CHAPTER 3

ADVANCED CAPITAL
BUDGETING DECISIONS
LEARNING OUTCOMES

After going through the chapter student shall be able to understand

 Current trends in Capital Budgeting
 Dealing with Risk in Investment Decisions

 Internal and External Factors affecting capital budgeting decision

 Methods of incorporating risk in Capital Budgeting
 Adjusted Present Value

 Optimum Replacement Cycle

1. CURRENT TRENDS IN CAPITAL BUDGETING

While discussing the capital budgeting or investment evaluation techniques at Intermediate Level,
we have assumed that the investment proposals do not involve any risk and cash flows of the project
are known with certainty. This assumption was taken to simplify the understanding of the capital
budgeting techniques. However, in practice, this assumption is not correct. In-fact, investment
projects are exposed to various types of factors some of which are as follows:
(i) Inflation
(ii) Change in technology
(iii) Change in Government Policies
Now let us discuss the impact of each factor in a detailed manner.

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 3.22.2 ADVANCED FINANCIAL MANAGEMENT

1.1 Impact of Inflation on Capital Budgeting Decisions

Adjustment for inflation is a necessity for capital investment appraisal. This is because inflation will
raise the revenues & costs of the project. The net revenues after adjustment for inflation shall be
equal to net revenues in current terms. The considerations, which cause distortion, are:
(1) Depreciation charges are based on historical costs. Tax benefits accruing from depreciation
charges do not keep parity with inflation.

As annual after-tax cash inflow of a project is equal to

(R – C – D) (1 – T) + D = (R – C) (1 – T) + DT
Where,
R  Revenue from project
C  Costs (apart from depreciation) relating to the project
D  Depreciation charges
T  Tax Rate
Here (R – C) (1 – T) tends to move in line with inflation as inflation influences revenues & costs
similarly. DT does not depend on inflation as depreciation charges are based on historical costs.
The effect of inflation is to reduce the actual rate of return.
Example:
Initial outlay of a project – ` 80,000

Expected life – 4 years

Salvage value – Nil
Annual revenues – ` 60,000
Annual costs other than depreciation – ` 20,000
Tax Rate – 50%
Depreciation on straight-line basis presuming as if there is no inflation.
Year 1 2 3 4
Revenues ` 60,000 ` 60,000 ` 60,000 ` 60,000
Costs other than depreciation ` 20,000 ` 20,000 ` 20,000 ` 20,000
Depreciation ` 20,000 ` 20,000 ` 20,000 ` 20,000
Taxable profit ` 20,000 ` 20,000 ` 20,000 ` 20,000

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 ADVANCED CAPITAL BUDGETING DECISIONS 3.3
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Tax ` 10,000 ` 10,000 ` 10,000 ` 10,000

Profit after tax ` 10,000 ` 10,000 ` 10,000 ` 10,000
Net cash inflow ` 30,000 ` 30,000 ` 30,000 ` 30,000
If there is inflation @ 10% applicable to revenues & cost of project.
Year 1 2 3 4
Revenues ` 66,000 ` 72,600 ` 79,860 ` 87,846
Costs other than depreciation ` 22,000 ` 24,200 ` 26,620 ` 29,282
Depreciation ` 20,000 ` 20,000 ` 20,000 ` 20,000
Taxable profit ` 24,000 ` 28,400 ` 33,240 ` 38,564
Tax ` 12,000 ` 14,200 ` 16,620 ` 19,282
Profit after tax ` 12,000 ` 14,200 ` 16,620 ` 19,282
Net cash inflow ` 32,000 ` 34,200 ` 36,620 ` 39,282

The actual net cash flow stream after deflating for inflation rate of 10% .
Real Net Cash Flow ` 29,091 ` 28,264 ` 27,513 ` 26,830

So actual net cash flows are less than net cash flow if there is no inflation.
(2) Costs of capital considered for investment appraisals contain a premium for anticipated inflation.
Due to inflation investors require the nominal rate of return to be equal to:
Required Rate of Return in real terms plus Rate of Inflation.
Formula
RN = RR + P
RN Required rate of return in nominal terms.
RR Required rate of return in real terms.
P  Anticipated inflation rate.
If cost of capital (required rate of return) contains a premium for anticipated inflation, the inflation
factor has to be reflected in the projected cash flows.
If there is no inflation, then it has to be discounted at required rate of return in real terms.
Illustration 1
Determine NPV of the project with the following information:

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 3.42.4 ADVANCED FINANCIAL MANAGEMENT

Initial Outlay of project ` 40,000

Annual Cash Flow from the Project (Without inflation) ` 15,000
Useful life 4 years
Cost of Capital (Including inflation premium of 10%) 12%

Solution

Annual Cash Flow of project is ` 15,000.

