Capital Budgeting

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CAPITAL BUDGETING DECISIONS

Should we build thisplant?

SEEMA CHAKRABARTI

The investment decisions of a firm are generally known as the capital budgeting, or capital expenditure decisions.

The firm’s investment decisions would generally include expansion, acquisition, modernisation and replacement of the long-term assets. Sale of a division or business (divestment) is also as an investment decision.

Decisions like the change in the methods of sales distribution, or an advertisement campaign or a research and development programme have long-term implications for the firm’s expenditures and benefits, and therefore, they should also be evaluated as investment decisions.

TYPES OF INVESTMENT DECISIONS

One classification is as follows: Expansion of existing business Expansion of new business Replacement and modernisation

Yet another useful way to classify investments is as follows: Mutually exclusive investments Independent investments Contingent investments

AN EXAMPLE OF MUTUALLY EXCLUSIVE PROJECTS

BRIDGE vs. BOAT to get products across a river.

TYPES OF CASH FLOWS

Normal or Conventional Cash Flow : One change of signs. Cost (negative CF) followed by a series of

positive cash inflows.

• Non-normal or unconventional Cash Flow: Two or more changes of signs. Most common: Cost (negative CF), then string

of positive CFs,then cost to close project. Example: Nuclear power plant, strip mine.

These are generally:

Long-term decisions; involving large expenditures.

Have long term consequences.

Difficult or expensive to reverse.

Capital Budgeting Methods

Discounting Criteria

NPV BCR IRR

PBP ARR

Non Discounting Criteria

NET PRESENT VALUE

NPV of a project is the sum of the present values of all the cash flows positive as well as negative that are expected to occur over the life of the project.

The formula for NPV is:

31 202 3

NPV(1 ) (1 ) (1 ) (1 )

NPV(1 )

C CC CC

k k k k

NET PRESENT VALUE

Where, Ct = cash flow at the end of year t n = Life of the project k = discount rate (given by the projects

opportunity cost of capital which is equal to the required rate of return expected by investors on investments of equivalent risk).

C0 = Initial investment 1 / (1 + k )t = known as discounting factor or

PVIF i.e present value interest factor.

CALCULATING NET PRESENT VALUE

Assume that Project X costs Rs 2,500 now and is expected to generate year-end cash inflows of Rs 900, Rs 800, Rs 700, Rs 600 and Rs 500 in years 1 through 5. The opportunity cost of the capital may be assumed to be 10 per cent.

2 3 4 5

1, 0.10 2, 0.10 3, 0.10

4, 0.10 5, 0.

Rs 900 Rs 800 Rs 700 Rs 600 Rs 500NPV Rs 2,500

(1+0.10) (1+0.10) (1+0.10) (1+0.10) (1+0.10)

NPV [Rs 900(PVF ) + Rs 800(PVF ) + Rs 700(PVF )

+ Rs 600(PVF ) + Rs 500(PVF

10)] Rs 2,500

NPV [Rs 900 0.909 + Rs 800 0.826 + Rs 700 0.751 + Rs 600 0.683

+ Rs 500 0.620] Rs 2,500

NPV Rs 2,725 Rs 2,500 = + Rs 225

ACCEPTANCE RULE OF NPVAccept the project when NPV is positive

NPV > 0Reject the project when NPV is negative

NPV < 0 May accept or reject the project when NPV is zero NPV = 0

( A project will have NPV = 0, only when the project generates cash inflows at a rate just equal to the opportunity cost of capital)The NPV method can be used to select between mutually exclusive projects; the one with the higher NPV should be selected.

ADVANTAGES OF NPV METHOD

It considers time value of money. It is a true measure of profitability as it uses the present values of all cash flows (both outflows & inflows) & opportunity cost as discount rate rather than any other arbitrary assumption or subjective consideration. The NPVs of individual projects can be simply added to calculate the value of the firm . This is known as “Principle of value additivity”.It is consistent with the shareholders wealth maximization principle as whenever a project with positive NPV is undertaken, it results in positive cash flows and hence the increase in the value of the firm.

DISADVANTAGES OF NPV METHOD

It is difficult to estimate the expected cash flows from a project. Discount rate to be used is very difficult to determine.Since this method does not consider the life of the projects, in case of mutually exclusive projects with different life, the NPV rule, tends to be biased in favour of the longer term project.Since NPV is expressed in absolute terms rather than relative terms it does not consider the scale of investment.

