Chapter 13 Capital Budgeting Decision Making

13.1 Introduction to Capital Budgeting Techniques

The goal with capital budgeting is to select the projects that bring the most value to the firm. Ideally, we’d like to select all of the projects that add value, and avoid those that lose value. In an ideal situation, we can raise sufficient financing to undertake all of these value adding projects. By default, we will assume most firms are operating in this environment.

Some firms, however, have the additional limitation of using capital rationingWhen a firm has limited funds to dedicate to capital projects, and projects compete for these limited funds., in that they have a determined amount of funds available to allocate to capital projects, and the projects will compete for these funds. This can occur if the firm has difficulty accessing capital markets, for example. Under capital rationing, some projects that add value might not have sufficient funds to proceed, so the goal is to select the subset of profitable projects that maximizes value. There exist linear programming techniques that can be used when faced with a capital rationing constraint; they are, however, beyond the scope of this text.

We’ll look at three popular decision making techniques: Payback Period, Net Present Value (NPV), and internal rate of return (IRR). There exist a multitude of lesser used techniques, many of which are variants of these three most popular, but these three are the most commonly used today.

13.2 Payback Period

Our first decision making technique is very intuitive and very easy to calculate. Payback periodThe amount of time until our initial investment is recovered. is the amount of time until the initial investment is recovered. For example, a project costs $100 and we earn $20 (after tax) a year. We will have our $100 back in five years. Simple enough!

Cash flows may be uneven, but this barely adds to the complexity. Consider the same project that cost $100, but earns $40 the first year (all after-tax), $30 the second year, $25 the third year, $20 the fourth year and $20 the fifth year? What is our payback period now? We receive our $100th investment during the 4th year, so our payback period is between 3 and 4 full years. Some companies will always round up to the next higher year (“Our investment will be fully paid back in four years…”). Others will add some “precision” by attempting to figure out what fraction of the year has passed. The result is comprised of two parts: the number of full years and the partial year. The number of full years is our initial result, rounded down (in our example, three). If a balance remains then the partial year is the remaining cost at the beginning of the year divided by the cash flow that year. That gives us a portion of the year that it takes to get the balance of the project paid off.

In our example, $95 has been recovered in the first three years, leaving $100 − $95 = $5. Since we will receive $25 dollars in the fourth year, our partial year is $5 / $20 = 0.25. Our total payback period is then 3 + 0.25 = 3.25 years.

Companies that utilize payback period will set a maximum threshold that all accepted projects must remain under. If projects are mutually exclusive, then typically the one with the shortest payback period is chosen.

Payback Period in Action

Gator Lover’s Ice Cream is a small ice cream manufacturer. Gator Lover’s Ice Cream wants to either open a new store (Project A) or buy a new machine to mass produce ice cream to sell to supermarkets (Project B). The relevant cash flows are shown in Table 13.1 "Gator Lover’s Ice Cream Project Analysis".

Table 13.1 Gator Lover’s Ice Cream Project Analysis

	Project A	Project B
Initial Investment	($48,000)	($52,000)
Year	Operating Cash Inflows (after-tax)
1	$15,000	$18,000
2	$15,000	$20,000
3	$15,000	$15,000
4	$15,000	$12,000
5	$15,000	$10,000
Total Years 1–5	$75,000	$75,000

Figure 13.1 Timeline for Project A

Figure 13.2 Timeline for Project B

Let’s calculate the payback period for both projects. Project A cost $48,000 and earns $15,000 every year. So after three years we have earned $45,000, leaving only $3,000 remaining of the initial $48,000 investment. The cash flow in year four is $15,000. The $3,000 divided by $15,000 gives us 0.2.

$$\text{Payback Period Project A}=3+\frac{\mathrm{3,000}}{\mathrm{15,000}}=3.2 \text{years}$$

Project B cost $52,000 and earns back uneven cash flows. In year one the project earns $18,000, in year two it earns $20,000 and it earns $15,000 in the third year. At the end of the second year it has earned back $18,000 + $20,000 = $38,000, leaving $52,000 − $38,000 = $14,000. In the third year the project earns $15,000. The balance of $14,000 will be paid off by the $15,000 earned that year. The $14,000 is divided by the $15,000 to give us 0.93.

$$\text{Payback Period Project B}=2+\frac{\mathrm{14,000}}{\mathrm{15,000}}=2.93 \text{years}$$

If our threshold is 4 years, then both projects would be viable. If the projects are independent, then both should be undertaken. If the projects are mutually exclusive, then we would pick Project B, as the payback period is shorter.

