capital budgeting rules

7/23/2019 Capital Budgeting Rules

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Capital Budgeting Rules: NPV, IRR,

Payback, Discounted Payback, AARCFA DECEMBER 15 EXAMS

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The material in this blog post is useful to the candidates preparing for:Level I of CFA Exams.

Today, we talk about an important topic that appears in corporate finance of level I which is the

criteria used for capital budgeting. That is, we talk about techniques used in deciding whether to

accept new projects or not: NPV, IRR, Payback, Discounted Payback, AAR.

Categories of Plans

1. Replacement Projects:decisions to replace old equipment those are among the easier of

capital budgeting techniques. It is important to decide whether to replace the equipment when

it wears out or to invest in repairing the machine.

2. Expansion Projects:These are decisions whether to increase the size of business or not

they are more uncertain than replacement projects.

3. New products and services:These are decisions whether to introduce new products and

services or not they are more uncertain than both replacement and expansion projects.

4. Safety and environmental projects:These are the projects required by governmental

agencies and insurance companies these projects might not generate revenue and are not

for profits; however, sometimes it is important to analyze the cash flows because the costs

might be very high that they require analysis.

Basic Principles of Capital Budgeting

Capital budgeting usually uses the following assumptions:

1. Decisions are based on cash flows not income

2. Timing of cash flows is important
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3. Cash flows are based on opportunity cost: cash flows that occur with an investment

compared to what they would have been without the investment

4. Cash flows are analyzed on after-tax basis:

5. Financing costs are ignored because they are incorporated in WACC that is why counting

them twice would be considered double counting

Costs Concepts of Capital Budgeting

Some important capital budgeting concepts that managers find very useful are given below:

1. Sunk costs:costs that already incurred (i.e. paid for marketing research study) Today costs

should not be affected by sunk costs

2. Opportunity costs:what a resource is worth for next-best use Those costs should be

considered (i.e. if you use a warehouse, the current market value should be considered)

3. Incremental cash flow:the cash flow that is realized with the project that is, the cash flow

with a decision minus the cash flow without the decision

4. Externality:the effect of an investment on other things apart from the investment. Those can

be positive or negative and should both be considered.

Cannibalization is an example of an externality where an investment takes customers andsales from another part of the company those should be considered in the analysis because

they are incremental cash flows (i.e. they wouldnt occur unless for the project)

More about projects

Some important comparisons in capital budgeting are:

Conventional versus nonconventional cash flows:

Conventional:Initial outflow followed by series of inflows (i.e. change of sign only occurs

once). That is, you can have + + + + + +, + + +, or + and still be considered

conventional cash flows because the sign changes only once.

Nonconventional:Initial outflow followed by series of inflows and outflows (i.e. change of

sign occurs more than once). Examples of those include + + + -, + + -, or + + +.

Independent versus mutually exclusive projects:


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Independent projects:Cash flows are independent of each other. You can use both A and

B; there isnt overlap between projects. Projects here are being evaluated that could potentially

all be selected as long as their projected cash flows will produce a positive NPV or generate an

IRR greater than the firms hurdle rate.

Mutually exclusive projects:Projects that compete directly with each other (i.e. you own

some manufacturing equipment that must be replaced. Two different suppliers present a

purchase and installation plan for your consideration). Sometimes there are more than two

projects and you select one from group.

Unlimited funds versus capital rationing

Unlimited funds:It assumes the company can raise funds for all profitable projects.

Capital rationing:It exists when a company has fixed amounts of funds to invest. If the

company has more project than funds, it must allocate the funds among the projects.

Project sequencing:

One last important concept here is project sequencing where many projects are evaluated

through time; that is, investing in one project gives the option to invest for other projects in the

future. For example, you can decide to open a mall this year and if the financial results are

favorable after 5 years, you will build a hotel next to the mall.

Investment Decision Criteria

We need to ask ourselves the following questions when evaluating decision criteria:

1. Does the decision rule adjust for the time value of money?

2. Does the decision rule adjust for risk?

3. Does the decision rule provide information on whether we are creating value for the firm?

Investment Decision Criteria: (1) Payback Period

Payback is the number of periods after which the initial investment is covered. The main question

used in the payback period is: how long does it take to get the initial cost back in a nominal sense?

Computation Method:

1. Estimate the cash flows


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2. Subtract the future cash flows from the initial cost until the initial investment has been

recovered

Decision Rule:

The decision rule is to accept if the payback period is less than some preset limit.