It would be inconsistent to discount these real cash flows at 12% (nominal rate of return).
There are two alternatives:
(i) Either to restate the cash flow in nominal term and discount at 12% or
(ii) Restate the discount rate in real terms and use this to discount the real cash flows.
NPV using (i) approach
Since inflation rate is 10% a year, real cash flows may be stated in nominal cash flows as follows:
Nominal Cash Flow = (1 + Inflation Rate) Real Cash Flows
Year Real Cash Flows Nominal Cash flows
1 15000 15,000 × 1.10 = 16,500
2 15,000 15,000 × (1.10)2 = 18,150
3 15,000 15,000 × (1.10.)3 = 19,965
4 15,000 15,000 × (1.10)4 = 21,962

NPV using nominal discounting rate 12%

16,500 18,150 19,965 21,962
+ + + - 40,000
(1.12) (1.12)2 (1.12)3 (1.12) 4

= ` 14,732 + ` 14,469 + ` 14,211+ ` 13,957 – ` 40,000

= ` 17,369 (Approx)
NPV using (ii) approach
To compute NPV using (ii) approach, we shall need real discount rate, which shall be computed as
follows:
1+ Nominal Discount Rate
Real Discount Rate= −1
1 + Inflation Rate
1+ 0.12
Real Discount Rate= − 1 = 0.0182 i.e. 1.8%.
1 + 0.10

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 ADVANCED CAPITAL BUDGETING DECISIONS 3.5
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NPV = ∑ cft − Io
t =1

Where t = Time Period

cft = Annual Cash Flow
Io = Initial Outlay

Accordingly NPV of the project

15,000 15,000 15,000 15,000
+ 2 + 3 + - 40,000
(1.0182) (1.0182) (1.0182) (1.0182)4

= ` 14,732 + ` 14,469 + ` 14,210+ ` 13,956 – ` 40,000

= ` 57,367 – ` 40,000 = `17,367(Approx)
NPV based on consideration that inflation rate for revenue and cost are different shall be computed
as follows:
N.P.V. = nΣt=1 [{Rt (1+ir) - CttΣr=1(1+ic)} (1-T) + DtT] / (1+k)t - I0
Rt revenues for the year ‘t’ with no inflation.
ir annual inflation rate in revenues for ‘r th ’ year.
Ct costs for year ‘t’ with no inflation.
ic annual inflation rate of costs for year ‘r’.
T  tax rate.
Dt depreciation charge for year ‘t’.
I0 initial outlay.
k  cost of capital (with inflation premium).
Illustration 2
XYZ Ltd. requires ` 8,00,000 for a project. Useful life of project - 4 years. Salvage value - Nil.
Depreciation Charge ` 2,00,000 p.a. Expected revenues & costs (excluding depreciation) ignoring
inflation.

Year 1 2 3 4
Revenues ` 6,00,000 ` 7,00,000 ` 8,00,000 ` 8,00,000
Costs ` 3,00,000 ` 4,00,000 ` 4,00,000 ` 4,00,000

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 3.62.6 ADVANCED FINANCIAL MANAGEMENT

Applicable Tax Rate is 60% and cost of capital is 10% (including inflation premium).
Calculate NPV of the project if inflation rates for revenues & costs are as follows:

Year Revenues Costs

1 10% 12%
2 9% 10%
3 8% 9%
4 7% 8%

Solution
Computation of Annual Cash Flow

(i) Inflation adjusted Revenues

Year Revenues (`) Revenues (Inflation Adjusted) (`)

1 6,00,000 6,00,000(1.10) = 6,60,000
2 7,00,000 7,00,000(1.10)(1.09) = 8,39,300
3 8,00,000 8,00,000(1.10)(1.09)(1.08) = 10,35,936
4 8,00,000 8,00,000(1.10)(1.09)(1.08)(1.07) = 11,08,452

(ii) Inflation adjusted Costs

Year Revenues (`) Revenues (Inflation Adjusted) (`)

1 3,00,000 3,00,000(1.12) = 3,36,000
2 4,00,000 4,00,000(1.12)(1.10) = 4,92,800
3 4,00,000 4,00,000(1.12)(1.10)(1.09) = 5,37,152
4 4,00,000 4,00,000(1.12)(1.10)(1.09)(1.08) = 5,80,124

(iii) Tax Benefit on Depreciation = ` 2,00,000 x 0.60 = ` 1,20,000

(iv) Net Profit after Tax
Year Revenues Costs Net Profit Tax Net after
(Inflation (Inflation (`) (`) Profit
Adjusted) Adjusted) (3) = (1) - (2) (4) = 60% (`)
(`)(1) (`)(2) of (3) (3) - (4)
1 6,60,000 3,36,000 3,24,000 1,94,400 1,29,600
2 8,39,300 4,92,800 3,46,500 2,07,900 1,38,600

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 ADVANCED CAPITAL BUDGETING DECISIONS 3.7
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3 10,35,936 5,37,152 4,98,784 2,99,270 1,99,514

4 11,08,452 5,80,124 5,28,328 3,16,997 2,11,331

(iv) Present Value of Cash Inflows

Year Net after Tax Benefit on Cash Inflow PVF@ PV
Profit Depreciation 10%
(`) (`) (`) (`)
1 1,29,600 1,20,000 2,49,600 0.909 2,26,886
2 1,38,600 1,20,000 2,58,600 0.826 2,13,604
3 1,99,514 1,20,000 3,19,514 0.751 2,39,955
4 2,11,331 1,20,000 3,31,331 0.683 2,26,299
9,06,744

