Chapter 2

CAPITAL BUDGETING
CAPITAL BUDGETING:

Capital Budgeting is the process of determining which capital expenditure project should be
accepted amongst various projects and given an allocation of funds from the firm.

Allocation of capital resource’s function involves organisation’s decision to invest its resources in
long-term assets like land, building facilities, equipment, vehicles, etc.

Kinds of Capital Budgeting Decisions:

Business firms are confronted with three types of capital budgeting decisions which are –

a) Accept-reject decisions:
Business firm is confronted with alternative investment proposals. If the proposal is accepted, the
firm incur the investment and not otherwise. Broadly, all those investment proposals which yield a
rate of return greater than cost of capital are accepted and the others are rejected. Under this
criterion, all the independent proposals are accepted.

b) Mutually exclusive decisions:

It includes all those projects which compete with each other in a way that acceptance of one
precludes the acceptance of other or others.

c) Capital rationing decisions:

Capital rationing refers to the situations where the firms have more acceptable investments
requiring greater amount of finance than is available with the firm. It is concerned with the selection
of a group of investment out of many investment proposals ranked in the descending order of the
rate of return.

CAPITAL BUDGETING TECHNIQUES

Traditional or non-discounted cash flow techniques:

These techniques do not discount the cash flows to find out their present worth.
Payback Period This technique estimates the time required by the project to recover the firm’s
Method initial outlay, through cash inflow.
Payback Period=Initial Investment / Annual cash inflows

Where the cash inflows are not uniform, cumulative cash inflows will be
calculated and by interpolation exact payback period can be calculated.
Decision Rule:
Accept the project if the payback period computed is less than the maximum
set by the management.
In case of multiple projects, the project with shorter payback period will be
selected.
Average Rate of ARR = Average Profits / Initial Investment
Return (ARR) or Decision Rule:
 Accounting Accept the proposal if ARR > Minimum rate of return (cut off rate).
Rate of Return Reject the project if ARR < Minimum rate of return (cut off rate).
Method In case of multiple projects, the project yielding a higher rate of return will be
preferred.
Modern or Discounted cash flow techniques:
Under this method, the cash flow discounted at the project’s discount rate to the present time, is
a present value.
Net Present NPV=P.V of Cash Inflows−P.V of Cash OutflowsNPV
Value Method (OR)
(NPV) NPV=P.V of future Cash Flows−Initial Cash OutflowNPV

Modified NPV Under this modified approach, terminal value of cash inflows is calculated
using reinvestment rate.
Thereafter, MNPV is determined with present value of such terminal value of
the cash inflows and present value of the cash outflows using cost of capital (k)
as the discounting factor.
Terminal Value=CF(1+r)n−t
MNPV=TV  (1+K)n−Initial InvestmentMNPV

Internal Rate of The internal rate of return refers to the rate at which P.V of cash inflows and
Return (IRR) P.V of cash outflows are equal.
In other words, it is the rate at which NPV of the investment is zero.
Step 1: Calculate PVAF using the following formula:
PVAF=Initial Investment / Average cash inflows
Step 2: Find out in present value annuity table, for given period at what
percentage value is nearest to our calculated PVAF. Such percentage will be
the approximate IRR.
Modified IRR Step 1: PVC = Present Value of the cash outflows or Initial investment
Step 2: Terminal Value (TV) = Σ CF (1+r) ⁿ⁻ᵗ
Step 3: PVC = TV / (1+MIRR) ⁿ
Modified NPV or Modified IRR may be used to resolve the conflict in ranking of
the alternative projects under NPV and IRR methods.
Profitability Profitability Index=P.V of Future cash flows / Initial Investment
Index (PI)
Method

Decision Rule:

Internal rate of return

Proposal Net Present Value Profitable Index (PI)
(r)
Accept Positive ≥k >1
Indifferent Zero =k =1
Reject Negative <k <1
In case of more than one project/proposal, the project with higher NPV/IRR/PI will be selected.

