fm chapter five

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CHAPTER FIVECHAPTER FIVECAPITAL BUDGETINGCAPITAL BUDGETING

Chapter Objectives

• explain capital budgeting ;

• determine the capital outlay of projects;

• determine the payback period, NPV, IRR& ARR of an investment project; and

• identify the limitations of payback period, NPV, IRR& ARR .

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INTRODUCTIONINTRODUCTION

CAPITAL BUDGETING = INVESTING in Long-term Assets

'Capital Budgeting' refers to long-term planning for proposed capital outlays and their financing.

Capital Budgeting: It is the Process of selecting viable investment projects.

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5.1. Investment Outlay (The 5.1. Investment Outlay (The Net Initial Investment)Net Initial Investment)

The term Investment Outlay (net initial investment), as used here, refers to the relevant cash outflows to be considered when evaluating a prospective capital expenditure.

The net initial investment occurs at time zero - the time at which the expenditure is made.

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Cont…Cont…

The net initial investment is calculated by subtracting all cash inflows occurring at time zero from all cash outflows occurring at time zero.

The following table provides a general format for computing net initial investment:

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Format for Determining Format for Determining Net Initial Investment Net Initial Investment

Project cost or cost of new fixed assets XXX

Add: Cost of installation, insurance, transport XX

Add: Positive net working capital XX

Deduct Cash inflows from the proceeds of old fixed asset disposal

XX

A(D) Taxes (tax savings) on old asset disposal

XX

Net Initial investment (or net initial cash outflows)

XXX

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Example: 1Example: 1

Let us assume that the Lalibela Corporation wants to introduce new production machinery. The cost of the needed machinery is Br. 1,000,000. The machinery is expected to last for 4 years, after which time it will have a scrap value of Br. 8,000. The corporation spends Br. 19,000 in transporting the machinery from the manufacturer and in installing the machinery in its plant.

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Cont…Cont…

The corporation pays for the machinery by making a down payment of Br. 100,000 and finances the remainder with a bank loan. What will be the net initial investment for the new production machinery?

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Solution Solution

The net initial investment is Br. 1,019,000. This is the sum of the cost of the machinery and the transportation and installation expenses (Br. 1000,000 + Br. 19,000). Scrap value of the new machinery and financing arrangements are not included in the computation.

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Cont…Cont… In the case of replacement decisions,

the existing fixed assets may be sold if the new fixed assets are to be purchased. (in such case use the previous format for calculation Net initial investment)

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Cont…Cont…

The rules that determine the tax impact of selling a depreciable asset are summarized below:

1. If an asset is sold for less than its book value, the company realizes a decrease in its tax liability equal to 40 percent (assume) of the difference between the selling price and the book value of the asset.

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Cont…Cont…

2.If the asset is sold for its book value, there is no impact on corporate taxes.

If the asset is sold for more than its BV but for an amount equal to or less than its original cost, the corporation incurs an increase in its tax liability equal to 40 % of the difference between the selling price and the BV of the asset.

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Cont…Cont…

4.If the asset is sold for more than its original cost, the corporation incurs an increase in its tax liability equal to the tax on the capital gain plus the tax on the recaptured depreciation.

The capital gains tax is 20 % of the difference between the selling price and the original cost. The tax on the recaptured depreciation is 40 % of the difference between the original cost &BV.

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Example: 2 Example: 2

Assume a new line of machinery is purchased to replace existing machinery by XYZ Corporation. The new machinery costs including installation cost amounts Br.2,500,000 and an expected salvage value of Br.250, 000 after ten years. The existing machinery originally cost Br. 800,000 and has a current book value of Br. 100,000.Based on the following independent assumptions with regard to old machinery disposal value, compute NII of the project.

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Cont…Cont…1. Assume that the existing asset is sold for a scrap value of

Br. 10,000.

Solution

The corporation realizes a tax savings of .40(Br. 100,000 - Br.10,000) =Br.36,000.

The net initial investment of the project is:

Project and installation costs: Br. 2,500,000

Proceeds form old machinery disposal: - 10, 000

Tax savings on asset disposal: - 36, 000

Br. 2,454,000

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Cont…Cont…

2.Assume that the existing asset is sold for the amount of its book value.

Solution

There is no tax impact from the sale.



Proceeds from old machinery disposal: - 100,000

Br.2, 400,000

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Cont…Cont…3.Assume that the existing asset is sold for Br.

150,000.

Solution

The corporation incurs an increase in its tax liability of .40(Br. 150,000–Br. 100,000)=Br. 20,000.



Proceeds from old machinery disposal:- 150, 000

Tax on recapture of depreciation: + 20, 000

Br. 2,370,000

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Cont…Cont…4. Assume that the existing asset is sold for Br. 1M.

