valuation of cash flows investment decisions capital bud

• Explain why the NPV rule leads to optimal decisions • Compute the internal rate of return of an investment proposal.. 6.6 Comparing Projects with Different LivesSuppose a firm with a r

Global Financial Management

Valuation of Cash Flows Investment Decisions and Capital Budgeting

Copyright 1999 by Alon Brav, Campbell R Harvey, Stephen Gray and Ernst Maug All rights reserved No

part of this lecture may be reproduced without the permission of the authors.

Latest Revision: August 23, 1999

6.0 Overview:

This class provides an overview of capital budgeting - determining which investments afirm should undertake The net present value (NPV) rule, which is widely used inpractice, is developed and illustrated with several examples A number of alternativeevaluation techniques including internal rate of return and payback period are alsoillustrated, highlighting potential problems with their use The NPV technique isillustrated in the context of choosing between mutually exclusive projects and projectswith different lives

6.1 Objectives:

After completing this class, you should be able to:

• Compute the net present value of an investment proposal

• Explain why the NPV rule leads to optimal decisions

• Compute the internal rate of return of an investment proposal

• Explain the limitations of the IRR as an investment appraisal criterion

• Compute the payback period of an investment proposal

• Determine whether a particular investment proposal should be undertaken.

• Determine which (if any) of a set of investment proposals should be undertaken whenthe firm is capital constrained

• Determine which (if either) of two mutually exclusive investment proposals withdifferent lives should be undertaken

• Compute the appropriate cash flows to use in the NPV analysis

6.2 Projects and Cash Flows

Every decision the firm makes is a capital budgeting decision whenever it changes thecompany’s cash flows Consider launching a new product This involves a phase wherethe new product is advertised and distributed Hence the firm will have cash outflows forpaying advertising agencies, distributors, transportation services etc Then, for a period oftime, the firm has cash inflows from the sale of the product in the future Alternatively,consider the decision to make or buy a certain component the firm needs as an input itcurrently purchases from another company Making the input requires payments for laborand materials, but saves payments to the supplier, and all these cash inflows and outflowsare affected by that decision Many other decisions affect the company’s cash flows:

• Choice of distribution channel

• Purchases of buildings

• Choice of geographical location

• Purchase of another company or sale of a division

• Leasing or buying a certain piece of equipment

• Reducing dividend payments in order to pay down bank debt

The difficulty with making these decisions is that typically many cash flows are affected,and they usually extend over a long period of time Investment appraisal criteria help us

in analyzing capital budgeting decisions by aggregating the multitude of cash flows intoone number

But which cash flows? If we decide to make a component, should the cost of the factory

building where it is made be included? What about the salary of the sales manager if a

new product is launched? The answer to this question is clear and simple: All cash flows

have to be included in our analysis whenever they are affected by the decision! Hence,

if launching a new product implies hiring a new sales manager, then her salary isincluded If the sales manager would continue to be employed anyway, then her salary is

a cash outflow the company would incur even if the product were not launched, and thenher salary is not included Similarly, the factory building may have been there alreadywithout any other use for the firm (then don’t include it), or it could have been sold (theninclude foregone cash inflow from not selling it) Alternatively, it may exist, but using itfor making a component may force us to lease another building (then include these lease

payments) These cash flows are also called incremental cash flows, since they always

compare the cash flows for a base scenario (do not launch product, do not makecomponent) with an alternative scenario The differences of the cash flows in the baseand the alternative scenario are the incremental cash flows We denote these incremental

cash flows by X t, where Xt>0 indicates that the firm’s cash inflow increases in time t as a

result of the decision, and Xt<0 indicates the opposite Hence, from a point of view ofcapital budgeting procedures, a decision is completely characterized by the stream ofincremental cash flows:

L

We will often refer to cash flow streams like (1) as "projects", since the classical problem

for capital budgeting was an investment problem However, any decision that is reflected

in changes in the company’s cash flows can be analyzed using the techniques discussed inthis lecture

Analytically, characterizing the decision by a stream of cash flows as in (1) presents uswith two challenges:

• We have to estimate these cash flows X for all periods in the future where thedecision under consideration has an impact on the cash flows This impliesforecasting We turn to this problem in section 6.13 below

• We have to use some investment appraisal method in order to analyze decisionswhere X is positive for some periods, and negative for others We have to understand

the time value of money in order to proceed correctly We discuss the solution to this

problem in the following sections

• The incremental cash flows estimated here are typically uncertain, and we have totake into account that some cash flows are certain, whereas others depend on the state

of the economy We return to the problem of risk later in the course There we shallsee that we can take care of the riskiness of projects by using adequate discount rates