Pros and Cons:

Pros Cons

1. Easy to understand.

2. Biased towards liquidity.

1. Ignores the time value of money.

2. Uses an arbitrary cutoff oint.

!. Ignores cash flows beyond the cutoff date.

". Biased against long#term ro$ects such as %&' and n

Example:

Estimate the payback period for:

Year 0 1 2 3 4

CF #1()((( ")*(( ")*(( !)((( 2)(((

Solution:

To find the payback period, we need to find the cumulative cash flows first

Year 0 1 2 3 4

CF #1()((( ")*(( ")*(( !)((( 2)(((

CCF #1(((( #**(( #1((( 2((( "(((

The payback period occurs when the cumulative cash flows changes from negative to positive. That

is, it occurs between years 2 and 3. Because we still have to recover 1000 after second year, the

payback period is: 2 + 1000/3000 = 2.33 years.


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Investment Decision Criteria: (2) Discounted Payback Period

Discounted payback is the number of periods for the cumulative discounted cash flows to recover the

initial investment. The main question used in the discounted payback period is: how long does it take

to get the initial cost back in a real sense?

Computation Method:

1. Estimate the cash flows

2. Discount these cash flow

3. Subtract the future discounted cash flows from the initial cost until the initial investment has

been recovered

Decision Rule:

The decision rule is to accept all projects with the discounted payback period less than a preset

limit.

Pros and Cons:

Pros Cons

1. Considers time value of money.

2. Easy to gras.

!. Biased towards liquidity.

1. If you discount values) then you might want to use +P

discounted aybac- wont be easier to analy/e.

2. It may re$ect ro$ects with +P, 0 (.

!. Uses an arbitrary cut#off oint

". It ignores cash flows after cut#off oint.

*. Biased against long#term ro$ects new %&' ro$ects

Example:

Estimate the discounted payback period at 10% discount rate for:

Year 0 1 2 3 4

CF #1()((( ")*(( ")*(( !)((( 2)(((


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Solution:

To find the discounted payback period, we need to find the cumulative discounted cash flows first:

Year 0 1 2 3 4

CF #1()((( ")*(( ")*(( !)((( 2)(((

DCF #1()((( ")(3(.31 !)413.(1 2)2*!.3" 1)!55.(!

CDCF #1()((( #*)3(3.(3 #2)13(.(6 5!.65 1)"23.63

The discounted payback period occurs when the cumulative discounted cash flows changes from

negative to positive. That is, it occurs between years 2 and 3. Because we still have to recover

2,190.08 after second year, the payback period is: 2 + 2190.08/2253.94 = 2.97 years.

Investment Decision Criteria: (3) Average Accounting Return

There are many different definitions for average accounting return. The most commonly used one is

the average net income to average book value. Note, however, that the average book value depends

on how the asset is depreciated.

Computation Method:

1. Estimate the net incomes

2. Estimate the book values

3. Estimate average net incomes

4. Estimate average book value (i.e. for straight-line depreciation, average book value is

[historical value salvage value]/2)

Decision Rule:

We accept the project if the AAR is greater than a preset rate.

Pros and Cons:

Pros Cons


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1. Easy to calculate.

2. +eeded information will usually be available.

1. It is not a true rate of return.

2. 7ime value of money is ignored.

!. Uses an arbitrary cut#off oint.

". Based on accounting net income and boo- values) not

and mar-et values.

Example:

Assume a company invests 400,000 in project depreciated using straight-line method over 4 years

with zero salvage value. The following table shows the revenues and operating expenses. CalculateAAR using 40% tax rate:

Year 1 2 3 4

Revenue 2(()((( 2*()((( !(()((( !2()(((

Operating Expenses 3()((( 1(()((( 12()((( 3()(((

Solution:

First, we find the net income where depreciation = (book value salvage value)/ useful life.

Deprecation is 400,000/4 = 100,000

Year 1 2 3 4

Revenue 2(()((( 2*()((( !(()((( !2()(((

Operating Expenses 3()((( 1(()((( 12()((( 3()(((

Depreciation 1(()((( 1(()((( 1(()((( 1(()(((

Taxes = 0.4 (ROED! ")((( 2()((( !2)((( *2)(((


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"et #nco$e 5)((( !()((( "6)((( 46)(((

Average net income = (6,000 + 30,000 + 48,000 + 78,000)/4= 40,500

Average book value = (400,000-0)/2= 200,000

Investment Decision Criteria:

(4) Net Present Value (NPV)

The net present value (NPV) is the present value of future after-tax cash flows minus initial

investment. It reflects the difference between the market value of the project and its cost.