In case of mutually exclusive projects, financial appraisal using NPV & IRR methods may provide
conflicting results. The reasons for such conflicts may be attributed to–
i. Difference in timing / pattern of cash inflows of the alternative proposals (Time Disparity)
ii. Difference in the amount of investment (Size Disparity)
iii. Difference in the life of the alternative proposals (Life Disparity)
Time disparity: Such conflicts may be resolved using modified NPV and IRR using reinvestment rate
applicable to the firm.
Size disparity: Such conflict may be resolved using incremental approach.
Steps:
 Find out the differential cash flows between the two proposals
 Calculate the IRR of the incremental cash flows
 If the IRR > Cost of capital, the project with greater non-discounted net cash flows should be
selected.

Life disparity
To resolve such conflict, compare the alternatives on the basis of their Equivalent Annual Benefit
(EAB) or Equivalent Annual Cost (EAC) and select the alternative with the higher EAB or lower EAC.
EAB=NPV × Capital Recovery Factor OR NPV ÷ PVIF A K ,N

EAC=PV of Cost ÷ PVIF A K ,N

Risk and Uncertainty:

Uncertainty refers to the outcomes of a given event which are too unsure to be assigned
probabilities, while risk refers to a set of unique outcomes for a given event which can be assigned
probabilities.
In investment decisions, cash outflows and cash inflows over the life of the project are estimated
and on the basis of such estimates, decisions are taken following some appraisal criteria (NPV, IRR,
etc.).
Risk and uncertainties are involved in the estimation of such future cash flows as it is very difficult to
predict with certainty what exactly will happen in future.
Therefore, the risk is referred as the variability in actual returns in relation to the estimated return.

Standard Deviation and Coefficient of Variation:

Standard Deviation is considered as the best measure of dispersion or variability.

Higher value of standard deviation indicates higher variability and vice versa. Higher variability
means higher risk.
As future cash flows cannot be estimated with certainty, it involves risk. Therefore, risk in
investment analysis can be measured by using standard deviation.
Investment proposal with lower standard deviation will be preferred.

Standard Deviation =  Σf(x−xˉ)2

Coefficient of Variation=Standard DeviationMean×100

Standard deviation is an absolute measure of risk analysis and it can be used when projects under
consideration are having same cash outlay.
If the projects to be compared involve different outlays/different expected value, the coefficient of
variation is the correct choice, being a relative measure.

Risk Adjusted Discount Rate (RADR) Method:

Risk adjusted discount rates method is used in investment and budgeting decisions to cover time
value of money and the risk. The use of risk adjusted discount rate is based on the concept that
investors demand higher returns from the risky projects.

High Risk Projects = Higher Discount Rate

Low Risk Projects = Lower Discount Rate
Risk Adjusted Discount Rate for Project is given by:

NPV=∑ {NC F t  (1+Kr) t}

RADR=Risk free rate +Risk premium RADR

Certainty Equivalent Approach (CE Approach):

This is another method of dealing with risk in capital budgeting in order to reduce the forecasts of
cash flows to some conservative levels.

The certainty equivalent approach may be expressed as:

NPV=∑ {❑t × NC F t  (1+Kr) t}

Where,
❑t = the certainty equivalent coefficient (assumes value between 0 and 1 and varies inversely with risk)
K f = risk-free rate of return
Certain cash flows = Estimated cash flows × certainty-equivalent coefficient (❑t )

Capital budgeting Techniques under uncertainty:

Risk can be defined as the chance that the actual outcome will differ from the expected outcome.
Uncertainty relates to the situation where a range of differing outcome is possible, but it is not
possible to assign probabilities to this range of outcomes.
There are three different types of project risk to be considered:
1. Stand-alone risk: This is the risk of the project itself.
2. Corporate or within-firm risk: This is the total or overall risk of the firm when it is viewed as
a collection or portfolio of investment projects.
3. Market or systematic risk: Market risk is essentially the stock market’s assessment of a
firm’s risk, its beta, and this will affect its share price.

Statistical Techniques for Risk Analysis:

a) Probability Assignment
b) Expected Net Present Value
c) Standard Deviation
d) Coefficient of Variation
e) Probability Distribution Approach
f) Normal Probability Distribution

Probability Assignment:

Probability may be defined as the likelihood of occurrence of an event.

