CAPITAL BUDGETING (PRINCIPLES & TECHNIQUES)

• Capital budgeting is the process of evaluating & selecting long-term investments that are consistent with the goal of shareholders’ wealth maximization.

• Types of investment decisions:1. Expansion & Diversification2. Replacement & Modernization• Investment Evaluation Criteria:1. Estimation of cash flows,2. Estimation of required rate of return (the opportunity

cost of capital),3. Application of a Decision Rule (Capital budgeting

techniques) for making the choice.

Evaluation Criteria

• Discounted Cash flow Techniques:

1. Net Present Value (NPV)

2. Internal Rate of Return (IRR)

3. Profitability Index (PI)

• Non-Discounted Cash flow Techniques:

1. Payback Period (PB)

2. Discounted Payback Period (DPB)

3. Accounting Rate of Return (ARR)

NDCF Techniques1. Pay Back period

• Payback(PB): Refers to the number of years required to recover the initial outlay of the investment.

• If the project generate constant annual cash flows, then PB = (Initial investment ÷ Annual cash inflow) = [Co ÷ C]

• In case of unequal cash inflows, the PB period can be found out by adding up the cash inflows until the total is equal to the initial cash outlay.

Pay Back period………..

• Acceptance Rule : Accept if PB< Standard payback & vice versa.

• Payback Period Reciprocal: • An alternative way of expressing the payback period=

[(1 ÷ Payback Period) X 100]; if a project has a payback of 2 ½ years, payback period reciprocal is 40%.

• The higher the payback period reciprocal ( and hence the lower payback period) the more worthwhile the project becomes.

Pay Back period………..

• Merits:1. Easy to compute and inexpensive to use;2. Emphasizes liquidity;3. Recognizes cash flows & a crude way to cope with risk.

• Demerits:1. Ignores the time value of money (magnitude & timing of

cash inflows);2. Ignores cash flows occurring after the PB period;3. No objective way to determine the standard pay back.

NDCF Techniques2. Discounted Pay Back period

• The number of years required in recovering the cash outlay on the present value basis.

• Cash inflows are discounted with the opportunity cost of capital of the said project.

• Still fails to consider the cash flows occurring (magnitude & timing) after the payback period.

NDCF Techniques3. Accounting Rate of Return(ARR) • ARR [ also known as ROI] method employs the

normal accounting technique to measure the increase in profit expected to result from an investment.

• An average rate of return found by dividing the average net operating profit [EBIT(1 – T)] by the average investment.

• Acceptance rule: Accept if ARR > minimum rate & vice versa.

Accounting Rate of Return…..

• Merits:1. Uses accounting data with which executives are

familiar;2. Easy to understand & compute;3. Gives more weightage to future receipts.

• Demerits:1. Ignores time value of money;2. Does not use cash flows3. No objective way to determine the minimum

acceptable rate of return.

DCF Techniques1. Net Present value (NPV)

• The difference between PV of cash inflows and PV of cash outflows is equal to NPV; the firm’s opportunity cost of capital being the discount rate.

• NPV =

• Acceptance Rule:• Accept if NPV > 0 (NPV is positive) & vice versa.• Project may be accepted if NPV = 0.

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Net Present value (NPV)

• Merits:1. Considers all cash

flows;2. Based on the concept of

time value of money;3. Satisfies the value

additivity principle (i.e.NPVs of two or more projects can be added);

4. Consistent with shareholders wealth maximization principle.

• Demerits:1. Requires estimates of

cash flows which is a tedious task;

2. Requires computation of the opportunity cost of capital which poses practical difficulty;

3. Sensitive to discount rates.

NPV sensitive to discount rates

• Example:

• Two projects A & B – both costing Rs.50 each. Project A returns Rs.100 after 1 year & Rs. 25 after 2 years. Project B returns Rs.30 after 1 year and Rs.100 after 2 years. At discount rates of 5% & 10%, what will be the NPV of the projects & their ranking ?

Solution

• Particulars NPV Rank NPV Rank5% 10%

Project A 67.92 II 61.57 IProject B 69.27 I 59.91 II• Ranking reversed when discount rate changed from 5%

to 10%.

• Happened due to cash flow pattern – impact of discounting becomes more severe for cash flows occurring later in the life of the project.

• The higher is the discount rate, the severe would be the discounting impact.

DCF Techniques2. Internal Rate of Return (IRR)

• The discount rate which equates the present value of an investment’s cash inflows and outflows is its internal rate of return; or

• The discount rate at which the NPV = 0.

• NPV =

• For Uneven Cash flows = IRR calculated by Trail & Error method.

• For Even Cash flows= NPV= (-) Initial Investment + Cash flows (PVFAn opportunity cost)

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IRR for Uneven Cash flows(Trail & Error Method)

• Steps:1. Select any discount rate to compute the PV of cash

flows;2. If the NPV is (+), try with a higher rate or vice versa;3. Process repeated till NPV is zero (in reality, if we can

identify two NPVs at lower as well as higher rate, we can use the method of interpolation to get the IRR).

