# 5 Capital Budgeting and Wealth Creation

We now turn to a critically important aspect of finance called Capital Budgeting. Remember from our time value of money concept map that two of the types of problems TVM solves are “wealth accumulation” and “choosing among alternatives.”

We know that “cash is king” and that the value of a stock is the present value of the cash-flow the stock generates. Firms create and accumulate wealth by producing and selling products.

From your study of microeconomics you know that firms take the factors of production (land, labor, capital and entrepreneurship) and create products. They then sell these products to generate cash-flows. The expected cash-flows along with the discount rate associated with the firm determine the value of the firm to the stockholders. These ideas are illustrated in the figure below.

The firm raises capital from three basic sources:

    1. It borrows money from investors by selling bonds.
2. It raises money from selling stock to investors.
3. It uses money from past profits.


The firm uses these funds to bring together (create) a “project.”

It can pay for the project immediately, over time, or a combination of the two. In the diagram, the firm pays $10 million for the project today. The firm uses the project to make and sell its product, which results in cash-flows over time, as shown in the time line. The process of capital budgeting uses a variety of methods to determine whether pursuing this project would be beneficial to the firm’s stockholders. We will consider 4 different capital budgeting criteria.  1. Net Present Value (NPV) 2. Internal Rate of Return (IRR) 3. Modified Internal Rate of Return (MIRR) 4. Payback Period The first three methods follow directly from TVM techniques. Method 4 ignores the time value of money. Watch the video on Capital Budgeting before going on to the details of the techniques. ## 5.1 Net Present Value Net present value is the first capital budgeting technique we will cover. It is the technique preferred by finance academics because it most directly relates to the impact doing a project has on the stockholders. Net present value requires two inputs to the analysis 1. The expected cash-flows 2. The appropriate discount rate In this unit we will take each of these inputs as given. Net present value, or NPV, is simply the present value of the positive cash-flows (the benefits) minus the present value of the negative cash-flows (the costs). $NPV=PV(positive\;cash\;flows)-PV(negative\;cash\;flows)$ where the discount rate is related to the riskiness of the firm and/or the project. Let’s use the numbers from the Capital Budgeting diagram and assume the appropriate discount rate is 5%. The present value of the cost is just$10 million since the cost is already at today.

The present value of the positive cash-flows (the benefit) at 5% is $11.753 million (you should be able to calculate this). The NET present value is then$1.753 million ($11.753 million -$10 million).

We interpret an NPV = $1.1753 million as, “if the firm did this project, stockholder wealth would increase by$1.753 million.” Clearly, all else equal, the stockholders would want the firm to do activities that increased their wealth. In general, we have

If $$NPV \geq 0 \rightarrow$$ the firm should do the project

When the firm should do the project, we say that the firm “should accept” the project. If the firm should not do the project, we say the firm “should reject” the project.

You might think that if the NPV = 0 that the investor would be indifferent between doing the project or not doing the project since when NPV = 0 the stockholder wealth doesn’t change. We will see shortly in the mini-lecture that this intuition is not correct and that when NPV = 0 the investor should still do the project because the project earns the investor’s “hurdle rate.”

When the firm has a choice of different projects AND it can only pick one of the projects, we say the projects are “mutually exclusive.” This brings us to the next decision rule.

When deciding which project to do among mutually exclusive projects, the firm should pick the project with the greatest NPV that is greater than or equal to zero.

Watch and study the mini-lecture on how to do the NPV technique.

### 5.1.1 How to use your calculator for Capital Budgeting

How to use the cash-flow function in the BA II to calculate NPV.

