7330 Lecture 02.1 Capital Budgeting Complications F10

8/11/2019 7330 Lecture 02.1 Capital Budgeting Complications F10

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Advanced Corporate Finance

Capital Budgeting Complications

Finance 7330Lecture 2.1

Ronald F. Singer


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Making Investment Decisions

We have stated that we want the firm totake all projects that generate positiveNPV and reject all projects that have anegative NPV. Capital budgetingcomplications arise when you cannot,either physically or financially undertake all

positive NPV projects. Then we have todevise methods of choosing betweenalternative positive NPV projects.


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Mutually Exclusive Projects

Time Modify Replace Difference0 -100,000 -250,000 -150,0001 105,000 130,000 25,000

2 49,000 253,500 204,500IRR?


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2 49,000 253,500 204,500IRR .40 .30 .25

Assume the hurdle rate is 10%


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2 49,000 253,500 204,500IRR .40 .30 .25NPV(@ 10%) 36,000 77,700 41,700

Notice the conflict that can exist between NPV and IRR.


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EXAMPLES OF CAPITAL BUDGETINGCOMPLICATIONS

1. Optimal Timing2. Long versus Short Life

3. Replacement Problem4. Excess Capacity5. Peak Load Problem (Fluctuating Load)

6. Capital Constraints


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These Capital Budgeting Complicationswill stop the Firm from taking all possiblepositive NPV PROJECTS. Thus, the firmis faced with the choice of two possibilities.

Remember: Goal is still Max NPV of allpossibilities


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We can divide these problems into three separate classes,each with their own method of solutions.(1) Once and for all deal.

Choose the one alternative having the highest NPV.(2) Repetitive Deal.

Choose the one alternative having the highestequivalent annual cash flow.

(3) Capital Budgeting ConstraintChoose the combination of projects having the highestNET PRESENT VALUE.


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Once and For all Deals

INVESTMENT TIMING:When is the optimal time to take on aninvestment project? Consider T possible times,

where,t = 1, ...T. Then each "starting time" can be considered a

different project in a set of T mutually exclusive

projects. Then find that t which Max:NPV(t)(1+r) t


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Example You are in the highly competitive area ofproducing laundry soap and detergents. You have a newproduct which you feel does a superior job in washingclothes, but you anticipate that the product will have

difficulty being accepted by the consumer. Thus youexpect that if you introduce the product now, you willhave to suffer a few years of losses until the product isaccepted by the consumer. A competitor is about tocome out with a similar product. You feel that if you

allow your competitor to come out with the product first,you can benefit from the time he spends acclimatingyour potential customers. However, you will then begiving up your competitive edge.


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The initial investment in the product hasalready been spent, is a sunk cost and canbe ignored for this problem. Theanticipated life of the productive process isten years from the time the product is firstproduced. Thereafter, there will be so

much competition that any new investmentin this product will have a zero NPV. Thediscount rate is 15%.


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Once and For all Deals Expected cash flows are:

CASH FLOW ($ MILLIONS )year (fromstart ofproject 1 2 3 4-10

_______________________________________________immediately -4 -3 -2 20

If introduced afterone year -1 1 3.5 19.5

If introduced aftertwo years 0 2 4 19

WHAT SHOULD YOU DO?


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Once and For all Deals NPV(0) (Introduced Immediately) is: 47.649 million

NPV(1) (Introduced in one year's time) is: 55.531 millionNPV(2) (Introduced in two year's time) is: 56.118 million

WHICH ONE OF THESE THREE OPTIONS SHOULDBE TAKEN?47.649 55.531 56.118

| | |0 1 2 3 4 5

Calculate NPV from time 0.


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ShortcutCalculate the annualized rate of change ofNPV. If delaying causes the NPV toincrease by more than the discount rate,the project should be delayed. If not, theproject should not be delayed.


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Once and For all Deals Caution

This method assumes that the project cannot be reproduced at a positive NPV afterthe initial life of the project. Otherwise, you have to also account for the fact that theproject that is started earlier can also be reproduced earlier. In that case, thealternatives look like:

START IMMEDIATELY0 10 20 30

_______________________________

ONE YEAR DELAY0 1 11 21 31

_________________________________

THIS LEADS TO THE SECOND CLASS OF PROBLEMS:


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Repetitive Deals

Mutually exclusive projects with differentStarting Times

Mutually exclusive projects with differentEconomic Lives

Replacement Decision

Management of Excess of Peak Capacity


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Alternatives with Different Lives

Example: YOU HAVE THE OPTION OFUNDERTAKING ONE OF TWO DIFFERENTWAYS OF ACHIEVING SOME GOAL. WHICHONE SHOULD YOU TAKE?(A) A Bridge costing 5M lasts 15 years(B) A Bridge costing 4M lasts 10 yearsBoth generate $1 Million in net revenues per year.

Let the Discount rate = 12% for each alternative. NPV (A) = $1.81 Million

NPV (B) = $1.65 Million


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Alternatives with Different Lives

Conceptually The NPV rule would say, take the project

with the highest Net Present Value. Thismay be wrong.

Consider what happens after ten years.In particular by year 30.


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Alternatives with Different Lives A

1.81 1.81 1.81..... _____________________________________0 5 10 15 20 25 30 35

B1.65 1.65 1.65 1.65

_____________________________________0 5 10 15 20 25 30 35

PV(A) over infinite horizon:

PV(A) = 1.81 + 1.81 + 1.81 + = 2,214,900(1.12) 15 (1.1) 30 PV(B) over infinite horizon:

PV(B) = 1.65 + 1.65__ + 1.65__ + .. = 2,435,700(1.12) 10 (1.12) 20


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Alternatives with Different Lives This "Equivalent Annual Cash Flow" (or Cost) is aconvenient way of examining the host of complicated,

mutually exclusive capital budgeting problems listedabove: These all involve

A TIMING PROBLEM(1) When to start project(2) When to "cash in"

ForestryWine

(3) Replacement(4) Short vs. Long lived Project(5) When and how to increase capacity

Can all be dealt with in a similar way?