Computation Method:

1. Estimate the expected future cash flows.

2. Estimate the required return for projects of this risk level.

3. Find the present value of the cash flows and subtract the initial investment.

WhereCFtis the cash flow at timet,ris the discount rate

for the investment and outlay is the investment cash flow at time 0.

Decision Rule:

We accept the project if the NPV is greater than zero. A positive NPV means that the project is

expected to add value to the firm and will therefore increase the wealth of the owners. Since our goal

is to increase owner wealth, NPV is a direct measure of how well this project will meet our goal.

Pros and Cons:

Pros Cons

1. +P, gives imortance to the time value of money.

2. In the calculation of +P,) both after cash flow and before cashflow over the life san of the ro$ect are considered.

1. +P, is difficult to use.

2. +P, cant give accurate decision if the amount of invmutually e8clusive ro$ects is not equal.


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!. Profitability and ris- of the ro$ects are given high riority.

". +P, hels in ma8imi/ing the firms value.

!. It is difficult to calculate the aroriate discount rate

". +P, may not give correct decision when the ro$ects

unequal life.

Example:

Estimate the NPV at 10% discount rate for:

Year 0 1 2 3 4

CF #1()((( ")*(( ")*(( !)((( 2)(((

Solution:

Investment Decision Criteria: (5) Profitability Index (PI)

The profitability index (PI) is very closely related to net present value (NPV). It is the present value ofcash flows dividend by the initial investments.

Computation Method:


2. Estimate the required return for projects of this risk level.

3. Find the present value of the cash flows and divide by the initial investment.

WhereCFtis the cash flow at timet,ris the discount rate for the investment

and outlay is the investment cash flow at time 0.

Decision Rule:


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We accept the project if the PI is greater than one. PI greater than one means that the project is

expected to add value to the firm and will therefore increase the wealth of the owners.

Pros and Cons:

Pros Cons

1. PI hels in ma8imi/ing the firms value.

2. PI is useful in cases of caital rationing.

1. PI cant give accurate decision if the amount of investmutually e8clusive ro$ects is not equal.

2. It may not be easy to understand.

Example:

Estimate the PI at 10% discount rate for:

Year 0 1 2 3 4

CF #1()((( ")*(( ")*(( !)((( 2)(((

Solution:

Investment Decision Criteria: (6) Internal

Rate of Return (IRR)

This is the most important alternative to NPV; it is often used in practice and is intuitively appealing.

It is based entirely on the estimated cash flows and is independent of interest rates found elsewhere.

Computation Method:


2. Estimate using trial and error the discount rate that makes NPV = 0

Written out in an equation form,


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Decision Rule:

Accept the project if the IRR if it is greater than the required return.

Pros and Cons:

Pros Cons

1. 9nowing a return is intuitively aealing : managers li-e to hearreturns.

2. It is a simle way to communicate the value of a ro$ect to

someone who does not -now all the estimation details.

!. If the I%% is high enough) you may not need to estimate arequired return) which often is a difficult tas-.

1. Unrealistic assumtion of reinvestment at I%% : unli-which assumes reinvestment at ;


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Therefore, the discount rate that makes NPV = 0 is between 17% and 18%. Keeping trial and error,

then IRR = 17.43%

IRR Alert

When using the IRR rule you have to be very careful from which standpoint you evaluate theinvestment: investor or financier.

EXCEL FILE

This file can be used to solve problems related to capital budgeting techniques. In the first sheet, and

after entering conventional stream of cash flows for maximum of 15 periods, the file will solve for

payback period, discount payback period, NPV and IRR; it also shows the NPV profile. In the second

sheet, you can find average accounting return for a project given its estimated revenues, operating

expenses and book value.

Which investment decision criteria to use?

