Lecture 6: Capital Budgeting Part 1

C. L. Mattoli

This week

In the book, chapter 8.

Intro In the beginning of the course, we looked at

the 3 main decisions that financial managers of a company need to make: capital structure, capital budgeting, and WC management.

Capital budgeting or allocation is, probably, the most important of the 3 since it will determine the very character of the business.

Also, since the capital budgeting decisions are basically what the business invests its money in, we also call it the investment decision of the firm.

Intro There will be many potential investment

opportunities facing the firm. The firm will need to replace old equipment

and it might decide to purchase new equipment for a new business or to enter a new market.

These decisions are not only important, to begin with, but they cover a long future time horizon and they are not easy to reverse.

Decision under Constraint The investment decision must be made

subject to a number of constraints. One is, obviously, that the firm will have

limited funds to invest. There will be no information about market

value of the project. More important, though, is that the goal of

management is to maximize owner’s value in the business.

Of course, even that goal must be carried out under the other constraints of the real world.

Value We have learned that the proper way to value

things is using DFCF methods. In the present context, then, we should value

potential projects for the firm by discounting the expected cash flows of the project.

Projects will also have initial investment, startup costs.

Thus, our method of valuing a project will be to value it on DFCF, then, compare that value to how much it will cost to start the project.

Value This is the essence of the Net present

value (NPV) method of valuing business projects.

The NPV of a project is the difference between the DFCF value and the initial investment outlay (IO) , i.e.,

IO

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Whole worth more than parts The idea behind business investment is that the

whole is worth more than the parts. A business buys a machine, adds labor and

materials, and produces a final product for sale at a price above the price of inputs.

As a more common, simple example, consider buying an old house and renovating it.

You pay $100,000 for the house. You get estimates of $20,000 from the plumber, $10,000 from the electrician, $30,000 for plaster and paint.

Whole worth more than parts Assume that you also have estimates from

real estate agents that the house, if perfect, would sell for $200,000.

Then, adding your costs (assuming the time involved for the project is short and you can neglect time value), your estimated cost is $160,000 versus potential sale of $200,000.

Thus, you have combined input of materials and labor to produce extra value of $40,000 ($200,000 – $160,000).

Business investment value As we said, previously, business investment

is similar to the above example: the output is worth more than the input.

However, in the case of a business investment, there is a longer time frame for the project.

Thus, we expect multiple future cash flows, and we must account for the time value of cash flows.

Also, those future cash flows are just estimates.

Business investment value Moreover, they are more complicated cash

flows, involving estimates of future costs of inputs, like labor and materials, as well as estimated sales prices and volumes, in future years.

The original investment outlay will involve purchase of PP&E as well as estimates of other startup requirements of WC.

The final ingredient is a proper choice of the RRR that will give investors enough of a return.

A first example Assume Craig wants to add dress making to

his businesses. He buys a sewing machine for $1,000, and he

assumes that it will last for 5 years. Craig estimates his inflows (dress sales) and

outflows (costs) over the five years. At the end of the 5 year project, Craig

believes that he can resell the used sewing machine for $100 as scrap (or as a used sewing machine).

The cash flows Assuming that the proper RRR for Craig is

15%, then, we have the situation displayed in the table, below.

Time 0 1 2 3 4 5line            IIO -1000Inflows 500 500 500 500 500Outflows 200 200 200 200 200Net inflow 300 300 300 300 300Salvage 100Net CF -1000 300 300 300 300 400Discounted 261 227 197 172 199PV inflows 1055

The outcome In the above table, we assume that the RRR for

Craig’s businesses is 15%. As you can see from the table, the DFCF value of

the net inflows is $1,055. Thus, the NPV = $1,055 - $1,000 = $55, which

means that the project is estimated to add $55 in value to Craig’s business above his RRR over the period.

Alternatively, if NPV had turned out to be a negative value, it would subtract from the net worth of the business.

The NPV Decision Rule From the above example and discussion, we

can come up with a decision rule for using NPV.

