The Choice

            The Capital Budgeting Mini-Case assignment asks the student to analyze two proposed acquisitions, Corporation A and Corporation B, in order to decide which would be the better acquisition. The student can chose only one of the acquisitions, because the acquiring company has a limited budget. The student is asked to analyze the two potential acquisitions using net present value (NPV), internal rate of return (IRR), payback (PB), discounted payback (DPB) and profitability index (PI). After conducting the analysis, I conclude that each of these measures favors the acquisition of Corporation B over Corporation A. To understand the analysis it is important to first understand each of these analytical tools.

Payback (PB)

            The simplest, yet most flawed, of these tools is called payback. The idea is to measure how long it will take an investor to receive an amount equivalent to his investment.  One fundamental flaw with payback is that it fails to distinguish between apples and oranges. It assumes that a dollar today has the same value as a dollar a year from now. However, this is not true for several reasons. The first reason is opportunity cost. By delaying receipt of a dollar to a point in the future, the investor loses his chance to invest in something else and receive a return on that investment. The second reason is risk. If we receive a dollar now, there is no risk that we will not receive the dollar. However, since none of us can be certain of the future, a delay in payment increases the risk that we will not receive the dollar at the promised future date. The third reason is inflation. Deflation is a theoretical possibility, but in the U.S. and most countries around the world, inflation is the rule. Assuming that a 10% discount rate is required to compensate an investor for accepting payment in twenty years, that $1 twenty years from now is worth only 15ȼ today.  Thus, one of the fundamental concepts of finance is to time adjust values so that they can all be compared at a common point in time. Theoretically, this can be done to any point in time. If we are comparing the value of cash flows, we can compare them as of today, as of a year from today, or as of 20 years from today, as long as all cash flows are all adjusted to reflect a common point in time. Most often the point in time used for such an analysis is the present. Thus, future cash flows must be discounted to reflect their present value (PV). Payback is flawed, because it fails to make a PV adjustment. Instead, it simply adds the nominal amounts of the cash flows together until the total of the nominal cash flow amounts is equal to the nominal investment amounts. The payback period is the point in time at which the nominal cash flows received equal the nominal investment paid. Thus, if the investment consisted on a single outlay at time zero of $100,000 and the investment produced cash flows of $20,000 per year, the payback period would be 5 years. $100,000 = $20,000 + $20,000 + $20,000 + $20,000 + $20,000.

            An additional flaw with payback is that there is not distinction for the timing of payments within the payback period. This problem also stems from the lack of a PV adjustment. Thus, both the example above ($100,000 investment with $20,000 per year cash flows) and an a project requiring a $100,000 investment with one $100,000 cash flow at the end of year five would produce an identical payback period of five years.

Discounted Payback (DPB)

            Discounted payback seeks to remedy the time value problem explained above by calculating the PV of each cash flow, so that we are using “real” rather than nominal values for the investment and the cash flow amounts. Thus, if the proper discount rate is 10%, this discount rate must be applied to each projected cash flow before the cash flows are added together to determine the payback period. The effect of this discounting is to lengthen out the payback period. Thus, as can be seen by the following numbers, the discounted payback period for a $100,000 investment with $20,000 per year nominal cash flows with a 10% discount rate is 7.3 years, rather than five years, as we saw above, when no present value adjustment was made.

           Another flaw, which applies to both payback and discounted payback, is that neither method provides information about cash flows which occur after the payback period. The payback period for the $100,000 investment above is the same whether the $20,000 per year payments end with year eight or continue for a hundred years. As we will see with other measures, the number of years during which the cash flows persist is important in calculating the value of a proposed project.

Profitability Index (PI)

            The profitability index is a ratio. The numerator is the PV of the cash flows projected for the project. The denominator is the PV of the investment required for the project. Thus, if the PI is greater than 1 that means that the project should be profitable. A PI of 1.2 means that the PV of the cash flows is 20% greater than the PV of the investment. The flaw with this measure is that it tells you nothing about the size of the project and thus nothing about its absolute value of the project. For example, a lemonade stand, which will cost $10 to build and stock, and which will produce $12 (PV) in cash flows will have a PI of 1.2. This is also true for a $1 billion manufacturing complex, which will produce $1.2 billion (PV) in cash flows. However, as we will see below, the lemonade stand will add only $2 in value to the firm investing in the project, but the manufacturing complex adds $200 million in value to the firm.

