Time out

13-11 There is another version of the PI that uses the present value of just the future cash flow as its numerator instead of the NPV. How would youexpected that version’s benchmark to change from the version of PI we initially discussed?.

13-12

Suppose you have a project whose discounted payback is equal to its termination date. What can you say for sure about its PI? ( Hint: What will the project’s NPV be?

Summary of Learning Goals

In this chapter, we apply time value of money (TVM) concepts to project valuation. While the mathematics here are very similiar to those used in the valuation of stocks, bonds, loans, the underlying intuition in valuing capital equipment project is very different. In project valuation, the main goal is to find project that convery enough monopoly power to the acquirer that they are worth more than they cost, even taking into account the cost of capital.

Of the capital budgeting techniques we have discussed, NPV is the hands-down winner, working equally well with normal or non-normal cash flows and with indepent or mutually exclusive projects. However, the NPV decision technique uses a statistic denominated in currency, which may not be the only pertinent unit of measurement if the firm faces time or resource constraints. In such situations, the additional capital budgeting techniques may provide valueable supplementary guidance in deciding whether to accept a project or not.

A summary of the relevant attributes and strengths and weakness of the various capital budgeting techniques is show down in table 13.16. As we can see, NPV does tend to be the most useful technique, but the others also have their place particluary for fimrs facing erither time or capital constraints.

Recent surveys asking practitioners which capital budgeting techniques they use in practice tend to support this idea, showing NPV to be the most frequently used techniques whwn making decisions.

However, the chocie of other techniques indicates that practitioners tend to favor the conceptually simpler techniques over the more complicated ones. For example, a recent survey by Ryan and Ryan of firms in the fortune 1000 indicates that, after NPV, IRR and regular payback are next most often used, with discounted payback, profitability index, and modified IRR being used the least. Their results are summarized in table 13.17

Analyze the logic underlying capital budgeting decision techniques.

All capital budgeting techniques attempt to achive the same thing, but they render different measurement units. Not only they do use different mesurements units, but almost all of them exclude some crucial informations and may thus give incorrect, inconclusive, or misleading answers.

The kind of “blurry” information with which to make decisions is especially evident when using rate-based decision rules to choose between or among mutually exclusive projects. Rate -based statistics represent summary cash flows, and those summaries tend to lose two important details: the investment size and cash inflows that occur after rather arbitary testing period.

Calculate and use the payback (PB) and discounted payback (DPB) methods for valuing capital investment opportunities. The payback technique tells us how long it will take the firm to earn bacj the money invested in a project . Discounted payback tells managers how log it will take to earn back the money invested pluys interest a market rates. Management can compute either statistic fairly easily, so PB adn DPB remain very popular techniques today. The techniques are particularly useful when firms face time constraints in repaying investors. Managers who are not quite comfortable with TVM principles feel more comfortable with PB and DPB. Neither method accounts for cash flows that occur after payback. Both methods are subject to managers sometimes arbitary maximum payback period as their benchmarks. Another way to describe these benchmarks is taht they are exogenously specified.

Calculate and use the net present value (NPV) method for evaluating capital investment oppurtunities. NPV is the best decision rule we have. This techniquehandles normal or non normal cash flows and independet or mutually exclusive projrcts well. Corporate decision makers do, however need to understand TVM principles thoroughly if they are to calculate decision statistics and then to comprehend exactly what the statistics say or don’t say.

Calculate and use the internal rate of return (IRR) and the modified internal rate of return (MIRR) methodsfor evaluating caopital investment opportunities. Managers find both the IRR and MIRR methods intuitively appealing, measuring what is best thought of as ‘expected’ rate of return to be earned from investing in a project. Unfortunately, the basic IRR statistic becomes unreliable when dealing with non-normal cash flows. The method may also choose the wrong project when it used to compare mutually exclusive projects with marked differences in timing and/ or scale of their cash flows.Third, IRR embodies a rather unreasonable assumption about the rate at which cash inflows from the project can be reinvested.

The MIRR decision rule explicitly alters IRR’s reinvestment rate assumption, implicitly curing any problems associated non-normal cash flows along the way. But, as a rate-based decision rule, it still suffers from invalidity when it is used to choose between or among mutually exclusive projects.

Use NPV profiles to reconcile sources of conflict between NPV and IRR methods. The main discrenpancy between the NPV choice and the IRR;’s/MIRR’s choice between mutuallly exclusive projects arises because of rate-based decision statistic attributes, which place undue preference for shorter-term, smaller projects rather than longer-term, larger-scale projects that might really give the firm a leg up. Since at times a rate-based decision metric is desirable but not necessaryly appropriate, we need to be able to explain exactly why the project with the largest IRR isn’t necessarily the best project.

Compute and use the profitability index(PI)

We presented a simple version of the profitability index that is simple arithmetic transsformation of the NPV into a rate-baseed decision statistic. Its one important attribute is that,

unlike the other rate-based statictics discussed in this chapter, it measures the excess return- the amount above and beyond the cost of capital for a project, rather than the gross return. Consequently, its appropriate benchmarks is zero, or anything larger than zero, rather than the cost of capital.

