Lecture Notes 3(1)

8/13/2019 Lecture Notes 3(1)

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Capital Budgeting Principles

and TechniquesLecture 3


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Net Present Value (NPV)

Net present value (NPV) is the sum of thepresent values of the projects future cash flowsminus the cost of the project.

Projects with positive NPVs add to shareholder

wealth; those with negative NPVs reduceshareholder wealth.

The net present value investment decis ionrule is invest in pos i t ive NPV projects and

reject negative NPV projects ! If two projects are mutually exclusive, accept

the one with higher net present value.


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Net Present Value Decision Rule The NPV rule is implemented as follows: Calculate the

present value of the expected cash flows generated by

the investment, using an appropriate discount rate, andsubtract from this present value the initial net cash outlayfor the project.

By taking into account all cash flows (and only cashflows), the time value of money, and risk (which isincorporated in the discount rate) NPV evaluates theprojects the same way that investors do. Therefore, it isconsistent with the objective of shareholder wealthmaximization.

The discount rate used in calculating an investmentsNPV, also called cost of capital or the required rate ofreturn, is the minimum acceptable rate of return onprojects of similar risk. It is determined by the requiredreturn in the market for investments of comparable risk.


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Net Present Value Formula The formula for NPV is

Net present Initial Present value ofvalue outlay future cash flows

where I0is the initial cash outlay, CFtis the net cashflow in period t, kis the cost of capital for the project,and nis the economic life of the investment.

= +

n

t

tt

n

n

k

CFI

k

CF

k

CF

k

CF

INPV

1

0

2

21

0

1

111

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Net Present Value Formula The initial outlay should include any investment in net

wo rk ing capi tal. Working capital refers to the money that

firm must invest in accounts receivable, inventory, and cashto support the sales and production of its products andservices. Initial investment in working capital must berecoveredat the termination of the project.

Net cash f lowis usually calculated as profit after tax, plusdepreciation and other non-cash charges, minus (plus) any

additions to (recovery of) working capital during the period,and minus (plus) capital expenditures (sales of fixed assets)during the period. This measure includes all project cashinflows and outflows and ignores non-cash items.Depreciation is added back to net income because it is anon-cash item.

Net CF= Profit after tax + Depreciation Change in networking capital Capital Expenditures

Net CF = (RevenuesCostsDepreciation)x(1T) +

Depreciation NWC CapEx, where T is the tax rate


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Application of NPV Rule Example:

Company ABC is considering a five year investmentproject which requires an initial investment in plant andequipment of $6 million.

The projects estimated revenue in year 1 is $8 million and$16 million in years 2 through 5. The projects estimated

costs in year 1 are $6.9 million and $12.1 million in years 2through 5. At the end of year five the plant will be scrapped and sold

for $1 million. Depreciation charges will be equal to $1 million each year.

Initial working capital requirement is $1.2 million which willbe recovered in year 5.

If the tax rate is 40% and ABCs cost of capital is 10%,what is the NPV of the investment project?


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Application of NPV Rule I0(Initial outlay) = $7.2 million

This includes the investment in plant and equipment of $6 million plus $1.2

million invested in working capital. Next estimate net cash flows

CF = (Rev. Cost Depr.)x(1 T) + Depr. NWC + Sale of plant

CF1= ( 8 6.9 1 )x(10.4) + 1 = 1.06CF2-4= (16 12.1 1 )x(10.4) + 1 = 2.74

CF5= (16 12.1 1 )x(10.4) + 1 + 1.2 + 1 = 4.94

Net cash flow in year 5 includes also cash received from the sale of the plant($1 million) and the recovery of net working capital ($1.2 million).Notice that the book value of the plant at the end of year 5 is exactly $1 millionbecause total depreciation amount for five years was $5 million and initialinvestment was $6 million. Since the plant is sold for its book value there are no

taxes associated with taxable gains or losses.

