Under capital rationing, only Projects A through C, calling for $5 million in investment, will be accepted. Although Projects D and E have returns exceeding the cost of funds, as evidenced by a positive net present value, they will not be accepted with the capital rationing assumption.
Net Present Value Profile
An interesting way to summarize the characteristics of an investment is through the use of the net present value profile. The profile allows us to graphically portray the net present value of a project at different discount rates. Let’s apply the profile to the investments we discussed earlier in the chapter. The projects are summarized again here:
|Cash Inflows (of $10,000 investment)|
|Year||Investment A||Investment B|
To apply the net present value profile, you need to know three characteristics about an investment:
1. The net present value at a zero discount rate. That is easy to determine. A zero discount rate means no discount rate. The values simply retain their original value. For Investment A, the net present value would be $2,000 ($5,000 + $5,000 + $2,000 − $10,000). For Investment B, the answer is $6,000 ($1,500 + $2,000 + $2,500 + $5,000 + $5,000 − $10,000).
2. The net present value as determined by a normal discount rate (such as the cost of capital). For these two investments, we use a discount rate of 10 percent. As previously summarized in Table 12-6, the net present values for the two investments at that discount rate are $180 for Investment A and $1,414 for Investment B.
3. The internal rate of return for the investments. Once again referring to Table 12-6, we see the internal rate of return is 11.17 percent for Investment A and 14.33 percent for Investment B. The reader should also realize the internal rate of return is the discount rate that allows the project to have a net present value of zero. This characteristic will become more apparent when we discuss our graphic display.
We summarize the information about discount rates and net present values for each investment here:
Note that in Figure 12-2, we have graphed the three points for each investment. For Investment A we showed a $2,000 net present value at a zero discount rate, a $180 net present value at a 10 percent discount rate, and a zero net present value at an 11.17 percent discount rate. We then connected the points. The same procedure was applied to Investment B. The reader can also visually approximate what the net present value for the investment projects would be at other discount rates (such as 5 percent).
In the current example, the net present value of Investment B was superior to Investment A at every point. This is not always the case in comparing various projects. To illustrate, let’s introduce a new project, Investment C, and then compare it with Investment B.
|Investment C ($10,000 Investment)|
Characteristics of Investment C
1. The net present value at a zero discount rate for this project is $3,200 ($9,000 + $3,000 + $1,200 − $10,000).
2. The net present value at a 10 percent discount rate is $1,560.
3. The internal rate of return is 22.51 percent.
Figure 12-2 Net present value profile
Comparing Investment B to Investment C in Figure 12-3, we observe that at low discount rates, Investment B has a higher net present value than Investment C. However, at high discount rates, Investment C has a higher net present value than Investment B. The actual crossover point can be viewed as approximately 8.7 percent. At lower rates (below 8.7 percent), you would choose Investment B. At higher rates (above 8.7 percent), you would select Investment C. Since the cost of capital is presumed to be 10 percent, you would probably prefer Investment C.
Why does Investment B do well compared to Investment C at low discount rates and relatively poorly compared to Investment C at high discount rates? This difference is related to the timing of inflows. Let’s examine the inflows as reproduced in the following table.
|Cash Inflows (of $10,000 investment)|
|Year||Investment B||Investment C|
Figure 12-3 Net present value profile with crossover
Investment B has heavy late inflows ($5,000 in both the fourth and fifth years), and these are more strongly penalized by high discount rates. Investment C has extremely high early inflows, and these hold up well with high discount rates.
As previously mentioned in the chapter, if the investments are nonmutually exclusive or there is no capital rationing, we would probably accept both Investments B and C at discount rates below 14.33 percent because they both would have positive net present values. If we can select only one, the decision may well turn on the discount rate. Observe in Figure 12-3 at a discount rate of 5 percent we would select Investment B, at 10 percent we would select Investment C, and so on. The net present value profile helps us make such decisions. Now back to basic capital budgeting issues.
Combining Cash Flow Analysis and Selection Strategy
Many of the points we have covered thus far will be reviewed in the context of a capital budgeting decision, in which we determine the annual cash flows from an investment and compare them to the initial outlay. To be able to analyze a wide variety of cash flow patterns, we shall first consider the types of allowable depreciation.