NPV = ` 9,06,744 – ` 8,00,000 = ` 1,06,744

1.2 Impact of change in technology on Capital Budgeting Decisions

Generally it has been observed that those making capital Budgeting decision evaluates the
proposals in monetary terms i.e. quantitative values and normally fails to consider critical factors i.e.
qualitative factor that can affect the future cash flows one of such factor is technology. It is important
to note that here we are not simply talking about decision to replace existing machinery with new
machine having improved technology rather we are talking about the impact of technology change
on capital budgeting. Now the question arises why it is important to analyze the impacts of change
in technology it is because of following reason:
 Change in technology can significantly alter production process.
 Changes can also yield benefits such as improved quality, delivery time greater flexibility, etc.
 Changed technology can also result in reduction in cost of capital
 Improved cash inflows can be achieved through technological changes.
 There may be need to incur additional cost in the form of additional capital expenditure.
 The sale volume can be impacted as the anticipated life cycle of the product can be shortened
because of change in consumer preference.
Now next question arises how to incorporate impact in capital budgeting decision. For this purpose
it is very necessary that once the project has been launched it should be reviewed on continuous
basis and if required it need to be revised in light of changes in the technology.

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 3.82.8 ADVANCED FINANCIAL MANAGEMENT

The various ways in which the impact of change in technology can be incorporated in capital
Budgeting decisions are as follows.

1. At the time of making Capital Budgeting decisions the risk of change in technology should be
considered using various techniques such as Sensitivity Analysis, Scenario Analysis,
Simulation Analysis etc. (discussed later in this chapter)

2. Once project has been launched analyse the impact of change in technology both positive or
negative and revise estimates in monetary terms.
3. If continuation of project is proving to be unviable then look for abandonment option and
evaluate the same (discussed later).
4. Suitably adjusting the discounting rate.

1.3 Impact of change in Government Policies on Capital Budgeting

Decisions
Government Policies are important external factors that impacts the capital budgeting decision
because directly or indirectly they affect the future cash flows of the firm that forms the basis of
capital budgeting decisions. It might be possible that Government Policy may not affect us, but it
may affect our supplier, buyers, customers, service providers etc.
The impact of changes in these policies can be positive as well as negative. What is more important
is that the impact of such should be analysed and if required the estimation should be revised
adequately. If required, the firm should consider the option to abandon the project (discussed in later
chapter of study material).
The change in Government Policy can be analysed under two headings:
i. Impact of change of Policies on Domestic Capital Budgeting Decision.
ii. Impact of change of Policies on International Capital Budgeting Decision.
While some Government policies are changed after a longer period, say five to ten years, some
change from quarter to a year. The impact of each policy may vary from each other. For example,
the policies such as New Industrial Policy 1991, might had drastically impacted the Capital Budgeting
decisions of various firms in the beginning period of 1990s due to opening of the doors of the Indian
Economy for the Global world. However, such types of policies normally come out after a longer
period. On the other hand, there are some policies of the Government that are announced/ reviewed
within a period of one year. Some of these are as follows:
 Fiscal policy: The use of government spending, taxation and borrowing to influence both the
pattern of economic activity and level of growth of aggregate demand, output and
employment.

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 Monetary Policy: Monetary policy refers to the use of monetary policy instruments which are
at the disposal of the central bank to regulate the availability, cost and use of money and
credit to promote economic growth, price stability, optimum levels of output and employment,
balance of payments equilibrium, stable currency or any other goal of government's economic
policy.
Generally, the change in monetary policy depends on the economic status of the nation. In India,
the monetary policy includes decisions on open market operations, variation in reserve
requirements, selective credit controls, supply of currency, bank rates (Repo Rates) and other rates.
Since in India members of Monetary Policy Committee (MPC) are required to meet at least four times
in a year generally changes in the policies related to above mentioned matters takes at least two to
three times in a year.
Now let us discuss how changes in Government Policies affect the Capital Budgeting decision under
two broad heads:
1.3.1 Impact of changes in Government Policies on Domestic Capital Budgeting
Decision.
(a) Since the change in interest rate are decided by Government through its Monetary Policy.
This can affect the Cost of Capital because the Cost of Debt is normally dependent on the
bank rate of interest as they are considered as one of the important factors to compute YTM.
Though this rate change may not much affect Capital Budgeting decision because they are
financed from long term source of finance but they may impact working capital decisions to a
great extent. The main reason behind is that the Bank Overdraft as one of the important
constituents of Working Capital and it may lead to change in cash flow estimation. Hence, it
is important that though small change in Bank Interest can be ignored but a major change
say about 100 basis points or so can impact cash flows of the firm and may call for revision
of estimations.
(b) Another important change (Government Policy) is related to Fiscal Policy, Since Fiscal Policy
forms the basis of Tax Rate and Annual Cash Flows are dependent on Rate of Depreciation
of Tax Rate, any drastic change in any of these two items may call for revision of estimated
cash flows.
1.3.2 Impact of changes in Government Policies on International Capital Budgeting
Decision.
(a) In International Capital Budgeting Decisions, the foreign exchange rate play a very important
role. As mentioned above the change in bank rate and money supply is decided as per
Monetary Policy, the change in any of these two impacts the rate of Foreign Exchange and it
may call for revision of estimates.