Internal Rate of Return (IRR)

            The internal rate of return is the discount rate at which the PV of the projected cash flows equals the PV of the investment. In other words, the IRR is the rate of return that will be generated by the project. Therefore if the IRR of a project is greater than the cost of capital to the firm, then the firm will receive a positive return by investing in the project. If the cost of capital to the firm is 10%, and the IRR of a project is 15%, then the firm can make 5% above its cost of capital by investing in the project. Like the profitability index, the flaw with IRR is that it tells us nothing about the size of the project or the absolute value of the project to the firm. The lemonade stand may not be distinguishable from the manufacturing complex, or worse the lemonade stand might appear from its IRR to be superior to the manufacturing complex, even though the lemonade stand adds little in value to the firm making the investment; whereas, the manufacturing complex might add hundreds of millions of dollars to the value of the firm.

            Another weakness of IRR is that it can lead to the mistaken assumption that money received from the project can be reinvested at the IRR rate. This may not be the case. Thus, comparing a project which lasts two years with a project which lasts five years may provide a distorted picture, since the money earned on the two year project may have to be reinvested at a lower rate of return in the future and at a point nearer in time  than money returned from the five year project. 

Modified Internal Rate of Return (MIRR)

            MIRR incorporates an assumption about the rate at which cash flows received from the project can be reinvested in the future. Often the firm’s weighted average cost of capital (WACC) is used for this assumption. Thus, if the WACC is less than the IRR, the MIRR will be lower than the IRR.

Net Present Value (NPV)

           NPV is the theoretically superior measure for determining the investment priority for proposed projects. This is because NPV tells you the value that will be added to a firm on day one of its investment in a project. NPV works by calculating the present value of each projected cash flow to be generated by the project. It then subtracts the PV of the investment required for the project. Since all outlays and cash flows have been calculated at their present value (in other words we are dealing solely with apples) by subtraction of the PV of the outlays from the PV of the positive cash flows, we obtain the present value of the project, itself.

           This method solves both the size and the duration problems encountered with the other measures. However, there is a cost. When compared with IRR, it is much more difficult to obtain the information to calculate NPV than to calculate IRR.

           To calculate NPV, we need to know the proper discount rate to be applied. This most method used to calculate the discount rate is the Capital Asset Pricing Model (CAPM). The CAPM equation is as follows: ER = RF + β (Rm - RF) 

           To use CAPM, we must determine the risk free interest rate of return (RF)for our particular economy. We must also determine the risk premium in the economy, which is the average rate of return on all risky assets in the economy minus the risk free rate (Rm - RF). Since actually calculating the amount involves knowing much more information than it is possible to know, we must decide on a proxy, such as the S&P 500 for the average return on risky assets. At this point we are just getting started.

           Now comes the issue of calculating β. β is the relative volatility (risk) of the particular project to the volatility of the market as a whole. This can be done using historical information, industry information, implied volatilities, etc. Entire books are written on how to best calculate β. Thus, while NPV is theoretically superior, it can be a difficult task to calculate a project’s NPV.

The Relationship between NPV and IRR

            In contrast, IRR requires only the projected outlays and projected positive cash flows. IRR is then calculated as that rate of return required to obtain an NPV of zero. Thus, the assumption is that if the cost of capital to the firm is less than the IRR, the return on the project will be positive. The greater the IRR for a particular project, the wider the gap between the cost of capital to the firm and the IRR, and thus the higher the return on the project, assuming that the projects being compared are comparable in size and duration.

The Project Comparison

           Comparing these different measures for the two proposed acquisitions, Corporation B is the clear winner over Corporation A. The numbers are as follows:

           Since the information is provided in the exercise to accurately calculate NPV, NPV should be the measure used to decide which acquisition should be selection. The NPV of Corporation B is nearly twice the NPV of Corporation A. Therefore, Corporation B is the best selection.
Not just NPV, but all of the measures lead to this conclusion. The IRR and MIRR for Corporation B are higher than Corporation A. The profitability index for Corporation B is higher than for Corporation A. Both the payback and discounted payback periods are shorter for Corporation B than for Corporation A. Thus, all measures lead to the conclusion that Corporation B should be selected over Corporation A.

Finance is Not Rocket Science

            Numbers can give the mistaken impression of precision, when we forget the very imprecise assumptions that go into calculating the numbers. An underlying assumption in physics is that the laws of physics are the same at any given point in space and time. While this assumption is not provable, it has functioned well for physicists. No one has discovered an exception to this assumption. Scientists are able to calculate the amount of fuel needed for a rocket to place a payload into orbit and the calculation works today, tomorrow and a hundred years from now. While we are safe assuming that the same laws of physics will apply a hundred years from now, the assumptions we must make about the future in finance are much less certain.

            Two key variables in the Capital Budgeting Simulation, which would have a dramatic impact on the results, are: 1) the discount rate applied to calculate NPV and 2) the assumptions about future sales revenue. The problem is that nobody knows what will happen in the future, and the farther out we try to project the less capable we are at making reasonable assumptions about the future.

