Lecture 5

Capital Budgeting

I. Types of projects

a. definition of project

b. mutually exclusive

c. independent

d. replacement

II. investment criteria

a. Net Present Value (NPV)

b. Payback, Discounted Payback

c. Accounting Rate of Return (AAR)

d. Internal Rate of Return (IRR)

e. Comparison of NPV and IRR

f. Profitability Index

Capital budgeting: the process of analyzing investment in long term assets (projects). A better description is strategic asset allocation, that is, how should the company's resources be allocated.

1. Types of projects

Projects can encompass almost anything that involves allocation of significant corporate resources. These may include which product or service to offer, whether to buy a new machine, or whether or not to buy a company. Referring back to our picture of the firm, capital budgeting has to do with what assets to put in the circle.

a. Project: is any potential real investment opportunity. We want to distinguish real assets from financial assets. Real assets create cash flows for the firm. Financial assets, such as stocks and bonds, are claims on the cash flows which are generated by the real assets.

b. Mutually exclusive: are projects such that if one is accepted, the others cannot be accepted (can do either, or, not both)

c. Independent: if projects are independent, then acceptance or rejection of one project has no effect on another (can do any or all).

d. Replacement: these projects examine whether we should keep an existing asset or replace it with a new one.

2. Investment criteria

Investment criteria are the methods or procedures by which we decide whether to accept or reject a particular project.

Assume: R=12% and Expected after-tax cash flows are:

a). Net present value: this method is precisely the same method we use to value financial assets. We first estimate the future cash flows associated with a project, and then discount those cash flows back to present values. The difference between the present value of the inflows and the present value of the outflows is called Net Present Value, or NPV for short. NPV also represents value added. The value of the company will change by the NPV amount.

(Note that net present value is simply economic cost-benefit analysis. Cash outflows are the costs and cash inflows are the benefits. The only difference is that the benefits and costs have to first be converted to present value dollars.)

If projects are independent, then the rule is to accept all projects which have a positive NPV. If projects are mutually exclusive, then the rule is to accept the project with the highest NPV. Note that this rule is consistent with the goal of maximizing the value of the firm.

We can define NPV as follows:

NPV =

where CFt = cash flow at time t and R = cost of capital. The above assumes the cash flow at time 0 is negative and other cash flows are positive. Cash flows can be positive or negative at any point in time, however.

Using the example above, NPV for project A and project B are below:

Discounted cash flows

If these projects were independent, then the firm would accept or do both of them. If the projects were mutually exclusive, the firm would accept project A.

b). Payback: involves calculating the number of years it takes to recover the initial investment. To compute payback, find where the cumulative cash flow becomes positive.

Cumulative cash flows:

Both projects recover the initial investment in the third year. To be more specific, we calculate the fraction of the third year as follows:

Project A: 2 + 500/3000 = 2 1/6 yrs;---------- Project B: 2 + 3000/3500 = 2 6/7 yrs

For independent projects the rule is to accept all projects which have a payback less than some predetermined number. For mutually exclusive projects, the rule is to accept the project with the shortest payback.

Problems with payback:

1) doesn't consider time value of money. Consider the following two projects and assume R=15% and our payback criteria is two years.

Payback: 2.5 for the `long' project 1.75 for the `short' project

NPV: 35.50 for the `long' project (11.81) for the `short' project

Besides ignoring the time value of money payback also ignores cash flows which occur after payback. In effect the `long' project's payback of 2.5 above ignores the cash flow in year 4. What is the effect on payback for project `long' if the cash flow in year 4 had been $10,000 instead of $100?

Some companies use payback however. The primary reasons are:

• it is easy to understand

• it is biased toward liquidity and implicitly adjusts for uncertainty of later CF's

• it may be `ballpark' correct

The time value of money problem can be solved by using discounted payback. Discounted payback first discounts (finds PV of) each cash flow, then calculates payback. A couple of comments about discounted payback. First, any project that `pays back' using discounted payback will have a positive NPV. Thus, some projects which do not satisfy an arbitrary payback cutoff but have positive NPV's may be rejected. Secondly, since discounted payback requires the same amount of information and steps as NPV, why not just use the NPV rule?

c). Average accounting return: is equal to some measure of average net income or profit divided by some measure of average investment. The problem with AAR is that a) it doen't consider the time value of money, and b) it focuses on income or profit rather than cash flow. In summary, it does not have any real economic meaning.

d). Internal Rate of Return (IRR): is that rate of return which causes the net present value of the project's expected cash flows to be 0. For independent projects the firm should accept all projects for which IRR exceeds the cost of capital. For mutually exclusive projects, the firm should select the project with the highest IRR.