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Key terms

Discounted payback (DPB), A capital budgeting method that generates decision rules and associated metrics that choose project based an how quickly they return their initial investment plus interest. (p.341)

Interset-rate cognizant, A decision-making process that includes the cost of capital calculation. (p 445).

Internal Rate Return (IRR), A capital budgeting techniques that generates decision rules and associated metrics for choosing projrcts based on the implicit expected geometrics average of a project’s rate of return.(p.347)

Modified internal rate of return (MIRR), A capital budgeting method that converts a project’s cash flows using a more consistent reinvestment rate prior to applying the IRR decision rule. (p.441)

Mutually exclusive projects, Group or pairs of project where you can accpet one but not all. (p.443)

Net Present Value, A technique that generates a decison rule and associated metirc for choosing project based on the total discounted value of their cash flows. (p.434)

Normal Cash Flows, A set of cash flows with all outflows occuring at the begining of the set.. (p. 430)

NPV profile, A graph of a project’s NPV as a function of the cost of capital. (p.439)

Payback (PB), A Capital budgeting technique that generates decision rules and associated metrics for choosing projects based in how quickly they retutn their initial investment.(p.430)

Profitability Index (PI), A decision rule and associated methodology for converting the NPV statistic into a rate-based metric. (p.448)

Self test Problem with solution

Assume you are evaluating two mutually exclusive projects, the cash flows of which appear bellow, and that your company uses a cost of capital of 8 percent to evaluate projects such as these.

a. Calculate the payback of project Ab. Calculate the discounted payback of Project Ac. Calculated the IRR of Project Ad. Calculated the MIRR of Project A

e. At which rate do these projects’ NPV profiles cross?f. Using the NPV method and asuumong a cost of capitall of 8 percent, which of these project

should be accepted?

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QuESTIONS

1. Is the set of cashflows depicted below normal or non-normal? Explain2. Derive an accept/reject rule for IRR similiar to equation 13-8 that would make the correct

decision on cash flows that are non-normal. But ehich always have one large positive cashflows at time zero followed by a series of negative cash flows.

3. Is it possible for a company to initiate two products that target the same market there are not mutually exclusive?

4. Suppose that your company used APV or all the present value Except –CF” to analyze budgeting project. What would this rule’s benchmark value be?

5. Under what circumstances could payback and discounted payback be equal?6. Could a project’s MIRR ever exceed its IRR?7. If you had two mutually exclusive, normal-cash-flow projects whose NPV profiles crossed at

all ponits, for which range of interest rates would IRR give the right accept/ reject answer?8. Suppose a company wanted to double the firm’s value with the next round of capital

budgeting project decisions. To what would it set the PI benchmark to make this goal?9. Suppose a company faced different borrowing and lending rates. How would this range

change the way that you ompute the MIRR statistic?

Problems

13-1 NPV with Normal Cash Flows, Compute the NPV for Project M and accept or reject the project with the cash flows shown below the appropriate cost of capital is 8 percent.

13-2 NPV with Normal Cash Flows compute the NPV statistic for project Y and indicate whether the firm should accept or reject the project with the cash flows shown below if the appropriate cost of capital is 12 percent

13-3 NPV with non normal cash Flows compute the NPV statistics for project U and recommend whether the firm should accept or reject the project with the cash flows shown below if the appropriate cost of capital is 10 percent.

13-4 NPV with non-normal Cash flows compute the NPV statistic for project K and recommend whther the firm should accept or reject the project with the cash flows shown below if the appropriate cost of capital is 6 percent.

13-5 Payback compute the payback statistic for project B and decide whether the firm should accept or reject the project with the cash flows shown below if the appropriate cost of capital is 12 percent and the maximum allowablepayback is three years.

13-6 Payback Compute the payback statistic for the Project A and recommend whether the firm should accept or reject teh project with the cash flows shown below if the appropriate cost of capital is 8 percent and the maximum allowable payback is four years.

13-7

Discounted Payback compute the discounted payback statistic for project C and recommend whether the firm should accept or reject the project with thw cash flows shown below if the appropriate cost of capital is 8 percent and the maximum allowable discounted paback is three years.

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13-8 Discounted pAyback compute the discounted payback statistic for proect D and recommend whether the firm should accept or reject the project with the cash flows shown below if the appropriate cost of capital is 12 percent and the maximum allowable discounted payback is four years.

13-9

IRR compute the IRR statistics for the Project E and note whether the firm should accept or reject the project with the cash flows shown below if the appropriate cost of capital is 8 percent.

13-10

IRR compute the IRR statistic for project F and note whether the firm shoild accept or reject the project with the cash flows shown below if the appropriate cost of capital is 12 percent.

13-11 MIRR, Compute the MIRR statistic for project I and indicate o accept or reject the project with the cash flows shown below if the appropriate cost of capital is 12 percent.

13-12 MIRR compute the MIRR statistic for project J and advise whether to accept or reject the project with the cash flowa shown below if the appropriate cost of capital is 10 percent.