To calculate the NPV for Project A

• Press CF then clear out all the work (press 2nd then CLR Work)
• For CF0 = enter -12,
• then hit Enter
• then hit the down arrow once (you’ll see C01)
• Press 5 then Enter (You’ll see C01 = 5.0000)
• then hit the down arrow twice (you’ll see C02)
• Press 5 then Enter (You’ll see C02 = 5.0000)
• then hit the down arrow twice (you’ll see C03)
• Press 2 then Enter (You’ll see C03 = 2.0000) (you’ve now entered the beginning cash-flow and the three following cash-flows)
• Press NPV (you’ll see I = )
• (enter the WAAC = Discount Rate) Press 5, then Enter
• Press the down arrow once (You’ll see NPV= )
• Then press CPT (you should then see NPV = -0.9753)

Which is the NPV of project A.

Calculate the IRR of Project B

Enter the cash-flows just like you would if you wanted to calculate NPV.

Instead of pressing “NPV” press “IRR” and then “CPT”

For project B you should get an IRR of 3.3791%

For project A you should get an IRR of 0.000%

Click here if you want to navigate to the end of the chapter, where you can get some practice calculating the NPV of a project using the practice questions widget.

## 5.2 Internal Rate of Return (IRR)

The second capital budgeting method for evaluating whether a firm should do a project is internal rate of return (IRR). Internal rate of return for a project is analogous to the YTM for a bond. YTM is the discount rate that sets the bond’s cash-flows equal to its price.

IRR is the discount rate that sets the net present value of the cash-flows of a project equal to zero. Formally we have:

where CF0 is the cost of the project and CF1 to CFN are the cash-flows from the project. You must use your financial calculators to solve for the value of IRR. The method you will use depends on what financial calculator you have. Check your manual for the specifics.

Interpretation of IRR

IRR is a return measure. We can use IRR to rank projects based on their return and also to compare the rate of return of a project to our cost of capital. The cost of capital (what it cost the firm to raise money from investors) can be viewed as a “hurdle rate.” The hurdle rate is just the minimum rate of return a project must earn for the firm to accept the project. A simple example will illustrate. Let’s say that you can borrow $1,000 from a bank for one year at simple interest of 5% (you will have to pay back the bank$1,050 in one year). You can invest the $1,000 in a project that earns 4% simple interest for one year. Would you invest in the project? No! If you invest in the project the$1,000 would only grow to $1,040 and you would owe the bank$1,050. You would lose $10. In this example, your cost of capital (hurdle rate) was 5%, but the project’s IRR was only 4%. With IRR, the rule for accepting the project is: If $$IRR \geq WACC \rightarrow$$ Accept project When the firm has mutually exclusive projects we use the decision rule: Among mutually exclusive projects, the firm should pick the project with the highest IRR that is greater than or equal to the firm’s WACC (weighted cost of capital). Why us IRR? IRR is often used because it makes it easy to compare a project to other investments, for example, bonds. If you have a project with an IRR of 5% and could invest in a bond with a YTM of 6%, you can easily compare the 5% to the 6%. However, IRR has its limitations. Limitations of IRR. One limitation of IRR is that it ignores the size of the project. We call this a “problem with scale.” An example will illustrate the idea. Let’s say I offer you one of two projects, A or B. Project A costs$1 and Project B costs $100. You buy project A and one year later it returns to you$1.50. Project A has a 50% return. Alternatively, you can buy project B for $100 and one year later it returns to you$110. Project B has a return of 10%. Even though project A has a rate of return five times as big (50% vs 10%) most investors would prefer project B because it increases their wealth by $10 and not just$0.50.

A second problem with IRR is that under certain patterns of the cash-flows (explained in the mini-lecture) it is possible to have more than one IRR for the same project. When this occurs, the IRR loses any of its economic interpretations. When there is more than one IRR, it should not be used for decision purposes.

A third problem of IRR is that when IRR > WACC the project under consideration is assumed to be earning a return in excess of a typical project of the firm (in equilibrium, on average, the firm’s projects will just earn the required rate of return which will equal the WACC). IRR assumes that as the cash-flows are received, they are reinvested at the IRR. This is not usually a good assumption. When a company has an exceptional project the cash-flows from that project get reinvested back in the company’s typical project. Under these conditions, the IRR overestimates the wealth creation of the project and overstates the actual return. We address this third limitation of IRR with MIRR.