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Mutually exclusive projects withdifferent Starting Times

Instead of assuming that this is a once andfor all deal, assume that the alternativescan be reproduced indefinitely. Note thatthis case differs from the Laundry DetergentExample treated above:1. How?2. What impact will this have on the timingdecision?


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Consider an example: The mutually exclusive decision,when to cut down a forest:In ten years with NCF of 47,000In eleven years with NCF of 53,000

In twelve years with NCF of 58,000

If this were a one-time-only deal, you would simplycalculate the NPV of each alternative:NPV of cutting in ten years: 15,132.74NPV of cutting in eleven years: 15,236.23NPV of cutting in twelve years: 14,887.16


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But, more realistically, you will be able to continuecutting down these trees every ten, eleven, ortwelve years. Which is the best alternative as a

repetitive procedure? The question is, what is better:(1) receiving an annuity of 47,000 every ten years

(2) receiving an annuity of 53,000 every eleven years(3) receiving an annuity of 58,000 every twelve years


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For any set of reproducible mutually exclusive projects withdifferent lives, you can:Find the NPV of each project through one repetition, and then findits Equivalent Annual Cash Flow (EACF), and choose the one withthe highest EACF.Where EACF is calculated as: that fixed payment (annuity) having

the same value and life of the project.So:EACF(10) = 2,678.12

EACF(11) = 2,566.98

EACF(12) You know this isn't the right one since it has a lowerpresent value but takes longer to produce

Thus you want to take the shorter lived project now.


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Replacement Decision Return to the first example, you choose project (2), and

now you are in the fifth year of that project. The project,as expected, is returning $19.5 million this year. Butproduction difficulties have resulted in a machine which

is wearing out faster than anticipated. So that yourexpected cash flow for the next five years will be:

0 1 2 3 4 5Cash Flow 19.5 18 17 16 15NPV of operatingCash Flows 62.54 50.54 38.61 26.24 13.39


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Replacement Decision A new production technology has been devised

which will cost $100 million and generate $39million for the next 7 years, with an anticipatedscrap value of 3 million at the end of the seventh

year. Should you replace the machine now,never, or plan to replace it some time in thefuture?

It is assumed that the scrap value of the oldmachine will be 0 if not replaced during the next5 years (the life of the old project), but can besold for 3 million at any time during the next fiveyears. The discount rate is assumed to be 12%.


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Replacement Decision Find the equivalent annual cash flow for the new

machine, net of the current scrap value.Net Cash Flow of Replacement Machine

0 1 2 3 4 5 6 7-97 39 39 39 39 39 39 42

NET PRESENT VALUE 82.344 million

EQUIVALENT ANNUAL CASH FLOW: 18.043 millionIRR 35.56%


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Replacement Decision Replace in the beginning of year 2. Note, simply

comparing NPV will not give the right answer, neither willlooking at incremental cash flow. This is because thereplacement has a different life than the current processand they are obviously mutually exclusive.Furthermore, and more important, the alternatives ofreplacing now versus not replacing now is not theappropriate alternatives. You can also replace nextyear, the year after, etc. The alternative which gives thegreatest incremental value relative to all the otherpossible alternatives could be calculated by looking atthe incremental cash flows from each alternative. But itis easier to simply calculate the EACF and compare thatto the current cash flow to see what to do.


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Capital Rationing

In this situation, the decision maker is faced witha limited capital budget. As a result, it may notbe possible to take all positive net present valueprojects. Under this scenario, the problem is to

find that combination of projects (within thecapital budgeting constraint) that leads to thehighest Net Present Value.

The problem here is that the number ofpossibilities become very large with a relativelysmall number of projects. Thus, in order tomake the problem "manageable", we cansystematize the search.


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Capital Rationing

Since we have a constraint, what we want to dois invest in those projects which gives us thehighest BENEFIT per dollar invested. (Thehighest bang per buck). What is the benefit?, it

is the Present Value of the Cash Flows. So thatwe would want to choose that set of projectswithin the capital budgeting constraint that givesthe highest:

Net Present ValueINVESTMENT

This ratio is called the profitability Index.


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Capital Rationing

For example, suppose we have a $13 million capitalbudgeting constraint, with 7 alternative capital budgetingprojects with the following projections.

Project NPV Investment

A 10 15B 8 10C 4 2.5D 6 5

E 5 2.5F 7 5G 4.5 3


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Capital Rationing

Rank by Profitability Index {(NPV/INV}Project Profitability Index Investment Total

E 2.0 2.5 2.5C 1.6 2.5 5.0

G 1.5 3 8.0F 1.4 5 13.0D 1.2 5B .8 10

A .667 15

COMBINATION WITH HIGHEST PROFITABILITY INDEX WITHINTHE CAPITAL BUDGET

(E,C,G,F) has a NPV of $20.5 million, and a cost of $13 million.


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Capital Rationing

However, if the budget were 15 million rather than 13million we would have a problem. Adding D would goover the budget and be infeasible, but the combinationCDEF has a higher NPV ($22 million) than the chosen

combination of ECGF. This is because the amountspent was only 13 million leaving 2 million in unspentfunds. In this case, we are better off choosing acombination which spends all the funds.

THE ONLY WAY TO DO THIS RIGHT IS TO DO A FULLBLOWN LINEAR PROGRAMING PROBLEM WITHCONSTRAINTS.

7330 Lecture 02.1 Capital Budgeting Complications F10

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