If an event is certain to occur, the probability of its occurrence is 1 but if an event is certain not to
occur, the probability of its occurrence is 0. Thus, probability of all events to occur lies between 0
and 1.

Probability estimates which is based on a large number of observations is known as an objective

probability.

Such probability assignments that reflect the state of belief of a person rather than the objective
evidence of a large number of trials are called personal or subjective probabilities.

Expected Net Present Value:

Once the probability assignments have been made to the future cash flows, the next step is to find
out the expected net present value. It can be found out by multiplying the monetary values of the
possible events by their probabilities.

The following equation describes the expected net present value.

ENC F t =NCFt × Probability ENCF_t

Where –

ENPV is the expected net present value,

ENC F t expected net cash flows in period t and
k is the discount rate.
 FORMULA SHEET
CHAPTER 2: CAPITAL BUDGETING

Present Value of Single Cash PV = Future Value

Flow
(1+i)t

Future Value of Single Cash FVt = PV * (1+i)t

Flow

Future Value of Annuity FVA = R (1+ i)t – 1

Present Value of Annuity PVA = R (1 + i)t – 1

i ( 1+i)t

Present Value of Perpetuity R

Present Value of R i-g

Growing

Perpetuity

Net Present Value

NPV = Sum of Discounted Cash Inflows – Discounted Cash Outflows

Pay Back Period

Average Rate of Return

Internal Rate of Return

or
Profitability Index

Standard Deviation

Certainty α=Certain Net Cash Flows

Equivalent Uncertain Net Cash Flow

Approach

NPV = α NCFt

(1 + Kf)t

α= the risk adjustment factor or the certainty equivalent coefficient

NCFt = the forecasts of net cash flow without risk adjustment Kf = risk- free rate
of return assumed to be constant for all periods
Expected NPV
ENPV = ENCFt

(1 + K)t

Where ENPV is the expected net present value, ENCFt expected net cash flows
in period t and k is the discount rate.

ENCFt = NCF * Probability

Illustration
Illustration 1:

A project costs Rs. 3,00,000 and yields annually a profit of Rs. 80,000 after depreciation @ 12% p.a.
but before tax of 50%. Calculate the payback period.

Illustration 2:

A project with an outlay of Rs. 12,000 yields Rs. 2,000, Rs. 3,000, Rs. 4,000 and Rs. 6,000 respectively
in the first, second, third and fourth year, the payback period will be calculated as thus:

Year Cash-inflow Cumulative cash-inflow

1 2,000 2,000
2 3,000 5,000
3 4,000 9,000
4 6,000 15,000

Illustration 3:

The following are the details relating to two projects:

Project X(Rs.) Project Y(Rs.)

Cost of Project 1,60,000 2,00,000
Estimated Scrap 16,000 24,000

Estimated Savings:
1st year 20,000 40,000
2nd year 30,000 60,000
3rd year 50,000 60,000
4th year 50,000 60,000
 5th year 40,000 30,000
6th year 30,000 20,000
7th year 10,000 - -
Calculate Payback Period and consider which project is better.

Illustration 4:

Calculate discounted payback period from the information given below:

Cost of Project Rs. 10,00,000

Life 5 years

Annual Cash inflow Rs. 4,00,000

Cut-off rate 10%

Illustration 5:

A company is considering the purchase of a machine. Management does not want to purchase a
machine if its payback period is more than 3 years and its rate of return of investment is less than
20%.

Two machines – X and Y are under consideration. Cost of each machine is Rs. 10,000 and working life
is 4 years. Scrap value is Rs. 1,200 and Rs. 400 respectively. Annual cash inflows are as under:

Year Machine Machine X Machine Y

Rs. Rs.
First 2,000 3,000
Second 3,000 4,000
Third 4,000 5,000
Fourth 8,000 5,000
Evaluate the two proposals and suggest as to which machine should be purchased?