Solution

The corporation incurs an increase in its tax liability of .20(Br. 1,000,000 – Br. 800, 000) + .40(Br. 800,000- Br. 100,000)= Br. 320,000.



Proceeds from asset disposal: - 1,000, 000

+ 320,000

Br. 1,820,000

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Project Evaluation: Project Evaluation: Alternative MethodsAlternative MethodsProject Evaluation: Project Evaluation: Alternative MethodsAlternative Methods

Payback Period (PBP)

Internal Rate of Return (IRR)

Net Present Value (NPV)

Accounting Rate of Return(ARR)

Payback Period (PBP)

Internal Rate of Return (IRR)

Net Present Value (NPV)

Accounting Rate of Return(ARR)

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Payback Period (PBP)Payback Period (PBP) It is defined as the number of years

required for an investment’s cumulative cash flows to equal net initial investment.

Thus, PB can be looked upon as the length of time required for a project to recover on its net initial investment from project’s expected cash inflows.

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Cont…Cont…

Computation of Payback period. When an investment’s cash flows are in annuity form, payback period can be computed by dividing the value of net annual cash inflow into the project’s net initial investment.

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An investment has the following net initial investment and net annul cash inflows:

Year NII Yearly Cash Inflows0 12,000 4,000

1

2

3

4

5

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Cont…Cont…

PB period = Net Initial Investment

Net Annul cash inflows

= Br. 12,000 = 3 years

Br. 4,000

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Compute the PB for the following cash flows, assuming a NII of Br. 13,000:

Year NII Yearly Cash Inflows CCF0 13,000 0 0

1 5,000 5,000

2 6,000 11,000

3 4,000 15,000

4 5,000 20,000

PBP = 2 years + Br. 2000/ Br. 4,000 = 2 years + 0.5 =2.5 years

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INDEPENDENT vs. MUTUALLY INDEPENDENT vs. MUTUALLY EXCLUSIVE PROJECTS:EXCLUSIVE PROJECTS:

Independent: A project that has nothing to do with other projects under investigation.

Example: Replace copy machine and build a new plant.

Mutually Exclusive: You only need one of these alternative projects.

Example: Buy IBM or Apple PC?

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Decision rule:Decision rule: Accept project if the PB years < years

set by corporate policy

For two mutually exclusive projects, choose the one that pays you back your initial cost the sooner.

Limitations of the PB Period Criterion Ignores the time value of money. Ignores CF occurring after the PB period.

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Merits of the Payback Merits of the Payback Period CriterionPeriod Criterion

1. Payback is an easy concept to understand.2. It is easy to compute.3. It is extremely easy to apply.4. It has a straightforward interpretation.5. It avoids making projections into the more

distant future. The more uncertain the future is, the stronger may be the case for the use of the payback period criterion.

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Net Present Value (NPV)Net Present Value (NPV)Net Present Value (NPV)Net Present Value (NPV)

NPV is the present value of an investment project’s net cash

flows minus the project’s initial cash outflow. It is measured in

Birr.

CF1 CF2 CFn (1+k)1 (1+k)2 (1+k)n

+ . . . ++ - ICOICONPV =

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Cont…Cont…

Since NPV can be positive, zero, or negative, attention must be paid to its algebraic sign. Decision rule:If independent project: Accept project if NPV > 0 Reject project if NPV < 0If mutually exclusive project: Accept the project with the highest NPV

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An investment alternative has a net initial investment of Br. 100,000 and produces a cash inflow annuity of Br. 14,000 for 16 years. Compute the NPV of the investment if the required rate of return (cost of capital) for the investment is 10 percent. Would you recommend accept or reject this project?

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SolutionSolution

The present value factor corresponding to a 16 years payment annuity discounted at 10 percent is 7.824 (see present value for annuity case table or your calculator). NPV is calculated as follows:

NPV = 14,000/(1.10) 1 + 14,000/(1.10) 2 +… + 14,000/(1.10) 16 - Br.100, 000

NPV = Br. 14,000(7.824) – Br. 100,000 = Br. 9,536

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Example 2Example 2Refer the following data for project L and S.

Compute NPV for both & decide which is acceptable

If the projects are independent

If the projects are mutually exclusive

The minimum required rate of return or discounting rate or the project’s cost of capital is 10%

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Expected Net Cash Flow

Year Project L Project S0 (100) (100)

1 10 90

2 60 30

3 80 50

(9.09 +49.59 + 60.11) -100 = NPVL = 18.79

(81.82+24.79+37.57) -100 NPVS = 44.18

If the projects are independent, accept both

If the projects are mutually exclusive, accept Project S since NPVS > NPVL.