The project should be accepted since it has a positive NPV of $3.03 million

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Strengths and Weakness of NPV Rule NPV rule is consistent with shareholder wealth maximization. NPV obeys the value add i t iv i ty p r inc ip le. This means that

the NPV of a set of independent projects is just the sum of theNPVs of the individual projects

Value additivity principle implies that the value of a firm equalsthe sum of the values of its component parts. Consequently,when a firm undertakes a series of projects, its value

increases by an amount equal to the sum of the NPVs of theaccepted projects. This means that when confronted with mutually exclusive

projects, a firm should accept the one with the highest NPV asit will make the largest contribution to shareholder wealth.

The weakness of NPV is that many managers and non-

technical people have hard time understanding the concept.Time value of money and cost of capital are not intuitivelyobvious to most people.

Finally, NPV requires computation of a proper discount rate,which is not trivial as we will see later.


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Alternative Investment Evaluation Criteria

Although NPV is the theoretically correct technique for

evaluating investments, there are other capital budgetingmethods

These methods can be divided into two broad categories:non-discounted cash flow (non-DCF) methods anddiscounted cash flow (DCF) methods

Non-DCF methods: Payback

Accounting Rate of Return

DCF methods:

Discounted Payback Internal Rate of Return (IRR)

Modified Internal Rate of Return (MIRR)

Profitability Index (PI)


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Payback The payback per iod is the length of t ime

necessary to recoup the ini t ial out lay fromnet cash f lows.

From the earlier example of ABC company theinitial outlay is $7.2 million (including investmentin plant and equipment and working capital).

By the end of third year the cumulative net cashflow will be $1.06 + $2.74 + $2.74 = $6.54million. This leaves another $7.2 - $6.54 = $0.66million until payback. Assuming that cash flows

are spread evenly throughout the year, paybackwill occur in another 0.66/2.74 = 0.24 years. So payback period is 3.24 years.


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Payback: Decision Rule Decision rule is simple:

Projects with a payback less than a specified

cutoff period are accepted, whereas those with a

payback beyond this figure are rejected.

In our example, if ABC company has a three-year payback requirement then the investmentproject would be rejected, otherwise with a fouryear cutoff period the project would be accepted.

Usually the riskier is the project the shorter is therequired payback period.


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Payback: Strength and Weakness Payback is easy to understand and simple to

apply. However it has two major weaknesses: It ignores the time value of money.The timing of cash

flows is of critical importance because of time value ofmoney. Payback assigns the same value to a dollar

received at the end of the payback period as it does toone received in the beginning. It ignores the cash flows beyond the payback period.In

our example the project is expected to generate $7.68million in years 4 and 5; with a cutoff period of three

years these cash flows are ignored in evaluating theproject.

The payback method is biased against long-termprojects; if a quick payoff is not forthcoming, theproject will be rejected.


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Discounted Payback Period This is a modification of payback method which corrects one of its

weaknesses, the time value of money.

Discounted payback method is the length of t ime required for thepresent value of cash inf low s to equal the cost of ini t ia l ou t lay. Again, from the example of ABC company the present values of net

cash flows are as follows:

Year CF x PV Factor = PV Cumulative PV1 1.06 0.9091 0.96 0.962 2.74 0.8264 2.26 3.223 2.74 0.7513 2.06 5.284 2.74 0.6830 1.87 7.155 4.94 0.6209 3.07 10.22

The cumulative present value of the project at the end of year four is

$7.15 million. So the discounted cash back period is slightly over 4years. Again, this method ignores the cash flow in year five. If the required

cutoff period was 4 years this project would be rejected, although theproject would increase the value of ABC company by $3.03 million (itsNPV).


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Accounting Rate of Return Accounting rate of return(also known as average rate

of returnor average return on book valueor returnon investment) is the ratio of average after-tax profit toaverage book investment.

Average book value is calculated as the average of initial

outlay (including any investment in working capital) andthe ending book value, which is initial investment lessaccumulated depreciation (again including any recoveryof net working capital).