13.3 Net Present Value

Our next capital budgeting method we introduced when we discussed time value of money, and have used it to value stocks and bonds. Discounting all of the cash flows for an investment to the present, adding inflows and subtracting outflows, is called finding the net present value (NPV)Discounting all of the cash flows for an investment to the present, adding inflows and subtracting outflows.. The larger the NPV, the more financial value the project adds to our company; NPV gives us the project amount of value that a project will add to our company. Projects with a positive NPV add value, and should be accepted. Projects with negative NPVs destroy value, and should be rejected. It is generally regarded as the single best criterion for screening projects.

NPV considers the time value of money, because the cash flows are discounted back at the firm’s rate of capital (r). This rate, also called the discount rate or the required return, is the minimum return a firm must earn on a project to have the firm’s market value remain unchanged. If the amount earned on the project exceeds the cost of capital, NPV is positive, so the project adds value and we should do the project.

NPV decision criteria (independent projects):

• If the NPV is greater than zero (NPV > 0) than accept the project
• If the NPV is less than zero (NPV < 0) than reject the project.

If funds are unlimited then we would accept any project with a positive NPV. With mutually exclusive projects, we pick the highest NPV (or the least negative, if we need to pick one and all are below zero). Under capital rationing, we usually want to pick the set of projects with the highest combined NPV that we can afford.

Let’s look at the NPV for the two Gator Lover’s Ice Cream projects. Assume a discount rate of 10%.

Project A

Also written as:

NPV can be calculated by hand, by a financial calculator, or in a spreadsheet. The keystrokes for a financial calculator are as follows:

<CF> <2ND> <CLR WORK> −48000 <ENTER> <DOWN ARROW> 15000 <ENTER> <DOWN ARROW> 5 <ENTER> <NPV> 10 <ENTER> <DOWN ARROW> <CPT>

Note: Excel and other spreadsheet programs are tricky with regard to year 0. The NPV function expects flows to start at year 1. So any cash flows from year 0 need to be added separately.

To solve in a spreadsheet, the corresponding spreadsheet formula is:

=NPV(periodic rate, cash flows from period 1 to n) + net of initial cash flows

Using the numbers for Project A, the spreadsheet function looks like this:

=NPV(.10, 15000, 15000, 15000, 15000, 15000) + (−48000) = 8861.80

Project B

In this case, Project A has the higher NPV by $2,294.14 ($8,861.80−6,567.66). So we would pick Project A over Project B if they are mutually exclusive. If they are independent, we would accept both projects, since both NPVs are positive.

Figure 13.3 Project A NVP

Figure 13.4 Project B NVP

Net Present Value is the preferred tool by many financial managers, as it properly accounts for the time value of money and the cost of capital. The NPV rule easily handles both mutually exclusive and independent projects.

13.4 Internal Rate of Return

Internal rate of return (IRR)The discount rate where the NPV of an investment equals zero. is another widely used capital budgeting technique; essentially, it is the return we will receive over the life of our investment. It is calculated as the discount rate at which NPV equals zero. In other words, we set NPV equal to $0 and solve for r. This is the rate that makes the present value of the cash flows equal to the initial investment. Unfortunately, for some projects there is no easy way to arrive at this rate without using a “guess and check” method; thankfully, computers can do this quite quickly.

How do we know if the project is acceptable or not? Each project that uses internal funds has a cost of capital. If the rate we earn is more than the rate it costs us, then we should undertake the project as it adds to corporate value. If what we earn is less than what it cost us, then the project subtracts from corporate value, and we should not undertake it. To do this we compare IRR to the cost of capital. If the IRR is greater than the cost of capital we should undertake the project.

This decision criterion will only work if the cash flows are ordinary, meaning net outflows early in the project followed by inflows afterward. When cash flows are not ordinary, IRR can produce unusual, sometimes multiple, results.