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Interpretation of the NPV Interpretation of the NPV CriterionCriterion

If NPV equals zero, the project’s rate of return equals the minimum required rate of return.

If NPV is negative, the project’s rate of return is less than the minimum required rate of return.

A positive NPV represents the amount by which time adjusted profits exceed the minimum required profits.

A negative NPV represents the amount by which time adjusted profits fall short of the minimum required profits.

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Merits of the NPV CriterionMerits of the NPV Criterion takes into account the time value of money

takes into account the CF of a project over its entire life span unlike PB period criterion.

NPV is measured in dollars or in birr, it provides a common denominator for:

Evaluating individual investments. Choosing from competing investment proposals. Measuring the impact on shareholder wealth

produced by the set of investments that constitutes the firm’s capital budget.

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Limitations of the NPV Criterion Limitations of the NPV Criterion

more difficult to compute than PB period.

a careful interpretation is required because it does not provide a measure of a project’s actual rate of return.

It may not give good results while comparing projects with unequal lives and unequal net initial investment costs.

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Internal Rate of Return (IRR)Internal Rate of Return (IRR)Internal Rate of Return (IRR)Internal Rate of Return (IRR)

IRR is the discount rate that equates the present value of the future net cash flows from an investment project with the project’s initial cash outflow. Or It is defined as the discount rate that produces a zero NPV.

CF1 CF2 CFn (1+IRR)1 (1+IRR)2 (1+IRR)n

+ . . . ++ICO =

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Cont…Cont…

the IRR is the actual rate of return that a project earns when profits and the time value of money are taken into account.

Note that it is stated as a percentage rate.

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Decision ruleDecision rule

If IRR is greater than the cost of capital, accept the project;

if IRR is less than the cost of capital, reject the project.

Other things being equal, when two projects have the same net initial investment but different IRRs the project with higher IRR is preferred.

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Cont…Cont…

Computation of IRR

Cash Flows Are in Annuity Form

Cash Flows are Not in Annuity Form

IRR can be computed very easily

computation IRR can become tedious

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In the discussion of the NPV criterion (example 1), a project that required a NII of Br. 100,000 produced 16 annual cash flows of Br. 14,000 each. It required a 10 % rate of return, and had an NPV of Br. 9,536.

Since the NPV is positive at a discount rate of 10 %, the project’s actual rate of return exceeds 10%. Dividing the NII by the value of one net cash inflow and, then, locating the resulting quotient in the present value annuity table, helps to obtain the IRR for this project.

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Cont…Cont…Br.100,000/Br. 14,000 = 7.143

Table value IRR 7.379 11%6.974 12%

the project’s table value (7.143) is between table value of 6.974 and 7.379 in the present value annuity table.

When a more exact IRR is needed, the following steps typically will produce an IRR that is correct to, at least, one decimal point:

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Cont…Cont…

1. Identify the closest rates of return, as was done above.

2. Compute the NPV for each of these two closest rates.

• (NPV/11%) = Br. 14,000(7.379) - Br. 100,000 = Br. 3,306

• (NPV/12%) = Br. 14,000, (6.974) - Br. 100,000 = - Br. 2,364

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3. Compute the sum of the absolute values of the NPVs obtained in step 2.

Br. 3,306 + Br. 2,364 = Br. 5,670

4. Divide the smaller discount rate identified in step 1 in to the sum obtained in step 3. Then add the resulting quotient to the smaller discount rate:

Br. 3,306/ Br. 5,670 = .58

IRR = 11% + .58 = 11.58%

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Computation of IRR When Computation of IRR When CFs are Not in Annuity FormCFs are Not in Annuity Form

It is necessary to make a good first guess of the project’s IRR. This can be done in either of the following two ways:

1. If the cash flows, at least, approximate an annuity, dominance techniques can be applied.

2. If the cash flows display no general annuity pattern, a weighted average can be used.

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Dominance TechniqueDominance TechniqueLet us take a project with a NII of Br. 60,000, a required

rate of return of 13 %, and the following cash flows:

Year yearly Cash inflows

1 20,000

2 20,000

3 20,000

4 15,000

5 15,000

6 15,000

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Cont…Cont…The IRR for each of these replacement annuities is:Replacement TableAnnuity Value IRRBr. 20,000 60,000/ 20,000 = 3.0 24%Br. 15,000 60,000/ 15,000 = 4.0 12%

Which of the two IRRs provides the better first guess?

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Cont…Cont… Chances are that the IRR based on the Br.