The formula is

2

valuebookEndingoutlayInitial

n

tyearinprofittax-After

returnofrateAccounting

n

1t


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Accounting Rate of Return After-tax profit can be calculated as

(RevenuesCostsDepreciation)x(1T) In our example of ABC company:

After-tax profit in year 1 == (86.91)x(10.4) = $0.06 million

After-tax profits in years 2 through 5 == (1612.11)x(10.4) = $1.74 million

Initial outlay (including working capital) = $7.2 million

Ending book value = $2.2 million (book value of the

plant of $1 million plus recovery of working capital of$1.2 million)

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orreturnofrateAccounting


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Accounting Rate of Return: Strengths andWeakness

To apply this method a firm must specify a target rate ofreturn. Investments yielding a return greater than thisstandard are accepted, whereas those falling below itwould be rejected.

The project in our example would be accepted if ABCs

target rate of return was less than 29.9%. This method is simple to apply, but

It ignores the time value if money.It treats income derived inyear 1 the same as it treats income in year 5, though earlierincome is more valuable than later one.

It is based on accounting income instead of cash flow.Investorsvalue only cash provided by companies; accounting income notassociated with cash flows cannot be spent (consumed) andtherefore is of no value to investors.


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Internal Rate of Return (IRR)

Internal rate of return (IRR)is the discount rate thatsets the present value of the project cash flows equal tothe initial investment outlay. In other words IRR is thediscount rate that sets NPV equal to zero.

IRR is the rate of return earned on money committed toa capital investment and measures theprofitabilityof theinvestment.

It is calculated as the rate of return kfor which

In our example of ABC company IRR is calculated as

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Decision Rule for Using IRR and itsStrength

If the IRR exceeds the cost of capital for the project, thefirm should undertake the project; otherwise the projectshould be rejected.

The rationale for this rule is that any project yielding

more than its cost of capital will have a positive netpresent value.

In our example ABC company should invest in its projectif the cost of capital is less than 22.4%.

The strength of IRR method is that many firms preferIRR because managers visualize and understand moreeasily the concept of a rate of return than they do theconcept of a sum of discounted dollars.


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IRR: Weaknesses1. Lending or Borrowing?

IRR does not differentiate between lending- andborrowing-type transactions.

With some borrowing-type transactions (where initialoutlay is positive while future cash flows are

negative) the NPV of the project is increasing as thediscount rate increasing.

This is contrary to the normal relationship betweenNPV and discount rate.

Project CF0 CF1 IRR NPV (k= 10%)A (lending) -100 +150 50% $36.36B (borrowing) +100 -150 50% -$36.36


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IRR: Weaknesses2. Multiple rates of return.

When an investment has an initial cash outflow, a series of

positive cash inflows, and then at least one additional cashoutflow (negative cash flow), then there may be more than oneIRR!

The number of solutions may be as great as the number of signreversals in the stream of cash flows.

Example: The following project has three IRRsYear 0 1 2 3 .Cash flow -$200 +$1,200 -$2,200 +$1,200

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IRR: Multiple Rates of ReturnNPV Profile of Previous Example: Multiple IRRs

-40

-35

-30

-25

-20

-15

-10

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0

5

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0% 40% 80% 120% 160% 200% 240% 280%

Discount Rate

Netpresentvalu

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IRR: Weaknesses3. Mutually exclusive projects.

In the case of mutually exclusive projects when the firm has tochoose either one project or another, NPV and IRR can favorconflicting projects.

Example: Consider the following two projects:Cash Flow for Project

Year A B .0 -1,000 -1,0001 800 100

2 300 4003 200 5004 100 800NPV (k= 17%) $81.2 $116.8IRR 22.99% 21.46%

NPV and IRR give conflicting results when discount rate is lessthan the crossover rate- rate at which NPVs of mutuallyexclusive projects are equal. Crossover rate in this example is19.78%.

NPV and IRR are most likely to give conflicting results whenthe mutually exclusive projects are substantially different (i) inthe timing of cash flowsor (ii) in scale.