13-13

PI, Compute the PI statistic for Project Z and advise the firm whether accept or reject the peroject with the cash flows shown below if the appropriate cost of capital is 8 percent.

13-14

PI Compute the PI statistic for project Q and indicate whether you would accept or reject the project with the cash flows shown below if the appropriate cost of capital is 12 percent.

13-15 Multiple IRR s How many possible IRR could you find for the following set of cash flows?

13-16 Multiple IRRs How many posible IRRS could you find for the following set of cash flow?

Use this information to answer to next six questions. If a particular decision method should not be used, indicate why.

Suppose your firm is considering investing in project with the cash flow shown below, that the required rate of return on projects of this risk class is 8 percant, and that maximum allowable payback and discounted payback statistics for the project are 3.5 and 4.5 years, respectively.

13-17 Payback Use payback dicision rule to evaluate this project; should it be accepted or rejected?

13-18 Discounted Payback Use the discounted payback decision rule to evaluate this project; should it be accepted or rejected?

13-19 IRR Use the IRR decision rule to evaluate this project; should it be accepted or rejected?

13-20 MIRR use the MIRR dicision rule to evaluate this project; should it be accepted or rejected?

13-21 NVS Use the NVS dicision rule to evaluate this project; should it be accepted or rejected?

13-22 PI Use the PI dicision rule to evaluate this project; should it be accepted or rejected?

Use this information to answer to next six questions. If a particular decision method should not be used, indicate why.

Suppose your firm is considering investing in project with the cash flow shown below, that the required rate of return on projects of this risk class is 11 percant, and that maximum allowable payback and discounted payback statistics for your company are 3 and 3.5 years, respectively.

13-23 Payback Use the payback dicision rule to evaluate this project; should it be accepted or rejected?

13-24 Discounted Payback Use the discounted payback dicision rule to evaluate this project; should it be accepted or rejected?

13-25 IRR Use the IRR dicision rule to evaluate this project; should it be accepted or rejected?

13-26 MIRR Use the MIRR dicision rule to evaluate this project; should it be accepted or rejected?

13-27 NPV Use the NPV dicision rule to evaluate this project; should it be accepted or rejected?

13-28 PI Use the PI dicision rule to evaluate this project; should it be accepted or rejected?

13-29 NVP Profiles Graph the NPV profiles for both projects on a common chart, making sure that you identify all of the “ crucial “ points.

13-30 IRR Applicability For what range of posible interest rates would you want to use IRR to choose between these two projects? For what range of rates would you NOT want to use IRR?

13-31 Multiple IRRs Construct an NPV profile and determine EXACTLY how many nonnegative IRRs you can find for the following set of cash flows:

13-32 Multiple IRRs Construct an NPV profile and determine EXACTLY how many nonnegative IRRs you can find for the following set of cash flows:

Resesarch it! Business valuation

The capital budgeting decision techniques that we have discussed al have strength and weakness,But they comprise the most popular rules for valuing project. Valuing entire businesses, on the other hand, requires that some adjustments be made to various pieces of the methodologies. For example, one alternative to NPV used quite frequently for valuing firms is called adjusted present value (APV).

To explore these alternative decision rules, do a web search on google (www.google.com) for APV and answer the following questions:

1. What is APV, and how does it differ from NPV?2. What other business valuation models seem to be popular.

Integrated minicase Project Valuation

Suppose your firm is considering investing in a projectwith the accompanying cash flows, that the required rate of return on project of this risk lass is 11 percent, and the maximum allowable payback and discounted payback statistics for your company are 3 and 3.5 years, respectively.

Using every one of the capital budgeting decision methods discussed in this chapter, evaluate this project, indicating whether each decision rule would call for acceptance or rejection of the project.

Answer to time out13-1 Given that we are onlu going to be working projects with normal set of cash flows. The discounted payback will always be larger, as it will take longer for the present values time of the future, positive cash flows to sum to the initial cost than it will for the cash flow s themselves to do so.13-2 If the discounted rate is increased, the PVs of the cash inflows will decrease causing the discounted payback period to increase13-3 Because the cost is already include in the NPV; uisng it as the benchmark also would involve double-counting it.13-4 It should be equal to zero, because the cost of the bond to the purchaser should be exactly equal to the sum of the present values of the coupuns and the face value.13-5 No: If the cash flows are normal, some large interest rate has to exist at which the size of the present value of the future, positive cash flows becomes less than the initial negative cash flow.13-6 it should reject such a project would have the sums of the positive cash flows equal to the negative, initial cash flow which would have to result in a negative NPV given any positive interest rate.13-7 the project with the longer payback will have the lower IRR, as its cash flows will on avarage, be later than the other projects.13-8 only one, because there is only one change in sign of the cash flows: from nagative to positive between years 1 and 2.13-9 assuming the IRR exceeds the cost of capital, the MIRR should be less than the IRR because the MIRR uses a lower reinvestment rate assumtion.

13-10 you would solve the perpetuity formula for the interest rate by dividing the cash flow by the initial cost.13-11 it would use a benchmark of 1 instead of zero.13-12 it will have a PI and an NPV of zero.