Assume that the firm is in business and they already have a RRR demanded by their investors.

Indeed, given our discussion in Mod 4 (Securities valuation), shareholders will determine the value of the company’s stock based on DFCF valuation, using an appropriate RRR.

The NPV Decision Rule Then, a project with a positive NPV

will add value above the DFCF value of the firm, before taking on the project.

So, positive NPV projects should be accepted.

Alternatively, a negative NPV project will subtract value from the firm.

The NPV Decision Rule Thus, negative NPV projects should

be rejected. A zero NPV project will leave the

value of the firm unchanged, so it will neither add or detract from the value of the firm.

Thus, we would be neutral to taking on the project.

NPV & Risk An implicit assumption in the NPV methodology,

as we have described it, here, is that the risk of a project must be the same as the average risk of the firm.

We have chosen an “appropriate” discount rate to use in NPV that, as said earlier, is somehow connected to the rate at which investors discount the company’s CF’s to value its shares.

We have also learned, in the preceding module, that, in the marketplace for returns, there is a risk component to rates of return, in the market.

NPV & Risk It follows that the risk that investors

perceive in the firm has somehow been incorporated into their determination of the proper RRR for the firm.

As a result, when we use the RRR that is determined by those factors to calculate NPV of a project, the project must have the same risk as the general risk of the firm, or it will demand a different RRR.

NPV & Risk That can be a pretty stringent

requirement, if you consider the scope of projects and the scope of some firms.

For example, a new product would be a riskier than average venture.

On the other hand, a company that has a division that makes military tanks and another that makes chopsticks.

In such a company, the average risk will be different from the risks of each of its divisions.

NPV & Risk Indeed, the NPV method must be

revised to include different RRR’s for risks that are greater or less than average.

That kind of patch can be achieved by a number of formal and semi-formal means.

We leave further discussion of this to later.

A note on spreadsheet functions It is nice to have a bunch of built-in

functions in excel and other spreadsheet programs, but you should be on your guard.

In some cases, like for variance, which we shall cover later, there are several functions, and you should use the help function to find the one with the definition that you really want.

A note on spreadsheet functions In the case of NPV, the NPV function, in

excel, for example, is not the same as our definition. The excel function is actually just PV of multiple cash flows.

Thus, if you use a spreadsheet and you need to calculate NPV, you can use the NPV function, but you will have to additionally subtract out the initial investment outlay. Then, you will get the actual correct NPV, according to the true definition.

Payback Period: a non-DFCF rule There are a number of other decision rules for

investment. The first one that we cover is the payback

period, which does not account for time value.

Payback period is a natural concept that is examined in many different investment contexts.

In investment, we pay out money to buy an investment: our initial investment outlay.

Payback Period: a non-DFCF rule The payback period for an investment is

the amount of time, into the future, at which we, basically, break even, not accounting for time value, on our initial outlay.

Thus, to find the payback period, we subtract each years cash flow from the initial investment until it is completely recovered.

Payback Period: a non-DFCF rule In practice, the investment will probably

not be recovered in an integral number of years, but, instead, there will be a leftover amount in one year, which will be paid off in a fraction of a year.

For example, a payback period might be in 3 years, 4 months = 3 1/3 years.

In the next slide, we show the payback period calculation for our earlier project.

Payback Period Example The payback period is over 3 years but under

4. It is 100/300 = 1/3 year over 3 years.

Time 0 1 2 3 4 5line            IIO 1000Inflows 500 500 500 500 500Outflows 200 200 200 200 200Net inflow 300 300 300 300 300Salvage 100Net CF 300 300 300 300 400Payback paid 300 300 300

to go 700 400 100payback period =  3 1/3 

100/300 = 1/3

Payback Example In the example, we subtract year after year of

cash inflows from the original outflow. It takes 3 years of $300 of inflows to cover

$900 of the initial $1,000 outflow. Then, there is only $100 left, and that is less

than year 4’s cash flow. So, we take the leftover $100 and divide it by

year 4’s cash flow to find out what portion of a year it takes to cover the leftover.