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Crossover rate for Projects A and BNPV Profiles of Projects A and B, and Crossover Rate

-400

-200

0

200

400

600

800

1000

0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24% 26% 28% 30%

Discount rate

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Project B

.Crossover

rate


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IRR: Weaknesses3(i). Timing of Cash Flows

The conflict in the IRR and NPV rankings of projects Aand B arises because of differences in the timing of theircash flows, with most of As cash flows arriving in theearly years and most of Bs cash flows arriving in the

later years. The reason for conflicting rankings is that IRR implicitly

assumes that intermediate cash flows occurring duringthe life of the project can be reinvested at a rate equal toIRR, whereas NPV implicitly assumes a reinvestment

rate equal to the projects cost of capital. In such cases always trust NPV as it more realistically

represents the opportunity cost of funds.


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IRR: Weaknesses3 (ii). Scale Differences

Difference in the scale of projects (or difference in the

amount of initial investment) can lead to conflictingranking of projects.

Example: Consider the following two projects:

Cash Flow for Project

Year X Y .0 -100 -1,0001 140 1,250NPV (k= 15%) $21.8 $87.0IRR 40% 25%

NPV and IRR rules yield conflicting results. This isbecause NPV takes into account the size differences ininitial investment while IRR does not.

NPV rule in this case is correct, assuming there is nocapital rationing.


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Modified IRR (MIRR) Modified IRR solves some of the weaknesses associated

with IRR. MIRRis a discount rate at which the present value of aprojects annual cash outflows is equal the present valueof its terminal value, where the terminal value is found asthe sum of the future values of the cash inflows,

compounded at the firms opportunity cost of capital.

where COFrefers to cash outflows(negative numbers), or the cost ofthe project. And CIFrefers to cashinflows (positive numbers).

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Modified IRR: Calculation Lets go back to our old example of multiple IRRs and assume that the

cost of capital is 10%.Example: The following project has three IRRs.

Year 0 1 2 3 .Cash flow -$200 +$1,200 -$2,200 +$1,200

Present value at time 0 of all cash outflows is:2002,200/(1.10)2=2,018.18

Future value (at the end of projects life at time 3) of all cash inflows is:+1,200(1.10)2+ 1,200 = +2,652

We have separated all negative cash flows at time 0, and all positivecash flows at time 3.

Year 0 1 2 3 .

Cash flow -$2,018.18 +$2,652

The MIRR for this project is found as:

MIRR= 0.0953 or 9.53%(we have only one IRR here).

31

652,218.018,20

MIRR


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Modified IRR: Strengths andWeaknesses

Advantages of MIRR over IRR are that it: Solves the problem with borrowing-type projects (by

switching the places of negative and positive cashflows).

Solves the problem of multiple IRRs (by guaranteeingonly one cash flow sign reversal). Solves the problem with mutually exclusive projects

with differences in the timing of cash flows(byassuming intermediate cash flows are reinvested atthe opportunity cost of capital).

But, it still gives conflicting results with mutuallyexclusive projects with scaledifferences.


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Incremental IRR Since MIRR does not work with mutually exclusive projects

with scaledifferences, we can use incrementalIRR to make

a decision with such projects. Incremental IRR is the IRR of incremental cash flows.

If the incremental IRR exceeds the cost of capital, the firmshould undertake the larger project; otherwise the firm

should undertake the smaller project. Example. Assume k= 15%.

Cash Flow for ProjectYear X Y Incremental (YX) .0 -100 -1,000 -1000 - (-100) = -900

1 140 1,250 1,250 - 140 = 1,110NPV $21.8 $87.0 $65.2IRR 40% 25% 23.3%

Since Incremental IRR of 23.3% > 15%, accept larger

project.


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Profitability Index (PI) Profitability Index (PI), also known as the benefit-cost ratio, is the

present value of future cash flows divided by the initial cash

investment

The profitability index for ABC companys project is $10.23/$7.2 =1.42. In other words, this project returns a present value of $1.42 forevery $1 of the initial investment.

Decision rule:As long as profitability index exceeds 1, the projectshould be accepted.

Although for a given project NPV and PI give the same accept-rejectsignal, they sometimes disagree in the rank ordering of acceptableprojects when there are mutually exclusive projectsand when thereis capital rationing.

