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Capital budgeting Learning objectives

• Understand the concept of capital budgeting i.e. long term investments

• The nature and scope of investment decisions

• The methods of appraising the investment decisions

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Define

The decision as to which projects should be undertaken by a corporation is known as the

‘investment decision’, and the process is known as ‘capital budgeting’

Capital budgeting is essentially the process used to decide on the optimum use of scarce resources

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Steps in CBP

• Identify the Invst. Opportunities• Select the feasible ones• Evaluate the project as to whether or not the

proposal provides an adequate return to investors• Accept & implement the project• Online monitoring

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Investment evaluation techniques

Categorized into two groups

1. Non-discounting techniques:– Payback– (Average) accounting rate of return (ARR)

2. Discounting techniques– Net present value– Internal rate of return (IRR)– PI (profitability method)– TV (terminal value method)

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The payback technique

• This method involves determining the time taken for the initial outlay to be repaid by the project’s expected cash flows

• PB = Initial Investment (Co)Annual Cash Inflow (CI)

Unequal cash flowsCumulative cash inflow

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Example:

Year 0 1 2 3 4 5 6 Payback

Project B -2000 1500 200 0 300 200 300

Cum NCF 1500 1700 1700

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Example:

Year 0 1 2 3 4 5 6Project A -2000 600 400 900 200 200 200Cum CF 600 1000 1900

years 5.3200

1003 APayback

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Project Co C1 C2 C3 PB

X -4000 0 4000 2000

Y -4000 2000 2000 0

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Project Co C1 C2 C3

A -10000 +10000

B -10000 7500 7500

C -10000 2000 4000 12000

D -10000 10000 3000 3000

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Selecting project according PB

• When selecting among a number of projects, the one with the shortest payback period should be chosen

• However, there is little guidance on what an appropriate payback period should be, making it difficult to decide whether a project should be accepted or not.

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Limitations of PB • Calculation of payback period ignores the time value of money

• Cash flows that occur after the end of the payback time are ignored in the calculation of payback period. Yet, these latter cash flows may be significant in making the decision.

• Cutoff period is subjective

• Cannot rank projects that have the same PB

• Does not indicate the project wealth creation

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DPB

• Where cash flows are discounted

• PB is calculated

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Co C1 C2 C3 C4

X -4000 3000 1000 1000 1000

Y -4000 0 4000 1000 2000

CALCULATE THE PB & DPB @10%

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The ARR is given by:

Average /Accounting rate of return (ARR)

capital invested average

income averageARR

2/

/)1(

0

1

I

nTEBIT

ARR

n

t

t

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Example: Step 1

Calculate the ARR for a 2-year project that involves a machine costing Rs100 lacs and is expected to generate EBDIT of Rs 60 L & 70 L in years 1 & 2.

The machine is to be depreciated on a straight-line basis, and the corporate tax rate is 30%.

Calculate average net income

Year 1 2

EBDIT 60 70

Less depreciation 50 50

Taxable income 10 20

Less tax (30%) 3 6

Net income 7 14

Average = (7 + 14) / 2 = 10.5

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Example: Step 2

. Calculate average investment

Year 0 1 2

Machine cost 100 100 100

Less accum. depreciation 0 50 100

Investment 100 50 0

Average investment = (100 + 50 + 0) / 3 = 50

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Example: Step 3

Calculate the ARR

Step 4

Compare the ARR to a target or “cut-off” rate to accept or reject

%2150

5.10

capital invested Avg

income Avg

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Acceptance rule

• Acceptance rule:

• The ARR is compared with a predetermined ARR target, or ‘cut-off’ rate, to determine whether to proceed with a project

• When n projects then select the one with greatest ARR

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Limitations of ARRIs based on accounting figures which are not necessarily

related to cash flows and are based on accounting techniques that may vary from company to company

Ignores the time value of money

Requires an arbitrary target or “cut-off” rate, but there is little theoretical or other guidance in setting an appropriate target ARR

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Net present value (NPV)

• Calculate the PV of all future cash inflows and cash outflows that will result from undertaking a project

• These positive and negative present values are then netted off against one another to determine the net present value of the project

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Acceptance rule • The firm should accept all positive-NPV projects and reject

negative-NPV projects, because NPV is a measure of the increase in firm value (and therefore the wealth of the firm’s owners) from undertaking the project

• If the NPV of a project is zero, it is a matter of indifference as to whether the firm should undertake the project or pay the available cash back to shareholders

• This is because zero NPV indicates that the project yields the same future cash that the investors could obtain by investing themselves

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• The net present value is calculated as follows:

where:

CIFt =cash flow generated by the project in year t

k = the opportunity cost of capital

C0 = the cost of the project (initial cash flow, if any)

n = the life of the project in years

01 1

Ck

CIFNPV

n

tt

t

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• NPV is the sum of the present values of a project’s cash flows at the cost of capital

outflows

inflows

1 2 n0 1 2 n

C C C C NPV

1+k 1+k 1+kPV

PV

If PVinflows > PVoutflows, NPV > 0

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• Decision Rules– Stand-alone Projects

• NPV > 0 accept• NPV < 0 reject

– Mutually Exclusive Projects• NPVA > NPVB choose Project A over B

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Example:

Apply the NPV rule to a project that costs Rs 210 L and yields Rs 216 L in one year when the opportunity cost of capital is 7%.

LRsLL

CK

CIFNPV

n

tt

t

821007.1

216

10

1

Since the NPV is negative, it should be rejected.