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(b) Change in Tax Rates relating to Foreign Income or changes in provisions of Double Tax
Avoiding Agreement (DTAA) as decided in Fiscal Policy may call revision of estimates.

Thus, from above discussion it can be concluded that while estimating future cash inflows change
in the policies be forecasted and a proper provision should be incorporated in the expected cash
flows.

2. DEALING WITH RISK IN INVESTMENT DECISIONS

While discussing the capital budgeting or investment evaluation techniques at Intermediate Level in
the paper of Financial Management, we have assumed that the investment proposals do not involve
any risk and cash flows of the project are known with certainty. This assumption was taken to simplify
the understanding of the capital budgeting techniques. However, in practice, this assumption is not
correct. In-fact, investment projects are exposed to various degrees of risk.
There can be three types of decision making:
(i) Decision making under certainty: When cash flows are certain.
(ii) Decision making involving risk: When cash flows involves risk and probability can be
assigned.
(iii) Decision making under uncertainty: When the cash flows are uncertain and probability cannot
be assigned.

2.1 Risk and Uncertainty

Risk is the variability in terms of actual returns comparing with the estimated returns. Most common
techniques of risk measurement are Standard Deviation and Coefficient of Variation. There is a thin
difference between risk and uncertainty. In case of risk, probability distribution of cash flow is known.
When no information is known to formulate probability distribution of cash flows, the situation is
referred as uncertainty. However, these two terms are used interchangeably.

2.2 Reasons for adjustment of Risk in Capital Budgeting decisions

Main reasons for considering risk in capital budgeting decisions are as follows:
1. There is an opportunity cost involved while investing in a project for the level of risk.
Adjustment of risk is necessary to help make the decision as to whether the returns out of the
project are proportionate with the risks borne and whether it is worth investing in the project
over the other investment options available.

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2. Risk adjustment is required to know the real value of the Cash Inflows. Higher risk will lead
to higher risk premium and also expectation of higher return.

3. INTERNAL AND EXTERNAL FACTORS AFFECTING

CAPITAL BUDGETING DECISION
Risk arises from different factors, depending on the type of investment being considered, as well as
the circumstances and the industry in which the organisation is operating. Accordingly it these
factors can be divided following two broad categories:

3.1 Internal Factors

These factors are internal to the company, and they can further be divided into following categories:
3.1.1 Project-specific risk
Risks which are related to a particular project and affects the project’s cash flows. It includes
completion of the project in scheduled time, error of estimation in resources and allocation,
estimation of cash flows etc. For example, a nuclear power project of a power generation company
has different risks than hydel projects.
3.1.2 Company-specific risk
Risk which arise due to company specific factors like downgrading of credit rating, changes in key
managerial persons, cases for violation of intellectual property rights (IPR) and other laws and
regulations, dispute with workers etc. All these factors affect the cash flows of an entity and access
to funds for capital investments. For example, two banks have different exposure to default risk.

3.2 External Factors

These factors are external to the company, and they can further be divided into following categories:
3.2.1 Industry-specific risk
These are the risks which effect the whole industry in which the company operates. These risks
include regulatory restrictions on industry, changes in technologies etc. For example, regulatory
restriction imposed on leather and breweries industries.
3.2.2 Market risk
The risk which arise due to market related conditions like entry of substitute, changes in demand
conditions, availability and access to resources etc. For example, a thermal power project gets
affected if the coal mines are unable to supply coal requirements of a thermal power company etc.

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3.2.3 Competition risk

These are risks related with competition in the market in which a company operates. These risks are
risk of entry of rival, product dynamism and change in taste and preference of consumers etc.
3.2.4 Risk due to Economic conditions
These are the risks which are related with macro-economic conditions like changes in monetary
policies by central banks, changes in fiscal policies like introduction of new taxes and cess, inflation,
changes in GDP, changes in savings and net disposable income etc.
3.2.5 International risk
These are risk which are related with conditions which are caused by global economic conditions
like restriction on free trade, restrictions on market access, recessions, bilateral agreements, political
and geographical conditions etc. For example, restriction on outsourcing of jobs to overseas
markets.

4. METHODS OF INCORPORATING RISK IN CAPITAL

BUDGETING
Techniques of risk analysis in capital budgeting can be classified as below:

Probability

Statistical Variance or Standard

Techniques Deviation

Coefficient of Variation
Techniques of Risk Analysis

Risk-adjusted discount rate

Conventional
techniques
Certainty Equivalent

Sensitivity analysis

Scenario analysis
Others techniques
Simulation analysis

Decision Tree

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 ADVANCED CAPITAL BUDGETING DECISIONS 3.13
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4.1 Statistical Techniques

4.1.1 Probability
Probability is a measure about the chances that an event will occur. When an event is certain to
occur, probability will be 1 and when there is no chance of happening an event, probability will be 0.
Example:

Assumption Cash Flows (`) Probability

Best guess 3,00,000 0.3

High guess 2,00,000 0.6

Low guess 1,20,000 0.1

In the above example chances that cash flow will be ` 3,00,000, ` 2,00,000 and
` 1,00,000 are 30%, 60% and 10% respectively.
(i) Expected Net Cash Flows
Expected Net Cash flows are calculated as the sum of the likely Cash flows of the Project multiplied
by the probability of cash flows. Expected Cash flows are calculated as below:
E(R)/ENCF = ∑ni=1 NCFi × Pi

Where, E(R)/ENCF = Expected Net Cash flows

Pi = Probability of Cash flows
NCFi = Net Cash flows
Example:

Assumption Cash Flows (`) Probability Expected cash flow (`)

(1) (2) (3) (2×3)
Best guess 3,00,000 0.3 3,00,000 × 0.3 = 90,000
High guess 2,00,000 0.6 2,00,000 × 0.6 = 1,20,000
Low guess 1,20,000 0.1 1,20,000 × 0.1 = 12,000
Expected Net cash flow (ENCF) 2,22,000

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(ii) Expected Net Present Value

Expected net present value =
n
ENCF
ENPV = ∑ t
t=1 (1+k )
Where, ENPV = Expected Net Present Value
ENCF = Expected Net Cash Flows(including both inflows and outflows)
t = Period
k = Discount rate.

(a) Expected Net Present Value - Single period

Let us understand the calculation of Expected Net Present Value (ENPV) for a single period through
an illustration as follows:
Illustration 3
Possible net cash flows of Projects A and B at the end of first year and their probabilities are given
below. Discount rate is 10 per cent. For both the projects, initial investment is ` 10,000. Calculate
the expected net present value for each project. State which project is preferable?

Possible Project A Project B

Event Cash Flow (`) Probability Cash Flow (`) Probability
A 8,000 0.10 24,000 0.10
B 10,000 0.20 20,000 0.15
C 12,000 0.40 16,000 0.50
D 14,000 0.20 12,000 0.15
E 16,000 0.10 8 ,000 0.10

Solution
Calculation of Expected Value for Project A and Project B
Project A Project B
Possible Cash Probability Expected Cash Probability Expected
Event Flow Value Flow Value
(`) (`) (`) (`)
A 8,000 0.10 800 24,000 0.10 2,400

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 ADVANCED CAPITAL BUDGETING DECISIONS 3.15
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B 10,000 0.20 2,000 20,000 0.15 3,000

C 12,000 0.40 4,800 16,000 0.50 8,000
D 14,000 0.20 2,800 12,000 0.15 1,800
E 16,000 0.10 1,600 8,000 0.10 800
ENCF 12,000 16,000

The Net Present Value for Project A is (0.909 × ` 12,000 – ` 10,000) = ` 908
The Net Present Value for Project B is (0.909 × ` 16,000 – ` 10,000) = ` 4,544.
(b) Expected Net Present Value- Multiple period
Let us understand the calculation of Expected Net Present Value (ENPV) for multiple periods
through an illustration as follows:
Illustration 4
Probabilities for net cash flows for 3 years of a project are as follows:

Year 1 Year 2 Year 3

Cash Flow Probability Cash Flow Probability Cash Flow Probability
(`) (`) (`)
2,000 0.1 2,000 0.2 2,000 0.3
4,000 0.2 4,000 0.3 4,000 0.4
6,000 0.3 6,000 0.4 6,000 0.2
8,000 0.4 8,000 0.1 8,000 0.1

Calculate the expected net present value of the project using 10 per cent discount rate if the Initial
Investment of the project is ` 10,000.

Solution
Calculation of Expected Value

Year 1 Year 2 Year 3

Cash Prob. Expected Cash Prob. Expected Cash Prob. Expected

Flow Value Flow Value Flow Value
(`) (`) (`) (`) (`) (`)

2,000 0.1 200 2,000 0.2 400 2,000 0.3 600

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2.16 ADVANCED FINANCIAL MANAGEMENT

4,000 0.2 800 4,000 0.3 1200 4,000 0.4 1,600

6,000 0.3 1,800 6,000 0.4 2400 6,000 0.2 1,200
8,000 0.4 3,200 8,000 0.1 800 8,000 0.1 800

ENCF 6,000 4,800 4,200

The present value of the expected value of cash flow at 10 per cent discount rate has been
determined as follows:
ENCF1 ENCF2 ENCF3
Present Value of cash flow = + +
(1+k)1 (1+k)2 (1+k)3
6,000 4,800 4,200
= + +
(1.1) (1.1)2 (1.1)3

= (6,000 × 0.909) + (4,800 × 0.826) + (4,200 × 0.751)

= ` 12,573
Expected Net Present value = Present Value of cash flow - Initial Investment
= ` 12,573 – ` 10,000 = ` 2,573.
4.1.2 Variance
Variance is a measurement of the degree of dispersion between numbers in a data set from its
average. In very simple words, variance is the measurement of difference between the average of
the data set from every number of the data set. Variance is calculated as below:
2
Variance(σ2 ) = ∑nj= 1�NCFj − ENCF� Pj