Illustration 6:

ABC & SK Co. Ltd. is considering the purchase of a machine. Two machines, X and Y, are available
each costing Rs. 50,000 and salvage is estimated at Rs. 3,000 and Rs. 2,000 respectively. Earnings
after taxation are expected to be as follows:

Year Cash Flow

Machine X Machine Y
1 15,000 5,000
2 20,000 15,000
3 25,000 20,000
4 15,000 30,000
5 10,000 20,000
Evaluate the two alternatives according to:
a) The payback method;

b) Unadjusted Rate of Return Method;

c) Net Present value Method. A discount rate of 10% is to be used.

Illustration 7:

Rank the following investment proposals for A&G pvt. Ltd. in order of their profitability using (a)
Payback period method, (b) Accounting rate of return method and (c) Present value index method
(cost of capital – 10%):

Project Initial Outlay Annual Cash Flow Life

Rs Rs (in years)
A 96,000 15,000 12
B 48,000 10,000 8
C 80,000 14,000 10
D 40,000 9,000 8

Illustration 8:

A project costs Rs. 10,000 and cash inflows in the first, second, third and fourth years respectively is
Rs.2,000, Rs. 3,000, Rs. 5,000 and Rs. 6,000. Calculate time adjusted rate of return for the project.

Illustration 9:

SK & ABC Company Ltd. is considering the purchase of a new investment. Two alternative
investments are available (A and B) each costing Rs. 1,00,000. Cash inflows are expected to be as
follows:

Cash Inflows Investments A Investments b

Years Rs. Rs.
1 40,000 50,000
2 35,000 40,000
3 25,000 30,000
4 20,000 30,000
The company has a target return on capital of 10%. Risk premium rates are 2% and 8% respectively
for investments A and B. Which investment should be preferred?

Illustration 10:

There are two projects X and Y. each involves an investment of Rs. 40,000. The expected cash
inflows and the certainly coefficients are as under:

Year Project X Project Y

Certainty Certainty
Cash Inflow Cash Inflow
Coefficient Coefficient
Rs. Rs.
1 25,000 0.8 20,000 0.9
 2 20,000 0.7 30,000 0.8
3 20,000 0.9 20,000 0.7
Risk-free cut-off rate is 10%. Suggest which of the two projects should be preferred.

Illustration-11:

Two mutually exclusive investment proposals are being considered. The following information is
available:

Project A (Rs.) Project B (Rs.)

Cost 6000 6000
Cash inflow
Year Rs. Probability Rs. Probability
1 4,000 0.2 7000 0.2
2 8,000 0.6 8,000 0.6
3 12,000 0.2 9,000 0.2
Assuming cost of capital at 10%, advice for the selection of the project.

Illustration-12:

From the following information, ascertain which project is riskier on the basis of standard deviation:

Project A Project B
Cash Inflow (Rs.) Probability Cash Cash Inflow Probability (Rs.)
2,000 .2 2,000 .1
4,000 .3 4,000 .4
6,000 .3 6,000 .4
8,000 .2 8,000 .1

Illustration 13:

The management of SK & ABC Ltd. is considering which of the two mutually exclusive projects to
select. Details of each project are as follows:

Project A Project B
Probability Profit Probability Profit
(Rs. ‘000) (Rs. ‘000)
0.3 300 0.2 800
0.3 400 0.6 600
0.4 500 0.1 800
0.1 1600
Illustration 14:

Mr. ABC, a risky investor is considering two mutually exclusive projects A and B. You are required to
advise him about the acceptability of the project from the following information.

Project A(Rs.) Project B(Rs.)

Cost of the investment
50,000 50,000
Forecast cash flows per annum
for 5 years
Optimistic 30,000 40,000
Most likely 20,000 20,000
Pessimistic 15,000 5,000
(The cut-off rate may be
assumed to be 15%)
 CASE STUDIES
Question 1 - The Capital Budget Committee of SK company is making a preliminary screening of
capital expenditure proposals. The following proposals are under consideration:

Proposal Investment Annual Net Cash Service Life Present Value

Investment inflows (in Factor
(after tax but before years) at 20%
depreciation)

Rs. Rs.
A 31,300 6,000 10 4.192
B 97,400 20,000 20 4.870
C 98,075 25,000 10 4.192
D 27,200 4,000 15 4.675

Question 2 - Calculate the ‘pay-back period’, ‘average rate of return’ and ‘net present value’ for a
project which requires an initial outlay of Rs. 10,000 and generates year ending cash flows (after tax
but before depreciation) of Rs. 6,000; Rs. 3,000; Rs. 2,000; Rs. 5000 and Rs. 5,000 from the end of
the first year to the end of fifth year. The required rate of return is 10 percent and pays tax at 50
percent rate. The project has a life of five years and depreciated on straight line basis.