Thus, our payback period is 3 1/3 years.

Payback Decision Rule As the payback period (PBP) analysis is not

formal, to begin with, being a non-DFCF tool, the decision rule is not a hard and fast rule.

Companies simply choose a rather arbitrary number of years, usually just a few, as an acceptable PBP.

The rule is, then, accept projects that have PBP’s equal to or less than the stated PBP of the company, and reject those that take more than the standard to pay back.

Pros & Cons of Payback PBP neglects time value and makes an

arbitrary cutoff hurdle rate for projects. If there is only one hurdle rate for PBP,

then, the riskiness of projects is also ignored.

One of the most salient faults of PBP is that it completely disregards any cash flows that come after break-even, i.e., (forgetting about time value) profits.

Pros & Cons of Payback In that regard, it really neglects any more

than just recovering your initial investment, which misses the very spirit of investment: to make a decent return on investment.

Many established and proper companies do use PBP, either as a supplemental number for decisions or for small projects.

The latter case is due to the costs of coming up with detailed estimates on which to bases more formal analyses, like NPV.

Pros & Cons of Payback Having a short PBP, like 2 years, will bias

acceptance to projects that pay themselves off, fast, and free up cash.

It should also tend to limit losses. In the end, just as in any method of analyzing

the future, we have to use estimates that might be so wrong, and that will be especially true as the years into the future increase. The PBP has a natural bias to the early years.

Average Accounting Return Another non-DFCF method is called the

average accounting return (AAR) of a project or the accounting rate of return (ARR).

There are a number of different definitions of AAR, but they all have the general form: [average accounting profits from investment]/[average accounting value of investment].

In this course, we shall use the specific definition: average net income/average book value.

ARR Example Consider renting space for a dress shop. Assume that renovation an fittings cost

$100,000. The building owner will only give you a 5

year lease, so the store will close at that time.

Assume that the initial investment is depreciated over the 5 years, straight-line.

ARR Example Then, the average investment will be

[$100,000 (IIO) + $0 (terminal BV)]/2 = $50,000.

The estimated net incomes for the 5 years are $50,000, $75,000, $25,000, $0, and – $10,000.

Then, the average profit is [$50K + $75K + $25K + $0 – $10K]/5 = $28,000.

Thus AAR = $28,000/$50,000 = 56%

ARR Decision Rule Just like the PBP, the ARR method is a rule

of thumb (a heuristic, in the newer language of behavioral finance).

The choice of a hurdle rate is somewhat arbitrary.

Given a specified hurdle rate for ARR, then, accept projects that make the hurdle, and reject projects that do not make the hurdle (or target) rate or benchmark.

ARR Expose ARR uses accounting numbers so it will not give

a representation of return that has meaning in the economic sense.

The numbers used in ARR do not account for time value, so they mix numbers from different times.

The numbers, moreover, are not even cash flows: they are profits.

Like PBP, a benchmark rate is arbitrary, although we could compute the ARR for the firm as a whole and use that.

Advantage: easy to compute wil readily-available accounting numbers.

Internal Rate of Return A second DFCF method that we shall

examine is internal rate of return (IRR). We already encountered the concept of IRR

when we looked at bonds: the IRR solves the coupon bond equation for YTM.

The IRR method is also related to NPV. With NPV we begin with a given value for

RRR, and we compare the DFCF from the investment with the price, IIO, that we pay for the investment.

Internal Rate of Return On the other hand, IRR finds the RRR that

makes DFCF exactly equal to IIO. In other words, IRR is the rate of return that

equates the present value of the project’s cash flows to the initial outlay of the project.

Thus, we can write the equation form of IRR as:

Then, the required rate of return that makes NPV=0 is the IRR.

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Finding IRR As noted in our discussion of finding YTM, IRR

can not, usually, be found, directly, but must be found either with a financial function on calculator or spreadsheet or by trial and error.

In our earlier example calculation of NPV, we used RRR = 15%, and we found that NPV was positive.