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Example:

A company is considering whether to purchase a machine worth Rs 500,000 that will generate Rs 150,000 p.a. over the next 5 years. What is the NPV of this project, given an opportunity cost of capital of 10%?

618,68000,5001.0

1.11000,150

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15

001

Rs

Ck

kCIFC

k

CIFNPV

nn

tt

t

27

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• The advantages of NPV technique are:

• It always ensures the selection of projects that maximise the wealth of shareholders

• It takes into account the time value of money

• It considers all cash flows expected to be generated by a project

• Value additivity : NPV (A+B) = NPV(A)+NPV(B)

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• Limitations are:

• It requires extensive forecasts of the costs and benefits of a project, which can be problematic

• Ranking of projects changes with change in CFs / K

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Internal rate of return (IRR)

• The IRR technique is also based on a DCF model, but focuses on the rate of return in the DCF equation rather than the NPV

• The IRR is defined as the discount rate that equates the present value of a project’s cash inflows with the present value of the its cash outflows

• This is the equivalent of saying that the IRR is the discount rate at which the NPV of the project is equal to 0

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• A project’s IRR is the return it generates on the investment of its cash outflows– For example, if a project has the following cash flows

0 1 2 3

-10,000 2,000 4,000 6,000

• The IRR is the interest rate at which the present value of the three inflows just equals the NR 10,000 outflow

The “price” of receiving the inflows

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• Defining IRR Through the NPV Equation– The IRR is the interest rate that makes a

project’s NPV zero

outflows

inflows

1 2 n0 1 2 n

C C C: C IRR

1 IRR 1 IRR 1 IRRPV

PV

3434

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• Stated formally:

where:CIFt =the cash flow generated by the project in year t

C0 = the initial cost of the project (initial cash flow, if any)n = the life of the project in yearsirr = the internal rate of return of the project

01 1

0 Cirr

CIFn

tt

t

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• The unknown variable can be solved by trial-and-error

• NPV and IRR use the same framework and inputs, so they should result in the same accept/reject decision

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Acceptance of project• The decision rule is to accept a project if its

IRR is greater than the cost of capital and reject it if its IRR is less than the cost of capital

• When IRR > k : accept

• When IRR < k : reject

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Example:

Apply the IRR rule to a project that costs Rs100 L and yields Rs106 L in one year when the opportunity cost of capital is 7%.

%6

1001

1060

10 0

1

irr

Lirr

L

Cr

CIFn

ttt

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5432 irr1

4000

irr1

1000

irr1

2000

irr1

2000

irr1

100020000

Example:The IRR solved by trial and error.

YEAR 0 1 2 3 4 5Net cash flows

-2000 -1000 2000 2000 -1000 4000

To solve this problem using trial-and-error, you select a discount rate and substitute it into the equation. If the NPV is negative (positive) the discount rate is too high (low). By narrowing down the difference between the two rates, we can approach the IRR. In this case the IRR is approximately 31%.

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Short cut method for IRR

• Calculate the PB• Look in PV annuity table for the PB in the year

row• Find two rates close to the PB• Actual IRR by INTERPOLATION

DFrhDFrl

DFrPBrIRR

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• The project cost is Rs 36000 and is expected to generate CF of Rs 11200 p.a. for 5 years. Calculate the IRR

• Solution • PB = 36000/11200= 3.214 (PVAF)• Table PVAF look for PB in 5th row• 16% & 17%

%8.16199.3274.3

214.3274.316

%8.16199.3274.3

199.3214.317

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Limitations

It is difficult to calculate – in most circumstances it can only be found by trial-and-error

For projects involving both positive and negative future cash flows, multiple internal rates of return can exist

It can give an incorrect ranking when evaluating projects of different size

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PI- Profitability Method

• PI = PV of cash inflows

PV of cash outflows

Acceptance rule

When PV > 1

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Example

Initial investment of a project is 100000 and it generates CF of Rs 40,000, Rs30,000, Rs 50,000 and Rs 20,000 in year 1 through 4. calculate the NPV & PI of the project at 10%.

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Terminal value method • Here the assumption is that each cash flow is

reinvested at a certain rate of return from the moment it is received until the termination of the project.

• Example • Original outlay is 10,000, years 5, CF 4000 p.a. for

5yrs, k 10%.• In year 1&2 the CF reinvested at 6%• In year 3 to 5 the CFs reinvested at 8%

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Yr int Reinvst yrs

FVF TFV

1 4000 6 4 1.262 5048

2 4000 6 3 1.191 4764

3 4000 8 2 1.166 4664

4 4000 8 1 1.080 4320

5 4000 8 0 1.0 4000

22796

Find the PV of 22796 at 10% . 22796 X .621 = Rs 14156.3

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NPV Vs IRR

• SIZE DISPARITY PROBLEM

A B

Co -5000 -7500

C1 6250 9150

IRR 25 22

K 10%

NPV 681.25 817.35

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Time disparity problem

Yr A B0 105000 105000

1 60000 150002 45000 300003 30000 45000

4 15000 75000IRR 20 16NPV@8%

23970 25455

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Unequal lives project

• Two projects A with service life of 1 yr, B with 5 yrs. Initial investment in both projects 20,000 each.

• Project A CF 24000, B 5th yr 40200. at 10%

IRR NPV

A 20 1816

B 15 4900

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Lending & Borrowing type

Co C1 IRR NPV@10%

X -100 120 20% 9

Y +100 -120 20% -9