Year 1 2 3 4 5

Discount Rate at 10% .909 .826 .751 .683 .620

Question 3 - SK. Ltd. is considering the purchase of a new machine which will come out some
operations which are at present performed by labour X and Y are alternative models. The following
information’s are available:

Machine X Machine Y
Cost of Machine 15,000 24,000
Estimated life of machine 5 years 6 years
Estimated saving in scrap p.a. 1,000 1600
Estimated cost of indirect 600 800
materials
p.a.

Estimated savings in direct 9,000 12000

wages
p.a.

Additional cost of 700 1,100

maintenance
p.a.

Additional cost of supervision 1,200 1,600

 p.a.
Depreciation will be charged on a straight-line basis. A tax rate of 50% is assumed.

a) The pay back method;

b) Unadjusted return on average investment method; and

c) Net present value index method (cost of capital 8 percent)

Note: - The present value of Re. 1 @ 8% per annum received annually for 5 years is 3,993 and for 6
years are 4.623.

Question 4 - The following details of SK & ABC Co. relate to the two machines X and Y:

Machine X Machine Y

Cost Rs. 56,125 Rs. 56,125

Estimated Life 5 years 5 years

Estimated salvage value Rs. 3,000 Rs. 3,000

Annual income after tax and depreciation:

Year Rs. Rs.

I 3,375 11,375

II 5,375 9,375

III 7,375 7,375

IV 9,375 5,375

V 11,375 3,375

Overhauling charges at the end of third year Rs. 25,000 on machine Y. Depreciation has been
charged at straight line method. Discount rate is 10%, P.V.F. at 10% for five years are 0.909, 0.826,
0.751, 0.683 and 0.621. Suggest which project should be accepted.

Question 5 - ABC Ltd. is contemplating adding a new product line. The new product line would be
marketable for only five years, after which time it would have to be discontinued. The costs and
revenues that would be associated with the new line are:

Cost of equipment’s required 80,000

Working Capital needed 70,000

Salvage value of equipment in 5 years 10,000

Annual sales revenues 75,000

Annual out of pocket costs for salaries, advertising etc. 45,000

Overhaul of the equipment required in 4 years. 5,000

The company’s cost of capital is 12%. Would you recommend that the new line be introduced?
Ignore income tax. The Present value of Re. 1 for 5 years at 12% discount factor is .893, .797, .636
and .567.

Question 6 - From the following information, ascertain which project is riskier on the basis of
coefficient of variation:

Project A Project B

Cash Inflow (Rs.) Probability Cash Inflow Probability (Rs.)

2,000 .2 2,000 .1

4,000 .3 4,000 .4

6,000 .3 6,000 .4

8,000 .2 8,000 .1
 Practical Type Question
Question 1. SK Co. is considering the purchase of a Machine. Model ‘A’ and Model ‘B’ are available
for this purpose each costing Rs. 1,00,000. Estimated working life of each machine is 5 years and
salvage value is Rs. 4,000 and Rs. 6,000 respectively. Estimated annual cash flows are estimated to
be as under.

Year Machine A (Rs.) Machine B (Rs.)

First 60,000 20,000
Second 50,000 30,000
Third 40,000 40,000
Fourth 20,000 50,000
Fifth 20,000 60,000
Evaluate these proposals according to payback period method.