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Profitability Index: Mutually ExclusiveProjects

We already saw that when scale differences exist, NPV

and IRR may give conflicting signals. The same is true forPI.

Example: Consider again our old example with followingtwo projects:

Cash Flow for Project

Year X Y .0 -100 -1,0001 140 1,250NPV (k= 15%) $21.8 $87.PI 1.22 1.09

Though both NPV and PI give accept decision for bothprojects, they disagree about the ranking of these projects.

When there is a conflict of ranking the firm should selectthe project with the higher NPV (unless there is capitalrationing)!


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Profitability Index: Capital Rationing Capital rationingis a situation when firms constrain the

size of their capital budgets. Capital rationing may be

self-imposed or externally imposed. When constraints prevent the firm from undertaking all

acceptable projects, it must select among them thesubset of projects that gives the highest net presentvalue.

When all the initial outlays occur in the first period, asimple approach using PI is as follows: Calculate PI for each project,

Rank all projects in terms of their PIs, from the highest to the

lowest, Starting with the project having the highest PI, go down the list

and select all projects having PI>1 until the capital budget isexhausted.


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Profitability Index: Capital Rationing Example: A firm has a capital budget of $5,000 and the following

projects

Project Initial Outlay NPV Rank PI RankA 500 100 5 1.20 2B 500 70 6 1.14 6C 2,000 300 2 1.15 5D 3,000 480 1 1.16 4E 1,000 170 3 1.17 3

F 500 125 4 1.25 1

The projects selected under NPV rule are C and D with a combinedNPV of $780. Alternatively, PI selects projects F, A, E, and D with atotal NPV of $875.

NPV method does not necessarily select the best combination of

projects under capital rationing. PI method will select the optimal combination of projects if the entire

budget can be consumed by accepting projects in descending orderof PI. Projects are usually indivisible and applying the PI approachmay lead to an underutilized budget because the next availableproject might be too large. In this case PI method cannot be used.


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Mutually Exclusive Projects with DifferentEconomic Lives

Example: Finance Department has to choose between two copying

machines. Xerox costs $1,200, will last 5 years, and will require$300 of annual maintenance costs. Alternatively, Canon costs $750,will last only 4 years, and annual maintenance costs are $400.Which one should Finance Department choose?

One way to choose between these two machines is to compare thepresent values (NPVs) of their costs. Assuming 8% discount rate wehave:

Year Xerox Canon0 $1,200 $7501 300 4002 300 4003 300 400

4 300 4005 300NPV at 8% $2,398 $2,074

It looks like Canon is more preferable since it has higher NPV. Butthese two investments are not directly comparable because theyhave different economic lives.

M t ll E l i P j t ith Diff t


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One way to handle mutually exclusive investments with

unequal lives is to assume that at the expiration of theeconomic life of each asset, the firm will invest in newasset with identical characteristics. E.g., if we buy Xeroxtoday, we will replace it by Xerox again in 5 years. Thusdepartment will buy chains of Xeroxes or Canons.

Then we need to calculate equivalent annual cash flowof using mutually exclusive assets.

Equivalent annual cash flow (EACF)of an asset is anannuity that has the same life as the asset with presentvalue equal to the NPV of the asset.

It is calculated as:EACF = NPV/Present value annuity factor

nk1

11

k

1

NPVEACF

M t ll E l i P j t ith Diff t


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Buying a chain of Xeroxes is equivalent to paying $600 ayear, whereas a chain of Canons costs $626 a year.

Xerox is the preferred asset as its EACF is higher by $26. The rule for comparing mutually exclusive assets withunequal economic lives is: Compute the equivalentannual cash flow of each asset. Select the asset with thehighest equivalent annual cash flow.

600$

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S f C it l B d ti T h i


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Surveys of Capital Budgeting TechniquesUsed in Practice

Source: J. Graham and C. Harvey, How Do CFOs Make Capital Budgeting ANDCapital Structure Decisions? Journal of Applied Corporate Finance, Spring 2002

Lecture Notes 3(1)

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