• Interpolation Formula = Lower Discount Rate +

Difference between two Discount rates (NPV at Lower discount rate ÷ Absolute difference between two NPVs)

IRR for Even Cash flowsNPV= (-) Co + CI (PVFAn opportunity cost)

Q. An investment would cost Rs.20,000 & provide an annual cash flow of Rs.5430 p.a. for 6 years. If the opportunity cost of capital is 10%, identify project’s NPV & IRR.

A. NPV = -Rs.20,000 + Rs.5430(PVAF6,0.10) = - 20,000 + (5430 X 4.355) = Rs.3,648.

For IRR; NPV = -20,000 + 5430(PVAF6,r) = 0;or, 20,000 = 5430 (PVAF6,r) or, (PVAF6,r) = (20,000 ÷ 5430) = 3.683Rate which provides PVAF of 3.683 for 6 years is project’s IRR = (Approximately 16%).

Internal Rate of Return (IRR)……NPV Profile & IRR

• NPV of a project declines as the discount rate increases & for discount rates higher than the project’s IRR, NPV will be negative.

• If all NPVs and discount rates are plotted in a graph, we get NPV profile and the discount rate at which the NPV is zero can be identified as IRR, or

• The point where its NPV profile crosses the horizontal axis indicates a project’s Internal Rate of Return.

NPV Profile & IRR(Example)

Cash flow Discount rate

NPV

-20000 0% 12,580

5430 5% 7,561

5430 10% 3,649

5430 15% 550

5430 16% 0

5430 20% (1942)

5430 25% (3974)

Internal Rate of Return (IRR)……

• Acceptance Rule: Accept the project when r > k, and reject when r < k; may accept the project when r = k.

• Merits: Same as of NPV criterion.• Demerits:1. Requires estimates of cash flows which is a tedious

task;2. Does not hold the value additivity principle (i.e. IRRs of

two or more projects do not add);3. At times fails to indicate correct choice between

mutually exclusive projects;4. At times yields multiple rates;5. Difficult to compute.

DCF Techniques3. Profitability Index (PI)

• The ratio of present value of cash flows to the initial outlay is Profitability Index or Benefit Cost Ratio.

• PI = (PV of annual cash flows) ÷ (Initial Investment)

• Acceptance Rule:Accept the project when PI > 1.

• Example:The initial cash outlay of a project is Rs 100,000 and it can generate cash inflow of Rs 40,000, Rs 30,000, Rs 50,000 and Rs 20,000 in year 1 through 4. Assume a 10 per cent rate of discount. Calculate the PV of cash inflows at 10 % discount rate & the PI.

• Rs.12,350; & the PI = (Rs.12,350 ÷ Rs.1,00,000) = 1.235

Profitability Index (PI)…….

• Merits: 1) Considers all cash flows & recognizes the time value of money.

• 2) A relative measure of profitability used at the time of capital rationing.

• Demerits: 1) At times fails to indicate correct choice between mutually exclusive projects;

• 2) Like NPV method, PI criterion also requires calculation of cash flows and estimate of the discount rate. In practice, estimation of cash flows and discount rate pose problems.

Conventional and Non-conventional Cash Flows

• A conventional investment has cash flows the pattern of an initial cash outlay followed by cash inflows. Conventional projects have only one change in the sign of cash flows i.e., – + + +.

• A non-conventional investment, on the other hand, has cash outflows mingled with cash inflows throughout the life of the project. Non-conventional investments have more than one change in the signs of cash flows; for example, – + + + – ++ – +.

NPV Versus IRR

• Conventional Independent Projects:

In case of conventional investments, which are economically independent of each other, NPV and IRR methods result in same accept-or-reject decision if the firm is not constrained for funds in accepting all profitable projects.

NPV Versus IRR

• Lending and borrowing-type projects: • Project with initial outflow followed by inflows is a

lending type project, and project with initial inflow followed by outflows is a borrowing type project. Both are conventional projects.

Cash Flows (Rs)

Project C0 C1 IRR NPV at 10%

X -100 120 20% 9

Y 100 -120 20% -9

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.

NPV Rs 63

-750

-500

-250

0

250

0 50 100 150 200 250

Discount Rate (%)

NPV (Rs)

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.

Timing of Cash Flows

• Refers to a situation where cash flows of one project increases overtime & those of another decreases.

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%

Scale of Investment

• When costs of projects differ:

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

• Difference in the life span of two mutually exclusive projects can give rise to the conflict between NPV & IRR rules.

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%

Reinvestment Assumption(Reason - why NPV & IRR differs)

• The IRR method is assumed to imply that the cash flows generated by the project can be reinvested at its internal rate of return, whereas the NPV method is thought to assume that the cash flows are reinvested at the opportunity cost of capital.

Varying Opportunity Cost of Capital

• There is no problem in using NPV method when the opportunity cost of capital varies over time.

• If the opportunity cost of capital varies over time, the use of the IRR rule creates problems, as there is not a unique benchmark opportunity cost of capital to compare with IRR.

NPV Versus PI

• A conflict may arise between the two methods if a choice between mutually exclusive projects has to be made. Follow NPV method:

Project C Project D

PV of cash inflows 100,000 50,000 Initial cash outflow 50,000 20,000

NPV 50,000 30,000

PI 2.00 2.50