Question 2. From the followings details of SK Corporation relating to two projects, calculate the
payback period and suggest which project is better:

Project A Project B
Cost of the Project Rs. 1,80,000 2,00,000
Estimated Scrap Value 20,000 25,000
Estimated Savings:
1st year 25,000 35,000
2nd year 30,000 50,000
3rd year 45,000 70,000
4th year 50,000 65,000
5th year 40,000 30,000
6th year 30,000 20,000
7th year 10,000 -

Question 3. Cost of a Machine is Rs. 2,50,000 and its working life is estimated to be 5 years. Annual
cash inflows are as under:

Year I II III IV V

Annual Cash Inflows (Rs.) 60,000 70,000 60,000 90,000 50,000

Calculate:

A) Pay Back Period

B) Post Payback Period

C) Post Payback Profits

D) Index of Post Payback Profits

Question 4. SK Ltd. is considering the purchase of a new machine. Two machines A and B are
available, each costing Rs. 50,000. Earnings after taxation are expected to be as under:
 Cash Flow

Year Machine A Machine B

Rs. Rs.

1 15,000 5,000

2 20,000 15,000

3 30,000 20,000

4 15,000 30,000

5 5,000 20,000

Evaluate the two alternatives according to:

(a) Payback Period Method (b) Return on Investment Method (c) Present Value Index Method.
A discount rate of 10% is to be used.

Question 5. SK Ltd. is considering the purchase of a machine. Two machine X and Y are available
each costing Rs. 5,000. Earnings after taxation and depreciation on the basis of fixed instalment
system are expected to be as follows:

Year Machine X Machine Y

1 500 200
2 1,000 300
3 1,500 1,000
4 400 2,000
5 100 1,00
Evaluate the two alternatives according to:

(a) The payback period method, and

(b) Return on investment method.

Question 6. Given data for ABC Ltd.:

Initial Investment 20,000

Net Cash Inflow:

1st year 2,000

2nd year 2,000

3rd to 10th year 2,500

Work out net present value with a discount rate at 10% and express whether the investment will be
worthwhile. The P.V.F. @ 10% are as follows:

Year 1 2 3 4 5 6 7 8 9 10

P.V.F. .909 .826 .751 .683 .621 .564 .513 .467 .424 .386
Question 7. ABC Ltd. has to purchase a machine. Two models A and B are available. You are to
determine as to which machine should be purchased using

(i) Payback Period Method,

(ii) Unadjusted Rate of Return Method and
(iii) Present Value Index Method (Cost of Capital - 12%):

Particulars Machine A Machine B

Cost of Machine Rs. 42,000 Rs. 54,000

Working Life 4 years 5 years

Scrap Value Rs. 2,000 Rs. 4,000

Annual Savings after depreciation and tax:

1st year Rs. 12,000 Rs. 12,000

2nd year Rs. 16,000 Rs. 12,000

3rd year Rs. 10,000 Rs. 12,000

4th year Rs. 8,000 Rs. 12,000

5th year - Rs. 12,000

Question 8. Rank the following investment proposals in order of their profitability according to:

(a) Payback period method,

(b) Unadjusted rate of return method and

(c) Present value index method. The cost of capital is 10%.

Project No. Initial Quality Annual Cash Flow Life

Rs. Rs. (in years)
A 60,000 8,000 15
B 25,000 3,000 10
C 3,000 1,000 5
D 2,150 1,000 3
E 20,000 4,000 10
F 40,000 8,000 8

Question 9. Golden Brick Company has got up to Rs. 3,50,000 to invest. The following proposals are
under consideration:

Proposal Initial outlay Annual Cash Flow Life (years)

A 1,25,000 16,000 15
B 2,50,000 75,000 20
C 3,00,000 25,000 18
D 25,000 9,000 12
 E 1,00,000 26,000 11
Cost of Capital is 10%.

Rank these projects according to (i) Payback period and (ii) Net present value index method. Which
projects would you recommend?

Question 10. A project requires an initial outlay of Rs. 32,400. Its estimated economic life is 3 years.
The cash streams generated by it are expected to be as follows:

Year Estimated Annual Cash Flows (Rs.)

1 16,000
2 14,000
3 12,000
Compute its IRR. If the cost of capital to the firm is 12%, advise the management whether the project
should be accepted or rejected.