Here are our decision rules:

IRR decision criteria (ordinary cash flows ONLY):

• If the IRR is greater than cost of capital (IRR > WACC) than accept the project
• If the IRR is less than cost of capital (IRR < WACC) than reject the project.

Let’s find the IRR for Gator Lover’s Ice Cream potential projects by taking a look at Table 13.2 "Gator Lover’s Ice Cream: Internal Rate of Return".

If our WACC is 10%, then both projects should be accepted. IRR is, however, not acceptable for mutually exclusive projects! To see why, consider the following example—Which investment would you rather have:

1. Invest $10,000 now and receive a guaranteed $20,000 in one year.
2. Invest $1 now and receive a guaranteed $10 in one year.

Investment A is double your money (IRR = 100%) while investment B is ten times your money (IRR = 900%). But investment A is on a larger starting sum! We’d love to do investment B over and over again, since it has the higher return, but if we can only pick one of the two, then A is superior. Thus, the higher IRR doesn’t necessarily indicate the better investment.

IRR can be calculated by hand, by a financial calculator, or in a spreadsheet. The keystrokes for a financial calculator are similar as those for NPV, but at the conclusion we ask for IRR instead of entering an interest rate. For example, IRR for Project A is as follows:

<CF> <2ND> <CLR WORK> −48000 <ENTER> <DOWN ARROW> 15000 <ENTER> <DOWN ARROW> 5 <ENTER> <IRR> <CPT>

The answer of 16.99% is returned.

To solve in a spreadsheet, the corresponding spreadsheet formula is:

=IRR(cash flows from period 0 to n)

Using the numbers for Project A, the spreadsheet function looks like this:

=IRR(−48000, 15000, 15000, 15000, 15000, 15000) = 16.99%

13.5 Other Methods

So far we have learned payback period, NPV and IRR. These three are the most widely used and methods to evaluate capital projects, and are sufficient for most companies, but many other methods exist. Here we’ll discuss two other methods: Profitability index and MIRR.

Profitability index (PI)Present value return per dollar of investment. shows the relative profitability of any project: in essence, a ‘bang for your buck’ calculation. It is the present value per dollar of initial cost. The higher the profitability index, the better, and any PI greater than 1.0 indicates that the project is acceptable because it adds to corporate value.

For Gator Lover’s the PI’s are as follows:

The profitability index is higher for Project A. PI doesn’t work as well if the initial investment is spread out over time, or if the cash flows aren’t ordinary, which is why we prefer NPV.

Our final method of evaluating capital projects worth discussing is modified internal rate of return (MIRR)Internal rate of return assuming that the funds earned cannot be reinvested at IRR.. IRR is the expected rate of return if the NPV = 0. This assumes that early inflows will be reinvested at the return of the project itself! Often, the funds earned from a project cannot be reinvested at IRR, but instead earn a lower rate. Therefore, IRR can overstate the expected rate of return. To compensate for this overstatement, modified internal rate of return (MIRR) was created. MIRR assumes that funds can be reinvested at the weighted average cost of capital (WACC) or some other specifically stated rate.

In our IRR example, we used a hurdle rate of 10%. But what if the inflows could only be reinvested at 8%? To calculate MIRR, we would use the 8%. Lucky for us, spreadsheets have a function to do this quite easily:

=MIRR(cash flows from period 0 to n, rate for outflows, reinvestment rate)

Project A MIRR (reinvested at 8%) = 12.89%

Project B MIRR (reinvested at 8%) = 11.63%

Compared with our original IRRs of 12.88% for Project A and 15.43% for Project B, it’s easy to see that the reinvestment rate has a large impact. Some shortfalls, however: it’s harder to calculate (esp. without technology), and requires knowledge of the WACC. If we have the WACC, however, why not calculate NPV?

13.6 Comparing Projects with Unequal Lives

Ruth is deciding which shingles to put on her roof. Shingle A costs $1 per sq. ft. and is rated to last 10 years. Shingle B costs $1.40 per sq. ft. and is rated to last 15 years. If Ruth intends to stay in her house for the rest of her life, which shingle should Ruth select?

One particularly troublesome comparison that arises often is when two repeatable mutually exclusive projects have different time lengths. For example, we can use a cheaper substitute, but it won’t last as long, so we’ll need to replace it more frequently. How do we know which project is better?