In this lecture we take the discount rate rP appropriate for a project P as given

6.3 Net Present Value (NPV):

The investment appraisal measure we wish to propose here is the net present value, orNPV The NPV of a project is defined as the present value of all future cash flowsproduced by an investment, less the initial cost of the investment

Let Xt denote the dollar cashflow in time t and N the number of such cashflows Inaddition let rp denote the required rate of return and I the initial investment outlay TheNPV is defined as:

∑

=

−+

t

I r

X NPV

In determining whether to accept or reject a particular projected, the NPV decision rule is

Accept a project if its NPV > 0;

Reject a project if its NPV < 0;1

In other words, we accept all and only those proposals that have a positive net presentvalue, and reject all others In order to illustrate the computation of Net Present Values,

we consider a series of examples

153.0

$100111.0

11

1

1001

r NPV

p

N p

6.4 Why Net Present Value?

In this subsection we wish to motivate why accepting all and only positive NPVproposals is the correct decision rule Suppose you have the following investment project:

Project Cash Flow -100.00 -50.00 30.00 200.00

The discount rate is 10% It is easy to see that the NPV of this project is 29.6:

06.291.1

2001

.1

301.1

However, what does this number really mean? The 29.6 is exactly the additional amount

of money shareholders can spend today if they take the project Suppose there is only oneshareholder who owns the above project, and she can borrow and lend at 10% Then shecan do the following if she takes the project

• Spend 29.6 today and borrow the money from the bank

• Repay the loan by using the project cash flows

The point is to see that the project covers her liability from the bank loan completely Tosee this consider the following table:

Year 1997 1998 1999 2000

Now, turn the argument around and suppose the project had a cash flow of 150 in theyear 2000, everything else remaining the same Then the previous table would become:

Hence, if shareholders take positive NPV projects, then they can consume more than theycould without the project If they accept negative NPV projects, they have to cutconsumption in order to be able to finance the project.

6.5 More than two alternatives

In many cases, a firm will be faced with a choice of between more than two alternatives.For example, a firm may be considering whether to construct an office building or ashopping mall on a parcel of land, or to sell the land, or deciding whether to refurbish anold apartment building or turn it into a parking garage, or leave it in its current condition

In this case, the NPV rule is to undertake the project with the largest NPV, so long as it ispositive

$000,27001

.0

1.11

79.790

$000,3000,11.0

1.11

5 5

of this decision is $790.79>0, hence this decision generates a positive NPV and we accept

it The next decision is to purchase machine B rather than machine A This decisiongenerates incremental cash flows that can easily be computed from the tables above as:

Buy Machine B rather than Machine A

Hence, calculating the NPV of this gives us $-157.24<0, hence this decision is incorrect,since it generates a negative NPV Note that starting with project B would give us apositive NPV for buying machine B, and also a positive NPV for buying machine Arather than machine B, hence we come to the same conclusion We can summarize as:

It is optimal to make decisions that generate positive net present values of their incremental cash flows If there are more than two alternatives, it is optimal to choose the alternative that generates the highest NPV.

6.6 Comparing Projects with Different Lives

Suppose a firm with a required rate of return of 10% is considering the acquisition of anew machine to produce its product It is deciding between Machine A and Machine B.Machine A has a useful life of the 3 years and machine B has a useful life of 5 years Thepresent values of cash inflows and outflows over the lifecycle of each machine are asfollows:

Should the firm choose Machine A or Machine B?

Machine B has a higher PV of cash inflows relative to outflows, but it also has a usefullife of 5 years versus the 3 year life of Machine A Suppose that the output produced bythese machines is required for a long period of time Since machine A is going to be used

to produce the firm’s output, it is reasonable to assume that it will be replaced at the end

of year 3 and thus its NPV above is understated Assume that the firm will use themachine indefinitely Hence, at the end of the machine’s useful life it will be replaced byanother identical machine Machines of type A are replaced on a 3-year cycle andmachines of type B will be replaced on a 5-year cycle

When we calculate the NPVs of the two alternatives it is important that the decision is toreinvest each machine NPVs relate to the decision to use a particular machine, not to thephysical machine as such One way to compute the relevant NPV is to compare theannual equivalent cash flows of the two alternative projects Machine A has a PV of

$2,000, but at the required return of 10% we would be indifferent between $2,000 at the

beginning of period zero and the annual equivalent (AE) of:

27.804

$1.0

1.11

( )

i i

1.11

30001

−

=+

−

i i

NPV

Therefore, we can now compare the annual equivalent cash flows of the two proposalsand the decision rule is to accept the proposal with the highest annual equivalent cashflow Here AEA > AEB so the firm should accept project A

The rule is that for mutually exclusive projects with different lives it is not appropriate tocompare the PVs of cash flows of one investment cycle directly We should, instead,convert these PVs to annual equivalent cash flows (AE) where:

( )

i i

6.7 Alternative Evaluation Techniques

This section outlines several alternatives to the NPV rule These evaluation techniquesinclude:

• Internal Rate of Return (IRR)

• Payback Period

• Profitability Index

6.8 Internal Rate of Return (IRR)

The internal rate of return, IRR, of a project is the rate of return which equates the netpresent value of the project’s cash flows to zero; or equivalently the rate of return whichequates the present value of inflows to the present value of cash outflows The internalrate of return (IRR) solves the following equation:

IRR

X

(11)

In determining whether to accept or reject a particular project, the IRR decision rule is

Accept a project if IRR > rp

Reject a project if IRR< rp

Here rp is the required return on the project Hence, the IRR rule reverses the logic of the

NPV rule When we compute NPVs, we calculate the NPV for a given discount rate on

the project, and accept a project whenever the NPV is positive If we use the IRR rule, wecalculate that discount rate that makes the NPV equal to zero Both methods are related

A typical investment proposal will have cash outflows from capital expenditure at thebeginning, followed by cash inflows Then the NPV is a decreasing function of the

discount rate Hence, if the NPV is zero for some discount rate, it is positive for alldiscount rates below that, and negative for all discount rates above this In this case bothmethods come to the same conclusion.

We illustrate the use of the IRR rule, and some of the pitfalls of this approach via a series

Is this a worthwhile investment?

The internal rate of return of this project is the rate of return that solves:

You can see that the NPV of the project decreases as you increase the discount rate TheNPV-function cuts the horizontal axis at the IRR of 21.86% in this case For all discountrates above 21.86% the NPV of the project is negative, for all discount rates below theIRR the NPV of the project is positive, and since the discount rate is 10%, the projectshould be accepted Both decision rules come to the same conclusion.

6.8 Problems of the IRR

Several other problems of the internal rate of return are apparent by considering thefollowing table

10%

NPV @ 20%

Problem 1: Different Time Horizons

If we compare projects A and B, we see that project A has the higher IRR, whereas B has

a higher NPV Here the IRR fails to recognize the fact that investing money in project B

ensures that we obtain a superior return over a much longer time horizon (two periods),whereas project B gives the high return only for one period If we use the IRR criterionfor choosing between A and B, we assume implicitly that we can reinvest the cash flow

of 8000 at the end of period 1 at 60% for another year The NPV criterion recognizes thefact that we can reinvest the 8000 only at the cost of capital

Problem 2: Multiple IRRs

The IRR gives us no way to distinguish between projects A, B and E Project E comeswith a huge liability at the end This can occur, e g if a machine has dismantling costs atthe end, or if a project requires substantial environmental repairs upon termination(example: open cast mining) Then the equation:

Problem 3: Different scales

If we compare projects A and D on the basis of their IRRs, we would choose project Aover project D, even though project A has a lower NPV The IRR does not take intoaccount the scale at which we operate these projects However, if we are not capitalconstrained we should always invest the project which maximizes wealth, even if itrequires a larger capital outlay (and if we were capital constrained, we should pursue adifferent strategy altogether) There is no reasonable sense in which we can say thatproject A is more efficient Project D generates more wealth and should be chosen

Problem 4: Different signs of cash flows

Projects B and C have exactly the same IRRs, but one has a positive and the other one anegative NPV The IRR criterion does not account for the fact that with project B wehave cash outflows first, and cash inflows later, and the opposite with project C.Effectively, project B is an investment, where we invest money up front in order toreceive a return later Project C is a financing opportunity, where we receive money firstand have to repay it later If we apply the IRR criterion, we basically say “the higher thereturn the better” However, for financing we want to use the opposite criterion: Thelower the IRR, the lower the costs of financing, and the better we are off This problem isnot really an inconsistency, and we can take care of it by modifying the IRR criterion:

• If cash outflows are followed by cash inflows (investments), accept the project if theIRR exceeds the cost of capital (cutoff rate)