Where, NCFj = Net Cash Flow

ENCF = Expected Net Cash Flow
Pj = Probability
Variance measures the uncertainty of a value from its average. Thus, variance helps an organization
to understand the level of risk it might face on investing in a project. A variance value of zero would
indicate that the cash flows that would be generated over the life of the project would be same. This
might happen in a case where the company has entered into a contract of providing services in
return of a specific sum. A large variance indicates that there will be a large variability between the
cash flows of the different years. This can happen in a case where the project being undertaken is
very innovative and would require a certain time frame to market the product and enable to develop

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 ADVANCED CAPITAL BUDGETING DECISIONS 3.17
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a customer base and generate revenues. A small variance would indicate that the cash flows would
be somewhat stable throughout the life of the project. This is possible in case of products which
already have an established market.
4.1.3 Standard Deviation
Standard Deviation (SD) is a degree of variation of individual items of a set of data from its average.
The square root of variance is called Standard Deviation. For Capital Budgeting decisions, Standard
Deviation is used to calculate the risk associated with the estimated cash flows from the project.
Importance of Variance and Standard Deviation in Capital Budgeting: For making capital
budgeting decisions, these two concepts are important to measure the volatility in estimated cash
flows and profitability in an investment proposal. Both the concepts measures the difference between
the expected cash flows and estimated cash flows (mean or average). Variance measures the range
of variability (difference) in cash flows data while Standard deviation determines risk in an investment
proposal. An investment proposal in which expected cash flows are close to the estimated net cash
flow are seen as less risky and has the potential to make profit.
Standard deviation and Variance are two different statistical concepts but are closely interrelated.
Standard deviation is calculated as square root of variance, hence, variance is prerequisite for
calculation of SD.
Illustration 5
Calculate Variance and Standard Deviation of Project A and Project B on the basis of following
information:

Possible Project A Project B

Event Cash Flow (`) Probability Cash Flow (`) Probability
A 8,000 0.10 24,000 0.10
B 10,000 0.20 20,000 0.15
C 12,000 0.40 16,000 0.50
D 14,000 0.20 12,000 0.15
E 16,000 0.10 8,000 0.10

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Solution
Calculation of Expected Value for Project A and Project B

Project A Project B
Possible Cash Flow Probability Expected Cash Flow Probability Expected
Event (`) Value (`) (`) Value (`)
A 8,000 0.10 800 24,000 0.10 2,400
B 10,000 0.20 2,000 20,000 0.15 3,000
C 12,000 0.40 4,800 16,000 0.50 8,000
D 14,000 0.20 2,800 12,000 0.15 1,800
E 16,000 0.10 1,600 8,000 0.10 800
ENCF 12,000 16,000

Project A:
Variance (σ2) = (8,000 – 12,000)2 × (0.1) + (10,000 – 12,000)2 × (0.2) + (12,000 – 12000)2 × (0.4)
+ (14,000 – 12,000)2 × (0.2) + (16000 – 12,000)2 × (0.1)
= 16,00,000 + 8,00,000 + 0 + 8,00,000 + 16,00,000 = 48,00,000

Standard Deviation (σ) = Variance(σ 2 ) = 48,00,000 = 2,190.90

Project B:
Variance(σ2) = (24,000 – 16,000)2 × (0.1) + (20,000 – 16,000)2 × (0.15) + (16,000 – 16,000)2 ×
(0.5) + (12,000 – 16,000)2 × (0.15) + (8,000 – 16,000)2 × (0.1)

= 64,00,000 + 24,00,000 + 0 + 24,00,000 + 64,00,000 = 1,76,00,000

Standard Deviation (σ) = Variance(σ 2 ) = 1,76,00,000 = 4195.23

4.1.4 The Coefficient of Variation

The standard deviation is a useful measure of calculating the risk associated with the estimated
cash inflows from an Investment. However, in Capital Budgeting decisions, the management is
several times faced with choosing between many investments' avenues. Under such situations, it
becomes difficult for the management to compare the risk associated with different projects using
Standard Deviation as each project has different estimated cash flow values. In such cases, the
Coefficient of Variation becomes useful.

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The Coefficient of Variation calculates the risk borne for every percent of expected return. It is
calculated as:
Stanadrd Deviation
Coefficient of variation =
Expected Return/ Expected Cash Flow

The Coefficient of Variation enables the management to calculate the risk borne by the concern for
every unit of estimated return from a particular investment. Simply put, the investment avenue which
has a lower ratio of standard deviation to expected return will provide a better risk – return trade off.
Thus, when a selection has to be made between two projects, the management would select a
project which has a lower Coefficient of Variation.
Illustration 6
Calculate Coefficient of Variation of Project A and Project B based on the following information:

Possible Project A Project B

Event Cash Flow (`) Probability Cash Flow (`) Probability
A 10000 0.10 26,000 0.10
B 12,000 0.20 22,000 0.15
C 14,000 0.40 18,000 0.50
D 16,000 0.20 14,000 0.15
E 18,000 0.10 10,000 0.10
Solution
Calculation of Expected Value for Project A and Project B
Project A Project B
Possible Cash Flow Probability Expected Cash Probability Expected
Event (`) Value Flow Value
(`) (`) (`)
A 10,000 0.10 1,000 26,000 0.10 2,600
B 12,000 0.20 2,400 22,000 0.15 3,300
C 14,000 0.40 5,600 18,000 0.50 9,000
D 16,000 0.20 3,200 14,000 0.15 2,100
E 18,000 0.10 1,800 10,000 0.10 1,000
ENCF 14,000 18,000