In order to calculate the IRR you have to find the interest rate which solves the following equation:

0 =

You might note that this is exactly the same formula we used to calculate YTM if you substitute the price of the bond for CF0 and then moved it to the left-hand side. Therefore, just like YTM, there are two ways to solve for IRR:

1. trial and error

Pick a rate and then calculate NPV:

if NPV > 0 ==> try a larger %

if NPV < 0 ==> try a smaller %

2. Financial calculator or spreadsheet

In example above:

project b is easy to find ==> annuity w/ PV =10,000

project b: IRR = 14.96%

project a: try 15% ==> NPV = 10,465 > 0 ==> larger %

try 16% ==> NPV = 307 > 0 ==> larger %

try 18% ==> NPV = 5 ==> approx. 18%

• Independent => take both since IRR > cost of cap.

(18% and 14.96% > 12%)

• Mutually exclusive => take A, since IRR is higher

(18% > 14.96%)

Business executives like IRR because they are accustomed to thinking about rates of return and intuitively understand comparing the return on a project with the cost of capital.

Since business people are accustomed to thinking about rates of return, we should explore IRR a little further and compare it with NPV. It turns out that when the cash flow stream is non-traditional, that is not a cash outflow followed by several cash inflows, then IRR can give several answers or can give a misleading answer. This is the 'multiple solution' problem which is mentioned in most textbooks. Because NPV is always a correct criteria to use, we will compare NPV with IRR.

e) Comparison of NPV with IRR

If projects are independent, then NPV and IRR are mathematically equivalent and it does not make any difference which rule you use. To see this, consider the formula for NPV:

NPV =

Suppose that when we plug in the cost of capital for R in the above equation NPV is positive. We should do the project because the present value of the benefits (cash inflows) exceeds the present value of the costs (cash outflows). Now we want to calculate IRR. By definition IRR is the rate that causes NPV = 0. If discounting the cash flows at the cost of capital causes NPV to be positive, then we need to discount at a higher rate to cause the NPV to be 0. Therefore, whenever NPV is greater than 0, IRR is greater than the cost of capital. The two rules are equivalent.

Suppose instead that the projects are mutually exclusive. To compare NPV and IRR in this case it will be useful to construct a NPV Profile. A NPV Profile plots the NPV of a project at different costs of capital.

We can easily find three points for each project and then just connect the dots. The intersection with the vertical axis is the NPV when the cost of capital is 0. You simply add all the project cash flows to find this point. We also know the NPV when the cost of capital is 12%. We found previously that when the cost of capital is 12% project A has a NPV of 967, while project B has a NPV of 630. The intersection with the horizontal axis occurs when NPV = 0, which is the IRR. Project A intersects the axis at a rate of approximately 18%, while B intersects the axis at approximately 15%.

---- Graphed in class ----

There are a couple of other things to point out about this NPV profile. First of all, notice that the curve for project B is steeper than the one for project A. Recall that slope measures the `change in y' for a given `change in x.' Here we are looking at the change in NPV for a given change in R. Project B's cash flows are, on average, further away in time and hence are more sensitive to a change in the discount rate.

Secondly, note that for lower costs of capital, say 6%, project B has a higher NPV than project A. Thus, for a lower cost of capital NPV says choose project B, while IRR says choose project A. These are conflicting signals. We know from the previous discussion that NPV is always correct.

The reason IRR gives a different answer than NPV is a technical one. IRR is the same calculation as YTM and like YTM makes the same assumption about reinvestment of interim cash flows. That is, IRR assumes that interim cash flows can be reinvested at the IRR. NPV assumes interim cash flows can be reinvested at the cost of capital.

A similar problem occurs when two projects involve a difference in scale and IRR is used as an investment criteria.

Example: assume R = 10%

Based on the Internal Rate of Return (IRR), we would select project Y if these projects are mutually exclusive. However, Project Y's NPV = 818, while Project Z's NPV = 13,636

Project Z will add much more value to the firm. The problem here is, what is going to be done with the other 99,000. IRR in effect assumes the 99,000 can be invested at a 100% return.

Notice that we can divide project Z's cash flows into two parts, one of which is the same as project Y:

Project Z is the same as doing project Y, plus some other project having an IRR of 24% and a NPV of 12,818. You would only choose project Y if you could invest the other 99,000 in something at least this good.

f) Profitability Index (PI) - is the present value of cash inflows divided by the present value of cash outflows. The PI gives a measure of `bang per buck' or profitability per dollar invested. For mutually exclusive projects the rule is to take the project with the highest PI. For independent projects, the rule is to take the project with the highest PI. Note that whenever NPV > 0, the profitability index is greater than 1.

For our initial project A the PI is 1.0967 and for project B it is 1.063. For our last two projects Y and Z, the PI's are 1.818 and 1.12818, respectively.

The profitability index can also give misleading answers for mutually exclusive projects, as indicated by project Y and Z. It is true that the initial 1,000 invested is more productive or profitable for project Y, but the total value added is higher for project Z. PI is useful in situations involving capital rationing.

Summary:

As your book indicates, most companies will use several of these rules, though the trend has been toward NPV and IRR.

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