BENEFIT COST RATIO

It is calculated as:

Benefit-cost ratio = PVB / I

Where,PVB = present value of benefitsI = Initial investments

ACCEPTANCE RULE FOR BCR

BCR > 1 = Accept

BCR = 1 = Indifferent

BCR < 1 = Reject

EVALUATION OF BCR METHOD

Advantages of BCR method:

Since it considers the investment in the project, it is considered to be preferable to NPV method.

Disadvantages of BCR method:

It does not provide for a means through which a number of smaller projects can be combined to be compared to a bigger project.

Internal Rate of Return: IRR

0 1 2 3

CF1CF2 CF3

Cash Inflow

IRR is the rate of return that equates PV of cash inflows with investment outlay of a project. This is the same as forcing NPV = 0.

INTERNAL RATE OF RETURN METHOD

The internal rate of return (IRR) is the rate that equates the investment outlay with the present value of cash inflow received after one period. This also implies that the rate of return is the discount rate which makes NPV = 0.

The formula for calculating IRR is:

31 20 2 3

(1 ) (1 ) (1 ) (1 )

C CC CC

r r r r

INTERNAL RATE OF RETURN METHOD

Where,

Ct = cash flow at the end of year t n = Life of the project r = discount rate C0 = Initial investment 1 / (1 + r )t = known as discounting factor or

PVIF i.e present value interest factor.

CALCULATION OF IRRLevel or even Cash Flows: Let us assume that an investment would cost

Rs 20,000 and provide annual cash inflow of Rs 5,430 for 6 years.

The IRR of the investment can be found out as follows:

IRR = 16% approx.( Refer to PVAF table @ 3.685 for 6 yrs

NPV Rs 20,000 + Rs 5,430(PVAF ) = 0

Rs 20,000 Rs 5,430(PVAF )

Rs 20,000PVAF 3.683

Rs 5,430

NPV Profile and IRR

A B C D E F G H 1 NPV Profile

2 Cash Flow Discount

rate NPV 3 -20000 0% 12,580 4 5430 5% 7,561 5 5430 10% 3,649 6 5430 15% 550 7 5430 16% 0 8 5430 20% (1,942) 9 5430 25% (3,974)

Figure 8.1 NPV Profile

CALCULATION OF IRR

Uneven or non–normal Cash Flows: Calculating IRR by Trial and Error The approach is to select any discount rate to

compute the present value of cash inflows. If the calculated present value of the expected cash inflow is lower than the present value of cash outflows, a lower rate should be tried. On the other hand, a higher value should be tried if the present value of inflows is higher than the present value of outflows. This process will be repeated unless the net present value becomes zero.

CALCULATION OF IRR

A project costs Rs.16000 and is expected to generate cash inflows of Rs. 8000, Rs.7000 & Rs.6000 at the end of each year for next 3 years.

ACCEPTANCE RULE FOR IRR

Accept the project when r (IRR) > k (WACC).Reject the project when r (IRR) < k (WACC).May accept the project when r = k.In case of independent projects, IRR and NPV rules will give the same results if the firm has no shortage of funds.In case of projects with equal IRR & different NPV, select project with higher NPV as it is consistent with firm’s wealth maximisation objective.

ADVANTAGES OF IRR METHOD

It considers time value of money. It is a true measure of profitability as it uses the present values of all cash flows(both outflows & inflows) rather than any other arbitrary assumption or subjective consideration.In case of conventional independent projects NPV & IRR methods gives the same decision.Whenever a project with higher IRR than WACC is undertaken, it results in the increase in the shareholder’s return. Hence, the value of the firm also increases.

PROBLEMS WITH IRRLending & Borrowing projects: Project with initial outflow followed by inflows is a lending type project whereas a project with initial inflow followed by outflows is a borrowing project. Since IRR does not differentiate between lending and borrowing projects, a higher IRR may not always be a desirable thing.

Multiple IRR: In case of projects with non-normal or unconventional cash flows more than one IRR are generated which are misleading.

Mutually Exclusive projects: In case of mutually exclusive projects the results of NPV & IRR methods may conflict each other. This is because the IRR method does consider the scale of investment.

PROBLEMS WITH IRR

Different short term & Long term interest rates: Since the cash flows are discounted at the opportunity cost of capital, there arises a confusion regarding what rate is to be used for discounting, if the short term and long term lending rates are different.

LENDING & BROWING PROJECTSLending projects: Project with initial outflow followed by inflows is a lending type project.

Borrowing projects: Project with initial inflow followed by outflows is a borrowing project.

Cash Flows (Rs.)