Whenever in conflict, always use NPV. This is because NPV (1) is based on cash flows not

accounting data, (2) assumes reinvestment rate at WACC and (3) does not require arbitrary cut-off

point. These all are improvements over the other capital budgeting techniques. It is important to note

that NPV and IRR will generally give us the same decision except when:

1. Nonconventional cash flows cash flow signs change more than once

2. Mutually exclusive projects

Initial investments are substantially different

Timing of cash flows is substantially different

Before showing the conflict between NPV and IRR, we must first discuss the concept of NPV profile


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Caital Budgeting #

=olved Problems%atings>(?,iews> 21)4*6?@i-es> 55

Published byAimanshu =harma

=ee more

FINANCIALMANAGEME

NTSolved

ProblemsRushi Ahuja1SOLVED PROBLEMS CAPITAL BUDGETINGProblem 1
https://www.scribd.com/himanshus_73https://www.scribd.com/himanshus_73https://www.scribd.com/himanshus_73


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The cost of a plant is Rs. 5,00,000. It has an estimatedlife of 5 years after which it would be disposed o !scrapvalue nil". Pro#t before depreciation, interest and ta$es

!P%IT" is estimated to be Rs. &,'5,000 p.a.(ind out theyearly cash )ow from the plant. Ta$ rate *0+.Solutionnnual depreciation char-e !Rs. 5,00,0005" &,00,000Pro#t before depreciation, interest and ta$es &,'5,000/ epreciation &,00,000Pro#t before ta$ '5,000Ta$ 1 *0+ 22,500Pro#t after Ta$ 52,5003 depreciation !addedbac4" &,00,000herefore, cash )ow &,52,500Problem 2 cosmetic company is considerin- to introduce a newlotion. The manufacturin- euipment will costRs.5,60,000. The e$pected life of the euipment is 7years. The company is thin4in- of sellin- the lotion inasin-le standard pac4 of 50 -rams at Rs. &2 each pac4.It is estimated that variable cost per pac4 would beRs. 6

and annual #$ed cost Rs. 8,50,000. (i$ed cost includes!strai-ht line" depreciation of Rs. '0,000and allocatedoverheads of Rs. *0,000. The company e$pects to sell&,00,000 pac4s of the lotion eachyear. ssume that ta$is 85+ and strai-ht line depreciation is allowed for ta$purpose. 9alculate the cash)ows.Solution

Initil !"# o$t%o&9ost of euipments Rs. 5,60,000S$b"e'$ent !"# %o&":nits sold &,00,000Sales 1 Rs. &2/ Rs. &2,00,000/ ;ariable cost 1 Rs. 6/ 6,00,000/ (i$ed cost !8,50,000 < *


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0,000 < '0,000" *,50,000/ epreciation '0,000Pro#t before ta$ &,70,000Ta$ 1 85+ 7&,000Pro#t after ta$ ==,000epreciation !added bac4" '0,0009ash )ow &,6=,00

0There is no terminal cash in)ow. It may be noted thatthe allocated overheads of Rs. *0,000 -ave beeni-noredas they are irrelevant.Problem (

FINANCIAL MANAGEMENT

Solved ProblemsRushi Ahuja2%9 and 9o. is considerin- a proposal to replace one ofits plants costin- Rs. 60,000 and havin- awritten downvalue of Rs. 28,000. The remainin- economic life of theplant is 8 years after which it willhave no salva-e value.>owever, if sold today, it has a salva-e value of Rs.20,000. The new machinecostin- Rs. &,*0,000 is alsoe$pected to have a life of 8 years with a scrap value ofRs. &7,000. The newmachine, due to its technolo-icalsuperiority, is e$pected to contribute additional annualbene#t !beforedepreciation and ta$" of Rs. 60,000. (indout the cash )ows associated with this decision -iventhat theta$ rate applicable to the #rm is 80+. !Thecapital -ain or loss may be ta4en as not sub?ect to ta$".

Solution)Amo$nt in R"*+&. Initial cash out)ow@ &,*0,0009ost of new machine 20,000/ Scrap value of old machine &,&0,0002. Subseuent cash in)ows !annual"Incremental bene#t 60,000/


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Incrementaldepreciationep. An new machine 27,000ep. An oldmachine 6,000 22,000Pro#t before ta$ *7,000/ Ta$