            As I explained above, to calculate the discount rate we need a great deal of information. In large part we need information about how risky the particular project is. Often people make assumptions about risk based on historical data. However, the choice to use historical data assumes that the future will look like the past. In the simulation SAI has been in the business of manufacturing digital imaging integrated circuits for a few years. Thus, their calculations about the risk involved in expanding such a business could be based on their past experience with the business. They might even incorporate historical information from other businesses in their industry. But again, the assumption is that the future will look like the past.

            To avoid the assumption that the future will look like the past, SAI can look at implied volatility figures from market data. Implied means the volatility implied by actual trades in the market. For example, since options prices are based in part on volatility, it is possible to calculate the implied volatility from the price of the option. There is even a market for volatility derivatives, where prices are based on volatility alone. The argument in favor of using implied volatility is that in addition to using historical data market participants are also making an informed judgment about the future. Thus, implied volatility is a future looking measure of volatility.  While implied volatility is often better than relying strictly on historical data, there may not be any implied volatility numbers available for a particular type of project or the information available my impure. For example, SAI might look at options traded on the shares of other companies in the same integrated circuit market, but those companies may also sell other products and thus their implied volatilities reflect all of their businesses and not just their digital imaging integrated circuits business. Even with good implied volatility number, we are still limited by the fact that nobody can actually know the future. Often the future assumed by markets and the future, which actually comes to pass are very different.

            Using all of the information explained above, we can use CAPM to calculate a discount rate. The selection of the discount rate has a profound effect on NPV. While the simulation does not expressly state the discount rate uses, by reverse engineering the numbers in the simulation for the digital imaging integrated circuit project, I was able to calculate that the discount rate used is 18%. Based on the initial cash flow assumptions in the simulation, this produced an NPV for the integrated circuit project of $2,129. The following is a chart using the simulation’s cash flow numbers, but varying the discount rate from 1% to 30%. As you can see, NPV changes from $28,055 at 1% to -$7,676 and 30%.

            Revenue and thus cash flow projections face this same limitation. Nobody knows what they will actually turn out to be. The farther into the future we try to project, the less relevant information we posses and the less accurate these projections are likely to be. In the simulation, SAI recognizes the fact that the future in not likely to mirror the past. SAI understands that they are in a business which changes rapidly. They recognize that high tech products are replaced by other technologies over time. In response, SAI assumes that the business will terminate in five years. In one respect it is good that SAI is not making the assumption that the future will mirror the past, but there is not a lot of precision in SAI’s assumption that the project will terminate in five years. If the digital imaging integrated circuits they produce become outdated in three years, then the projects NPV calculated with the five-year assumption will have significantly over estimated the value of the business. In contrast, if the life of the integrated circuit business turns out to be seven years, then the NPV calculated using the five-year assumption will have significantly underestimated the value of the business.

           Even if the five year assumption turns out to be correct the level of sales four and five years in the future are very difficult to estimate. It may be that another technology will partially replace digital imaging integrated circuits in year three and cut the actual sales in half for year four and by three fourths in year five. Alternatively, a very popular product might sweep the market in year three which considerably increases the demand for digital imaging integrated circuits. None of these potential events can be known at the time that the cash flows must be estimated.
SAI is in an even more difficult position as it tries to estimate the discount rate and cash flows for its newly developed chip for data enabled cell phones. Since this is an entirely new business, they have no historical data at all to use as a basis for their estimates. Thus, they must use knowledge about how markets for similar types of products have functioned in the past. Because the demand for the chips will be derived from the demand for data enabled cell phones, SAI must rely on sales forecasts made by other companies for the cell phones which will use the chip. The forecasts made by other companies also have all the inherent limitations discussed above. The forecast that 12.5 million such phones will be sold in three years may itself be inaccurate.

           Further, SAI then has to estimate the percentage of those cell phone sales which will use their chip. They must do so with very incomplete knowledge about what their competitors in the industry are doing. It may turn out that a competitor develops a superior chip six months from now, which makes their cell phone chip obsolete. It might be that a competitor develops a manufacturing process two years from now which significantly reduces the cost of producing chips and drives the market price down significantly.

           The capital budgeting tools developed in recent decades are very valuable. They provide businesses with a rigorous method of evaluating their capital budgeting decisions. However, it is always important to keep in mind that these tools have not transformed finance into rocket science. It is still very much an art. Finance still requires its practitioners to exercise judgment and to understand the inherent limitations caused by our inability to actually know the future.

References

Damodaran, Aswath (2006). Applied Corporate Finance: A User's Manual.
Hoboken, NJ: John Wiley & Sons, Inc.

Ross, A. Stephen, Westerfield, Randolph W., Jaffe, Jeffrey (2005). Corporate Finance.
New York, NY: McGraw-Hill Irwin.

University of Phoenix. Capital Budgeting Simulation. Phoenix, AZ.