Watch the following to gain further understanding of the above principles

Click here for: In-Class Exercise 19: Capital Budgeting – NPV and IRR

Click here if you want to navigate to the end of the chapter, where you can get some practice calculating the IRR of a project using the practice questions widget.

## 5.3 Modified Internal Rate of Return (MIRR)

Given the third problem with IRR, we introduce the technique of modified internal rate of return (MIRR). With MIRR we follow the following process:

1. Discount all of the costs (negative cash-flows) at the financing cost of the project (this may not equal the WACC for the company)

2. Take the future value of all the positive cash-flows to the time period of when the project ends using the company’s WACC.

3. Find per period return of the project.

An example will illustrate. Project A has the following cash-flows

The company finance this project at a cost of 4%.

The firm’s WACC is 5%.

What is the MIRR for this project?

First take the present value of all the negative cash-flows at 4% the cost of the project financing. In this case we have two negative cash-flows: the $5 million is already at today so we just need to bring the$2 back to today at 4%. Add these together and we have a cost in PV terms of $6.8491 Million. Next we bring all the positive cash-flows to the last day of the project (here period 4) by taking the future value of each at 5%, the WACC. We add these up to get a benefit of$9.776 million. Finally, we find the rate of return using our financial calculators

N = 4, PV = -$6.8491, PMT = 0, FV =$9.776 which gives us I/Y = 9.303%

Which means the MIRR is 9.303%.

Calculate the IRR for this same project. You should get 9.96%. The MIRR is lower than the IRR because with the MIRR we assumed that the positive cash-flows were reinvested at the WACC, while the IRR assumed that they would be reinvested at 9.96%.

For illustrations of the MIRR process watch the video below.

Click here if you want to navigate to the end of the chapter, where you can get some practice calculating the MIRR of a project using the practice questions widget.

## 5.4 Payback Period

Payback period is a capital budgeting technique that is NOT based on the time value of money. As such it is not favored by academics. However, payback period does provide some information.

Payback period concerns the notion of how quickly you will “recover your initial investment.” For example, let’s say you purchase a high efficiency air conditioner for $2,000 today. The new air conditioner will save you$100 per month off your electric bill. If I asked you how long will it take before you recover your purchase price of $2,000, you would say 20 months ($2,000/$100). The idea behind payback is that the once you get back your initial investment, the additional cash-flows are just “bonus” and the quicker you get back the original investment the better. Consider the following project. buy the project today for$50. In one year, the project pays you $10. So as of year 1 you have a net amount in the project of$40 (“you’re down” $40) One more year goes buy and the project pays you$13. So as of year 2 you have a net amount in the project of $27 (“you’re down”$27)

Continuing in this fashion, as of year 3 you are down $11. Therefore we know that since you have -$11 at the end of year 3 and +$8 at the end of year 4, it takes 3 full years plus part of year 4 to “break-even” on your investment of$40. Here, “break-even” means to just recover your initial investment (you invested $50 and got back$50).

With an additional assumption that the cash-flows are earned “evenly” throughout the year, we can determine how much of the 4th year is needed to break even.

The figure below summarizes the process. Between year 3 and year 4 your accumulated cash-flows go from negative to positive, therefore, you know that it take three full years, PLUS part of the 4th year to break-even (highlight year 3). The project needs to make-up the negative cash-flow in year 3 (highlight year 3’s cash-flow). In year 4, the project earns $19 (highlight the cash-flow in year 4). Now, the total number of years is 3 plus the fraction of$19 needed to cover the $11. In this case we have 3+$11/$19, or that it takes 3.58 years to recover your investment. Let’s do another example. What is the payback period for the following project? takes two full years plus$9/\$12 = 0.75 of the 3rd year, therefore the payback period is 3.75 years.

Watch the video below for additional worked out examples of payback period the above principle.