1 80+ &5,200Pro#t after ta$ 22,7003 epreciation !added bac4" 22,000nnual cash in)ow 88,700Theamount of depreciation of Rs. 27,000 on the newmachine is ascertained as follows@ !Rs. &,*0,000/Rs.&7,000"8 B Rs. 27,000. It may be noted that in the-iven situation, the bene#ts are -iven in theincrementalform i.e., the additional bene#ts contributed by theproposal. Therefore, only the incrementaldepreciationof Rs. 22,000 has been deduced to #nd out theta$able pro#ts. The same amount of depreciationhas been added bac4 to #nd out the incremental annualcash in)ows.Terminl !"# in%o&,There will be an additional cash in)ow of Rs. &7,000 atthe end of 8

thyear whenthe new machine will be scrapped away.Therefore, total in)ow of the last year would be Rs.62,700 !i.e.Rs. 88,700 3 Rs. &7,000".Problem -CDE is interested in assessin- the cash )ows associatedwith the replacement of an old machine by a

newmachine. The old machine bou-ht a few years a-ohas a boo4 value of Rs. =0,000 and it can be sold forRs.=0,000. It has a remainin- life of #ve years after whichits salva-e value is e$pected to be nil. It isbein-depreciated annually at the rate of 20 per cent !written


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down value methd".The new machine costs Rs.8,00,000. It is e$pected to fetch Rs. 2,50,000 after #veyears when it will nolon-er be reuired. It will be

depreciated annually at the rate of ** &* per cent!written down valuemethod". The new machine ise$pected to brin- a savin- of Rs. &,00,000 inmanufacturin- costs.Investment in wor4in- capitalwould remain unaected. The ta$ rate applicableto the #rm is 50 percent.(ind out the relevant cash)ow for this replacement decision. !Ta$ on capital -ain loss to be i-nored".

FINANCIAL MANAGEMENTSolved ProblemsRushi Ahuja3SolutionInitil !"# %o&", Amt* )R"*+9ost of new machine 8,00,000/ Salva-e value of old machine =0,000*,&0,000S$b"e'$ent nn$l !"# %o&",)Amo$nt R"*.///+0r*1 0r*2 0r*( 0r*- 0r*Savin-s in costs !" &00 &00 &00 &00 &00epreciation on new machine &**.* 77.= 5=.* *=.5 26.*/ epreciation on old machine &7.0 &8.8 &&.5 =.2 '.8Th

erefore, incremental depreciation !%" &&5.* '8.5 8'.7 *0.* &7.=Fet incremental savin- ! < %" /&5.* 25.5 52.2 6=.' 7&.&Gess@ Incremental Ta$ 1 50+ /'.6&2.7 26.& *8.7 80.6Incremental Pro#t /'.' &2.' 26.& *8.= 80.5epreciation !added bac4" &&5.* '8.5 8


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'.7 *0.* &7.=Fet cash )ow &0'.6 7'.2 '*.= 65.2 5=.8Terminl !"# %o&,

There will be a cash in)ow of Rs. 2,50,000 at the end of5thyear when the newmachine will be scrapped away. So,in the last year the total cash in)ow will be Rs. *,0=,800!i.e. Rs.2,50,000 3 Rs. 5=,800".Problem #rm is currently usin- a machine which was purchasedtwo years a-o for Rs. '0,000 and has aremainin- usefullife of 5 years.It is considerin- to replace the machinewith a new one which will cost Rs. &,80,000. The costof installation will amount to Rs. &0,,000. The increase inwor4in- capital will be Rs. 20,000. The e$pectedcashin)ows before depreciation and ta$es for both themachines are as follows@

0er Ei"tin3 M!#ine Ne& M!#ine& Rs. *0,000 Rs. 50,0002 *0,000 60,000* *0,000 '0,0008 *0,000 =0,0005 *0,000 &,00,000The #rm useStrai-ht Gine Hethod of depreciation. The avera-e ta$on income as well as on capital -ains losses is80+.9alculate the incremental cash )ows assumin- salevalue of e$istin- machine@ !i" Rs. 70,000, !ii" Rs.60,000,

!iii" Rs. 50,000, and !iv" Rs. *0,000.

FINANCIAL MANAGEMENTSolved Problems


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Rushi Ahuja4Solution)Fi3$re" in R"*+Di4erent S!r5 Vl$e"

9ost of new machine &,80,000 &,80,000 &,80,000 &,80,0003 Installation cost &0,000 &0,000 &0,000 &0,0003 dditional wor4in- capital 20,000 20,000 20,000 20,000/ Scrap value 70,000 60,000 50,000 *0,000=0,000 &,&0,000 &,20,000&,80,000Ta$ liability savin- &2,000 8,000

capital budgeting rules

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