20,000 annuity will provide a better first guess because it is based on the cash flows that occur in the earliest years of the original project. An alternative is to take the arithmetic average of the IRRs of the two annuities as follows:

.24 + .12 =. 18 or 18% 2

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Cont…Cont…

NPV = Br. 20,000 (2.174) + 15,000(.516)

+ 15,000(.437) + 15,000(.370)

- 60,000 NPV = Br. 3,32.5

Since the NPV is positive, the actual IRR exceeds 18 percent. A second guess of the IRR at 21 percent is made, based on the size of the NPV.

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Cont…Cont…NPV for the project discounted at 21 % is: NPV= Br. 20,000(2.074) + 15,000(.467)

+ 15,000(.386) + 15,000(.319)

- 60,000 NPV = - Br. 940

Since the NPV is negative, the actual IRR is less than 21 percent.

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Cont…Cont… A third guess of the IRR at 20 % is made, based

on the preceding two guesses and their corresponding NPVs. The NPV for the project discounted at 20 percent is:

NPV = Br. 20,000(2.106) + 15,000(.482)

+ 15,000(.402) +15,000(.335)

- 60,000 NPV = Br. 405

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Thus, the actual IRR of the project is between 20 percent and 21 percent.

1. Compute the sum of the absolute values of the NPVs for the two closest rates:

Br. 940 + Br. 405 = Br. 1,3452. Divide the NPV of the smaller discount rate in to

the sum obtained above and then add the resulting quotient to the smaller discount rate:

Br. 405/ Br. 1,345 = .30IRR = 20% +. 30 =20.3%(actual IRR )

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Weighted AverageTechniqueWeighted AverageTechnique

Assume a project that requires a net initial investment of Br. 16,000 produces the following cash flows:Year Yearly Cash Flows

1. Br. 4,0002. 6,0003. 5,0004. 5,0005. 4,000

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Cont…Cont…Year Cash inflow Weight Cash inflow x Weight 1 Br. 4,000 5 Br. 20,000 2 6,000 4 24,000 3 5,000 3 15,000 4 5,000 2 10,000 5 4,000 1 4,000

Totals 15 Br. 73,000

Weighted average cf = Br. 73,000/15 = Br. 4,867

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Cont…Cont… The next step is to use the weighted average

cash inflow of Br. 4,867 as an annuity that replaces the original set of cash flows.

Br. 16,000/ Br. 4,867 = 3.288By looking at present value annuity table, the

number 3.288 corresponds, approximately, to an IRR of 16 percent.

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Cont…Cont…The NPV of the original project is now

calculated by using a 16 % discount rate:NPV = Br. 4,000(.862)=3448

+ 6,000(.743)=4458 + 5,000 (.641)=3205 + 5,000(.552)=2760 + 4,000(.476)=1904

- 16,000 NPV = - Br. 225

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Cont…Cont… a second guess of IRR at 15 % is made. The

NPV of the project discounted at 15% is: NPV = Br. 4,000(.870)=3480

+ 6,000(.756)=4536 + 5,000(.658)=3290 + 5,000(.572)=2860 + 4,000(.497)=1988 - 16,000

NPV= Br. 154

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Cont…Cont… IRR for the project is between 15 % & 16 %

Then Br. 225 + Br. 154 = Br. 379

Br. 154/ Br. 379 = .41

IRR = 15% + .41 = 15.41%

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Merits of the IRR CriterionMerits of the IRR Criterion

IRR takes into account the time value of money and it is a profit-oriented tool.

IRR considers the profitability of the project for its entire economic life.

The determination of cost of capital is not a pre-requisite for the use of IRR criterion and, hence, it is a better criterion than NPV

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Limitations of the IRRLimitations of the IRR The IRR is the most computationally

tedious

A more significant disadvantage of this criterion is its inability to consider the size of a project’s net initial investment.

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Accounting Rate of ReturnAccounting Rate of Return The ratio does not take into account the

concept of time value of money.

When comparing investments, the higher the ARR, the more attractive the investment.

ARR= Average NI Average Investment

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Cont…Cont… If the ARR is equal to or greater than the

required rate of return, the project is acceptable.

If it is less than the desired rate, it should be rejected.

When comparing investments, the higher the ARR, the more attractive the investment.

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Merits of ARR Method Merits of ARR Method

It is very simple to understand and use. Rate of return may readily be calculated

with the help of accounting data. They system gives due weight age to the

profitability of the project if based on average rate of Return.

It takes investments and the total earnings from the project during its life time.

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Demerits of ARR MethodDemerits of ARR Method

It uses accounting profits and not the cash-inflows in appraising the projects.

It ignores the time-value of money which is an important factor in capital expenditure decisions.

It considers only the rate of return and not the length of project lives.

The method ignores the fact that profits can be reinvested.

fm chapter five

Economy & Finance