That means, if we were setting out to find IRR by trail and error, we know that the value is greater than 15% because that value of RRR made the sum of DFCF larger than the IO.

We used the IRR function in excel to find the IRR for our dress-making project and found IRR = 17.23%.

RRR vs. NPV In the chart below we show RRR vs. NPV for

our project, known as an NPV profile

Finding IRR using excel As mentioned earlier, be careful when using

spreadsheet functions to understand what they are and how to use them to get the answers that you need.

The excel function is of the form IRR(values, guess), e.g., IRR(E16:J16,0.1)

At least one of the values must be negative and one positive.

The guess is any number: it just needs an RRR to start the trial and error.

IRR Decision Rules Since IRR is the return that makes

NPV=0, we can translate the decision rules for NPV into IRR.

Thus, if IRR is greater than the hurdle RRR, accept the project.

If it is less, reject. If IRR = the hurdle rate, the position is

neutral. This is displayed graphically, in the chart

in the slide, above.

More detailed information The general rules for using IRR were

given in the preceding slide, but we must embellish them.

First, the project must be an independent project, not dependent on anything else.

If CF’s are negative in more than the initial year, the IRR problem has multiple solutions, not just one, which makes a decision difficult.

More detailed information Even the evenness of CF’s can affect the

usefulness of IRR, for example, if CF’s are weighted in the early versus the later years.

A general disadvantage of IRR over NPV is that when a multi-year project has a certain IRR, the implicit assumption in PV DFCF is that intermediate year CF’s must be reinvested at the IRR rate.

More detailed information NPV assumes that intermediate CF’s are

reinvested at the RRR, which, since the RRR is the return that is being achieved by projects of the firm, in general, there should be reinvestment opportunities, in the future, at that general rate.

However, for IRR, if the IRR is substantially above the RRR, it is not reasonable to assume that we can reinvest at that high rate through other future projects.

Mutually Exclusive Projects Projects can be mutually exclusive (ME). That means choosing one but not both (or

all). For example, you want to buy a new

computer for your business. You evaluate the CF’s of using IBM, HP, or Lenovo.

In the end, you need only one computer system, so, choosing one eliminates the others.

Mutually Exclusive Projects Often, the ME nature of projects is subtle,

and a problem might not tell you that the projects are ME ... Figuring that out will be part of the problem.

If projects are not ME, they are independent.

Once that you figure out that a set of projects is ME, then, the decision will be to choose the one that has the highest NPV or IRR or whatever your criterion is.

ME example CF’s for two projects, B & C, are shown,

below. The NPV of B is $147 and C is $106, using a

10% RRR. IRR’s for the projects are 17.01% for B and

13.06% for C.

Time 0 1 2 3 4 5Project B -1000 450 380 300 200 100Project C -1000 100 125 300 460 600

NPV Profiles for B & C

Example Analysis In the above slide we show NPV profiles

for the 2 projects. When the 2 profiles are displayed, we find

out that there is a region, lower RRR’s, where the NPV of project B dominates those for project C.

Then, after an intersection point where both NPV’s are the same, at higher RRR’s, the NPV’s are higher for C than for B.

Example Analysis Thus, it appears that, depending on

the choice of RRR, the NPV analysis will give different choices for the better project.

Moreover, since we already found IRR, which is a fixed number for each project, there can be conflicting decisions from IRR and NPV.

Example Analysis We can actually find the intersection point by

finding the IRR of the differential cash flows of the two projects, i.e., CFA – CFB in each year.

The result is intersection RRR = 7.30%.

Time 0 1 2 3 4 5Project B -1000 450 380 300 200 100Project C -1000 100 125 300 460 600Delta 0 -350 -255 0 260 500

The lesson for ME, IRR, and NPV It will always be more appropriate to use NPV

over IRR. People care more about the money that they

make, NPV, versus their returns on investment, especially when IRR might not be a good rate for reinvestment, anyway.

Thus, if there are conflicting opinions from IRR and NPV for ME, go with the choice given by NPV.

