less than the discount rate of money. Wouldn’t you prefer to spend $20,000 to make the smaller investment of the two and then try to find a better investment for the other $80,000?
Capital Budgeting: The Basics ❧ 385 Now consider two equal investments. The following example illustrates why, when choosing
between two investments that are equal and mutually exclusive, it is correct to choose the investment that provides the higher NPV rather than the one that provides the higher IRR. In addition, the example shows that the investment with the higher NPV also has the higher MIRR. Finally, the example shows that the investment with the higher NPV and MIRR depends on the discount rate or cost of capital.
Example 12.8: Mayberry Investments is considering two mutually exclusive investments of $500,000. The future year-end cash flows over the five-year lives of the investments are as follows:
AlternativeA
$300,000 AlternativeB
The cost of capital (or discount rate) is 11.5 percent for both investments, and the future cash flows will be reinvested at 11.5 percent.
a. What are the NPV, IRR, MIRR, and years to break even for each alternative? b. Which investment should Mayberry choose? Give a justification for your response. c. At what cost of capital (or discount rate) are the NPVs and MIRRs of the two investments equal?
Solution: Figure 12-15 is a spreadsheet solution. The upper section of the spreadsheet shows results for both alternatives as well as for the difference between the two alternatives (i.e., for Alternative A minus Alternative B).
a. The results in Rows 14 to 17 show that A has a higher NPV and MIRR than B, but B has a higher IRR and breaks even sooner. The higher IRR and shorter break-even period of B is due to the timing of the cash flows, with B providing larger cash inflows for the first two years and A providing larger cash inflows for the last three years.
b. The choice between the two alternatives depends on the results for the difference between them. If we accept A and reject B, the results for the difference should be favorable. As the spreadsheet results show, the difference A – B provides a positive NPV, and A should therefore be accepted. If we had chosen B in preference to A, we would have rejected the positive NPV for the difference, which would
be a bad decision. (You should be able to show choosing B in preference to A results in a negative NPV for the difference B – A and B should therefore not be accepted.) c. The analysis in Rows 18 to 34 of Figure 12-15 shows that the choice between alternatives varies with the cost of capital (or discount rate) and reinvestment rate (which are set equal to one another in this analysis). For discount and reinvestment rates of 14.5 percent or less (Rows 20 to 31), Alternative A has higher NPVs and MIRRs and should be chosen, whereas for discount and reinvestment rates of 15.0 percent of more (Rows 32 to 34), Alternative B has higher NPVs and MIRRs and should be chosen. Note that the NPV of the difference A – B changes from a positive to a negative value as we pass through the range 14.5 percent to 15.0 percent.
To find the cost of capital at which the two alternatives are equal, we can use Excel’s Solver or Goal Seek tool to find the value of the cost of capital that makes the NPV of the difference A – B equal to zero. The results in Row 36 show that at a cost of capital of 14.85 percent, both Alternatives A and B have an NPV of $126,619 and an MIRR of 20.15 percent. At the same time, the difference A – B has an MIRR of 14.85 percent, which is the same as the cost of capital.
The conclusion to be drawn from this example is that IRR should not be used as a basis for choosing between two equal and mutually exclusive investments. As between the usual financial criteria (i.e., NPV, IRR, and MIRR), the proper choice is the investment with the higher NPV.
(Continued)
386 ❧ ® Corporate Financial Analysis with Microsoft Excel
Figure12-15
Analysis of Alternative Investments of Equal Amounts
1 Example 12-8: MAYBERRY INVESTMENTS
Alternative
3 A B A-B
4 Amount of investment
$0 5 Cost of capital
11.5% 6 Reinvest rate
After-tax 7 Year
After-tax
After-tax
cash flows
NPV
cash flows
NPV
cash flows NPV
13.44% 17 Years to break even
3.90 2.32 4.84 18 Analysis of Effect of Cost of Capital and Reinvestment Rate on NPV and MIRR Cost of Capital and 19 Reinvestment Rate
NPV MIRR
35 Conditions for Alternatives A and B equally attractive
Do not generalize beyond the choice of NPV as the correct choice between two equal and mutually exclu- sive investments. If the investments are not equal or if the discount and reinvestment rates vary independently of each other, you should make an analysis based on the specific conditions.
Before leaving this example, we might want to reconsider the basis for our choice. The time to break even is 3.90 years for Alternative A and 2.32 years for Alternative B. Suppose that the investments are risky and that future cash flows after three years might be substantially less than those projected or that the investments’ life- times might be shorter than five years. Alternative B might then be a better choice. In a later chapter we will include an analysis of the risks due to uncertainties in projected cash flows in the selection process.
Capital Budgeting: The Basics ❧ 387