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Project A
Variance (σ2) = (10,000 – 14,000)2 × (0.1) + (12,000 – 14,000)2 × (0.2) + (14,000 – 14000)2 × (0.4)
+ (16,000 – 14,000)2 × (0.2) + (18000 – 14,000)2 × (0.1)
= 16,00,000 + 8,00,000 + 0 + 8,00,000 + 16,00,000 = 48,00,000

Standard Deviation (σ) = Variance(σ 2 ) = 48,00,000 = 2,190.90

Project B:
Variance(σ2) = (26,000 – 18,000)2 × (0.1) + (22,000 – 18,000)2 × (0.15) + (18,000 – 18,000)2 × (0.5)
+ (14,000 – 18,000)2 × (0.15) + (10,000 – 18,000)2 × (0.1)
= 64,00,000 + 24,00,000 + 0 + 24,00,000 + 64,00,000 = 1,76,00,000

Standard Deviation (σ) = Variance(σ 2 ) = 1,76,00,000 = 4195.23

Projects Coefficient of variation Risk Expected Value

A 2190.90 Less Less
= 0.1565
14000

B 4195.23 More More

= 0.2331
18000

In project A, risk per rupee of cash flow is ` 0.16 while in project B, it is ` 0.23. Therefore, Project
A is better than Project B.

4.2 Conventional Techniques

4.2.1 Risk Adjusted Discount Rate
The use of risk adjusted discount rate (RADR) is based on the concept that investors demand higher
returns from the risky projects. The required rate of return on any investment should include
compensation for delaying consumption plus compensation for inflation equal to risk free rate of
return, plus compensation for any kind of risk taken. If the risk associated with any investment project
is higher than risk involved in a similar kind of project, discount rate is adjusted upward in order to
compensate this additional risk borne. Under this method, NPV is calculated as follows:
n
NCF
NPV = ∑ t
-I
t =1 (1+k )
Where, NCFt = Net cash flow
k = Risk adjusted discount rate (RADR)
I = Initial Investment
t = Period

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A risk adjusted discount rate is a sum of risk-free rate and risk premium. The Risk Premium
depends on the perception of risk by the investor of a particular investment and risk aversion of the
Investor.
So, Risk adjusted discount rate (RADR) = Risk free rate + Risk premium
Risk Free Rate: It is the rate of return on Investments that bear no risk. For e.g., Government
securities yield a return of 6% and bear no risk. In such case, 6% is the risk-free rate.
Risk Premium: It is the rate of return over and above the risk free rate, expected by the Investors
as a reward for bearing extra risk. For high risk projects, the risk premium will be high and for low
risk projects, the risk premium would be lower.

Illustration 7
An enterprise is investing ` 100 lakhs in a project. The risk-free rate of return is 7%. Risk premium
expected by the Management is 7%. The life of the project is 5 years. Following are the cash flows
that are estimated over the life of the project:

Year Cash flows (` in lakhs)

1 25
2 60
3 75
4 80
5 65

Calculate Net Present Value of the project based on Risk free rate and also on the basis of Risks
adjusted discount rate.
Solution
The Present Value of the Cash Flows for all the years by discounting the cash flow at 7% is
calculated as below:
Year Cash flows Discounting Factor Present value of Cash Flows
(` in lakhs) @ 7% (` In Lakhs)
1 25 0.935 23.38
2 60 0.873 52.38
3 75 0.816 61.20
4 80 0.763 61.04
5 65 0.713 46.35
Total of Present value of Cash flows 244.34
Less: Initial investment 100.00
Net Present Value (NPV) 144.34

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Now, when the risk-free rate is 7% and the risk premium expected by the Management is 7%, then
risk adjusted discount rate is 7% + 7% = 14%.
Discounting the above cash flows using the Risk Adjusted Discount Rate would be as below:
Year Cash flows Discounting Present Value of Cash Flows
(` in Lakhs) Factor @ 14% (` in lakhs)
1 25 0.877 21.93
2 60 0.769 46.14
3 75 0.675 50.63
4 80 0.592 47.36
5 65 0.519 33.74
Total of Present value of Cash flows 199.79
Less: Initial investment 100.00
Net present value (NPV) 99.79

Advantages of Risk-adjusted discount rate

(1) It is easy to understand.
(2) It incorporates risk premium in the discounting factor.
Limitations of Risk-adjusted discount rate
(1) Difficulty in finding risk premium and risk-adjusted discount rate.
(2) Though NPV can be calculated but it is not possible to calculate Standard Deviation of a given
project.
4.2.2 Certainty Equivalent (CE)
As per CIMA terminology, “Certainty Equivalent is an approach dealing with risk in a capital
budgeting context. It involves expressing risky future cash flows in terms of the certain cashflow
which would be considered, by the decision maker, as their equivalent, that is the decision maker
would be indifferent between the risky amount and the (lower) riskless amount considered to be its
equivalent.”
The certainty equivalent is a guaranteed return that the management would accept rather than
accepting a higher but uncertain return. This approach allows the decision maker to incorporate his
or her utility function into the analysis. In this approach a set of risk less cash flow is generated in
place of the original cash flows.