NPV versus IRR

Both are discounted cash flow techniques, so they are consistent with wealth maximisation

Both require detailed cash flow forecasts

Both give the same decision for independent projects with typical cash flow patterns

IRR Epilogue We have seen that NPV and IRR are

related. We have also seen that there are reasons

that NPV will win out over IRR, if there is a conflict, as can be the case in ME projects.

Still, many companies still use IRR because it gives a percentage return, which is, for some reason, easier for people to relate to than NPV dollar values.

IRR Epilogue An additional advantage of the IRR

is that it gives an indication of the ‘safety margin’ associated with a project. In particular, a higher IRR implies less risk of the firm being unable to recover its initial investment if projected cash inflows from the project prove to be too optimistic.

Example – IRR safety margin As an example of this, suppose two mutually

exclusive projects, C and D, with initial investments of $20,000 and $145,000, respectively, and a single net cash inflow after one year of $28,000 and $168,000, respectively.

If the cost of capital were 12% p.a., each project would have a NPV of $5000, and thus a firm would be indifferent between the two projects by the NPV criterion.

In tabular format, we have…………………..

Example – IRR safety margin C D

Initial Investment 20000 145000

Sole Cash Flow 28000 168000NPV (k=0.12) 5000 5000

However, project C has a greater safety margin in that the net cash flow at the end of one year could fall by up to approximately 28.6%

and the firm would still recover its investment. For project D, the net cash flow at the end of one year could only fall up to 13.7% if the firm were still to recover its investment.

The IRRs of projects C and D are 40% and 15.86% respectively, which gives an indication of the relative ‘safety margins’ associated with the projects.

286.0000,28000,8

137.0000,168000,23

The Profitability Index

The profitability index (PI) is similar to NPV, in that it compares the DFCF from the project to the cost, so it is also known as the cost-benefit ratio.

The PI is defined as PI = DFCF/IO, the discounted cash flow value of the project divided by the initial investment cost (outlay).

The Profitability Index If a project, for example, costs $1 million and

the DFCF value is $1.1 million, then, the PI = $1.1 million/$1 million = 1.1x

Thus, if PI > 1, accept; PI < 1, reject. However, the PI just gives a ratio, so there

might be cases for ME projects in which One has a higher PI but a lower actual NPV. Thus, in such cases, as was the case with IRR, the choice lies in the decision given by NPV.

Capital Budgeting Practice Although NPV seems to be the best method

for valuing profits, in that it is consistent with the goal of wealth maximization, it, after all, just based on estimates of future CF’s, which may or may not be realized.

In practice, many firms use NPV, but they also use other methods, even the non-DFCF methods, like PBP or ARR.

By using several methods, the firm is trying to cover the bases.

The textbook shows some results of surveys.

Summary Last week we learned techniques to figure

out how much we have to pay, in terms of investor returns (COC), to get money from investors

Now, we have to use that money for our business activities and invest it in business projects.

In order to stay in business, we have to be able to make at least as much money on our investment as we need to get to pay off our investors.

Summary Thus, our job becomes figuring out how to value the

investments that we make, in a manner that is consistent with how our investors value their money. In both cases, the answer is discounting future expected cash flow.

We, therefore, learned several techniques to value projects using discounted cash flow.

We also learned that we must adjust our thinking in deciding which cash flows to use and how to use them. We grouped these into several categories, like initial outlay (IO), Terminal Value, incremental intermediate cash flows, and changes in working capital.

Next week In the next module, we shall extend this

system of project selection and valuation to include some other factors, and we shall discuss the structure and process of capital budgeting, i.e., looking at the projects available and the money available and putting the two sides together in the real world.

That will also involve some additional techniques for comparing projects among themselves.

Learning activity

In chapter eight of the text (page 244), attempt

critical thinking questions 8.3 – 8.6 & 8.10 problems 1 – 7, 10, 15 parts a, b & c, 22, 25

and web questions 8.1 & 8.2.

END