Project Co C1 IRR NPV at 10%

X -100 110 10% 0

Y 100 -110 10% 0

LENDING &BORROWING PROJECTS

Cash Flows (Rs.)

X -100 110 10% 4.72

Y 100 -110 10% -4.72

Cash Flows (Rs.)

X -100 110 10% -4.3

Y 100 -110 10% 4.3

PROBLEM OF MULTIPLE IRRS

A project may have both lending and borrowing features together. IRR method, when used to evaluate such non-conventional investment can yield multiple internal rates of return because of more than one change of signs in cash flows.

Case of Ranking Mutually Exclusive Projects

Investment projects are said to be mutually exclusive when only one investment could be accepted and others would have to be excluded.Two independent projects may also be mutually exclusive if a financial constraint is imposed.The NPV and IRR rules give conflicting ranking to the projects under the following conditions: The cash flow pattern of the projects may

differ. That is, the cash flows of one project may increase over time, while those of others may decrease or vice-versa.

The cash outlays of the projects may differ. The projects may have different expected

lives.

RANKING MUTUALLY EXCLUSIVE PROJECTS

(Timing of Cash Flows) Cash Flows (Rs) NPV

Project C0 C1 C2 C3 at 9% IRR

M – 1,680 1,400 700 140 301 23%

N – 1,680 140 840 1,510 321 17%

Discount Rate Project M Project N

0 560 810

5 409 520

10 276 276

15 159 70

20 54 -106

25 -40 -257

30 -125 -388

5% 10% 15% 20% 25% 30%

Discount Rate

NPV INR 276/-

___ Project M

---- Project N

(Timing of Cash Flows)

10% discount is k/as Fisher’s intersection.

RANKING MUTUALLY EXCLUSIVE PROJECTS(Scale of Investment)

Cash Flow (Rs) NPV

Project C0 C1 at 10% IRR

A -1,000 1,500 364 50%

B -100,000 120,000 9,080 20%

(Project Life Span)

Cash Flows (Rs)

Project C0 C1 C2 C3 C4 C5 NPV at 10% IRR

X – 10,000 12,000 – – – – 908 20% Y – 10,000 0 0 0 0 20,120 2,495 15%

Modified Internal Rate of Return (MIRR)

The modified internal rate of return (MIRR) is the compound average annual rate that is calculated with a reinvestment rate different than the project’s IRR. Both NPV & IRR methods assume that the entire cash flow generated during the life time of the project is reinvested at project cost of capital (i.e k) & internal rate of return (i.e r) respectively in each of the above two methods.But, in MIRR the cashflows are assumed to be reinvested at cost of capital ( k) instead of internal rate of return ( r )as in IRR method.

PAY BACK PERIOD

It is the number of years required to recover a project’s cost, or how long does it take to get the business’s money back?

10 8060

0 1 2 3

CFCumulative -100 -90 50

Payback 2 + 30/80 = 2.375 years

PAY BACK PERIOD

Strengths of Payback:

1. Provides an indication of a project’s risk and liquidity.

2. Easy to calculate and understand.

Weaknesses of Payback:

1. Ignores the time value of money.

2. Ignores CFs occurring after the payback period.

3. It is a measure of capital recovery & not profitability.

PAY BACK PERIOD

DISCOUNTED PAYBACK PERIOD (DPBP)

10 8060

0 1 2 3

Cumulative -100 -90.91 -41.32 18.79

Discountedpayback 2 + 41.32/60.11 = 2.7 yrs

Discounted Payback: Uses discountedrather than raw CFs.

PVCFt -100

9.09 49.59 60.11

ACCOUNTING RATE OF RETURN

The accounting rate of return is the ratio of the average after-tax profit divided by the average investment.

A variation of the ARR method is to divide average earnings after taxes by the original cost of the project instead of the average cost.

ACCEPTANCE RULE OF ARR

This method will accept all those projects whose ARR is higher than the minimum rate established by the management and reject those projects which have ARR less than the minimum rate.

This method would rank a project as number one if it has highest ARR and lowest rank would be assigned to the project with lowest ARR.

ACCOUNTING RATE OF RETURN

The ARR method has certain advantages as:

It is very simple to understand.

Dependency on accounting data which is readily available.

Shows the profitability of the project.

ACCOUNTING RATE OF RETURNThe disadvantages of ARR include:

It is based on accounting profit rather than cash flows.

Time value of money is ignored.

It is inconsistent in the sense that the numerator represents the profit belonging to equity and preference shareholders whereas the fixed assets used in denominator rarely if ever represents contribution equal to equity & preference shareholders.

Capital Budgeting

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