If the projects are either independent or not repeatable, we can use NPV confidently. All positive NPVs should be selected if they are independent, and the highest NPV will indicate the best choice if they aren’t repeatable. But it can be the case that the highest NPV project can be inferior to a shorter project with a lower NPV.

To analyze this problem, we need to calculate the equivalent annual annuity (EAA)The steady cash payment received by an annuity with the same length and NPV as the project., which is the steady cash payment received by an annuity with the same length and NPV as the project. For example, we know that Gator Lover’s Ice Cream Project A lasted for 5 years and had an NPV of $8,861.80 at a rate of 10%. If we solve for the yearly payment of an annuity with a PV of $8,861.80, r = 10%, n = 5 years, and FV = 0, we get an EAA of $2,337.72. Thus, we should be indifferent between receiving the cash flows of Project A and receiving $2,337.72 per year for 5 years (since they both have the same NPV)!

Once EAAs are calculated for all projects being considered, it’s a simple matter of picking the higher one.

13.7 Approaches for Dealing with Risk

We have estimated the potential earnings from our projects, but what about the risk involved? What’s the likelihood that we estimated these cash flows properly? What the numbers are much worse? Ideally, the sytematic risk involved with our project has been accounted for by our WACC used (see previous chapter for discussion of this), but managers still need to account for projection errors and evaluate the potential range of outcomes. There are several ways to deal with risk in capital budgeting. We present two of the most common here: scenario analysis and sensitivity analysis.

Sensitivity analysisIndicates how much NPV will change if we change one particular variable. measures the sensitivity of our project to a change in one variable. Also called “what-if” analysis, it looks at how sensitive our outcome is to a change in one variable (for example, projected sales). Intuitively we know that our outcome is more dependent on certain inputs to our equation than to other inputs. If we change just that one variable (holding everything else constant), how much does the outcome change? Sensitivity analysis tells us by how much are we more sensitive to a change in sales than we are to a change in, say, WACC or some other variable. We can then dedicate resources to ensure a more accurate estimate for the inputs with the larger effects.

Scenario analysisUses several possible scenarios to determine the range of possible NPV outcomes. gives us several different ‘scenarios’ or likely outcomes for our project. We can analyze what will happen if we have a best-case, worst-case and most-likely-case scenario. This measures the variability of the returns and can present us with a variety of situations and financial outcomes so that we are adequately prepared for each one. In scenario analysis we can change many variables and estimate a new outcome. We can then look at the ‘range’ of possible outcomes by analyzing the difference between the best-case and worst-case scenarios.

For Project A, we had annual cash inflows (after-tax) of $15,000 for five years. But what if our worst-case scenario occurred and the annual cash flows were only $10,000 per year? Or what if, best case, we earned $20,000 per year? What would our NPV be under each of these different scenarios? Let’s calculate.

From Table 13.4 "Gator Lover’s Ice Cream: Best Case, Worst Case, and Likely Scenarios", we see that our previous NPV calculation was the most likely case and it had a positive NPV of $8,861.80. The best case provides NPV equal to $27,815.74 and the worst-case has a negative NPV of $10,092.13. The NPV rangeThe difference between the best-case scenario and the worst-case scenario NPV. is the difference between the best case and the worst-case or in this situation a range of $37,907.87. We can hopefully earn somewhere between a negative $10,092 and a positive $27,815. Obviously we hope for the $27,815! But it’s helpful to know that we may lose $10,092 under the worst-case scenario.

There are several other techniques a company can use to deal with risk in capital budgeting. Other, more sophisticated techniques exist (such as simulation analysis), but they are beyond the scope of this text.

13.8 The Bigger Picture

In many ways, this chapter is the culmination of all that has come before in the text. All of our discussion has given us the tools to evaluate projects and be informed about the financial value of projects that we might undertake. Managers can use these criteria to approve positive value projects, which should increase the value of the company. In future chapters, we examine what make up the cash flows that we are analyzing, and how we might influence the inputs of a project.

Every successful business argument for going forward with a project should be rooted in the information presented in this chapter. While there might be considerations beyond the finances, without a financial valuation it is impossible for a manager to grasp the implication on stakeholders’ value.

13.9 End-of-Chapter Assessment Problems