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Steps in the Certainty Equivalent (CE) approach

Step 1: Remove risks by substituting equivalent certain cash flows from risky cash flows. This can
be done by multiplying each risky cash flow by the appropriate α t value (CE coefficient)

Certain cash flow

  =
α1
Risky or expected cash flow t

Suppose on tossing out a coin, if it comes head, you will win ` 10,000 and if it comes out to be tail,
you will win nothing. Thus, you have 50% chance of winning and expected value is ` 5,000 (` 10,000
× 0.50) . In such case, if you are indifferent at receiving ` 3,000 for a certain amount and not playing
then ` 3,000 will be certainty equivalent and 0.3 (i.e. ` 3,000/` 10,000) will be certainty equivalent
coefficient.
Step 2: Discounted value of cash flow is obtained by applying risk less rate of interest. Since you
have already accounted for risk in the numerator using CE coefficient, using the cost of capital to
discount cash flows will tantamount to double counting of risk.
Step 3: After that, normal capital budgeting method is applied except in case of IRR method, where
IRR is compared with risk free rate of interest rather than the firm’s required rate of return.
Certainty Equivalent Coefficient transforms expected values of uncertain flows into their Certainty
Equivalents. It is important to note that the value of Certainty Equivalent Coefficient lies between 0
& 1. Certainty Equivalent Coefficient 1 indicates that the cash flow is certain or management is risk
neutral. In industrial situation, cash flows are generally uncertain and managements are usually risk
averse. Under this method, NPV is calculated as follows:
n
α𝑡𝑡 × NCFt
NPV = � -I
(1 + k)t
t=1

Where,
αt = Risk-adjustment factor or the certainly equivalent coefficient
NCFt = Forecasts of net cash flow for year ‘t’ without risk-adjustment
k = Risk free rate assumed to be constant for all periods
I = Initial Investment
Illustration 8
If Investment proposal costs ` 45,00,000 and risk free rate is 5%, calculate net present value under
certainty equivalent technique.

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Year Expected cash flow (`) Certainty Equivalent coefficient

1 10,00,000 0.90
2 15,00,000 0.85
3 20,00,000 0.82
4 25,00,000 0.78

Solution
10,00,000×(0.90) 15,00,000×(0.85) 20,00,000×(0.82) 25,00,000×(0.78)
NPV = + + + - 45,00,000
(1.05) (1.05)2 (1.05)3 (1.05)4

= ` 5,34,570
Advantages of Certainty Equivalent Method
1. The certainty equivalent method is simple and easy to understand and apply.
2. It can easily be calculated for different risk levels applicable to different cash flows. For
example, if in a particular year, a higher risk is associated with the cash flow, it can be easily
adjusted and the NPV can be recalculated accordingly.
Disadvantages of Certainty Equivalent Method
1. There is no objective or mathematical method to estimate certainty equivalents. Certainty
Equivalents are subjective and vary as per each individual’s estimate.
2. Certainty equivalents are decided by the management based on their perception of risk.
However, the risk perception of the shareholders who are the money lenders for the project
is ignored. Hence, it is not used often in corporate decision making.
Risk-adjusted Discount Rate Vs. Certainty-Equivalent
Certainty Equivalent Method is superior to Risk Adjusted Discount Rate Method as it does not
assume that risk increases with time at constant rate. Each year's Certainty Equivalent Coefficient
is based on level of risk impacting its cash flow. Despite its soundness, it is not preferable like Risk
Adjusted Discount Rate Method. It is difficult to specify a series of Certainty Equivalent Coefficients
but simple to adjust discount rates.

4.3 Other Techniques

4.3.1 Sensitivity Analysis
As per CIMA terminology, “Sensitivity Analysis a modelling and risk assessment procedure in which
changes are made to significant variables in order to determine the effect of these changes on the

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planned outcome. Particular attention is thereafter paid to variables identified as being of special
significance”.

Sensitivity analysis put in simple terms is a modelling technique which is used in Capital Budgeting
decisions, to study the impact of changes in the variables on the outcome of the project. In a project,
several variables like weighted average cost of capital, consumer demand, price of the product, cost
price per unit etc. operate simultaneously. The changes in these variables impact the outcome of
the project. Therefore, it becomes very difficult to assess, change in which variable impacts the
project outcome in a significant way. In Sensitivity Analysis, the project outcome is studied after
taking into account change in only one variable. The more sensitive is the NPV (or IRR), the more
critical is that variable. So, Sensitivity analysis is a way of finding impact on the project’s NPV (or
IRR) for a given change in one of the variables.
Steps involved in Sensitivity Analysis
Sensitivity Analysis is conducted by following the steps as below:
1. Finding variables, which have an influence on the NPV (or IRR) of the project.
2. Establishing mathematical relationship between the variables.
3. Analysing the effect of the change in each of the variables on the NPV (or IRR) of the project.
Illustration 9
X Ltd. is considering its new project with the following details:
Sr. No. Particulars Figures
1 Initial capital cost ` 400 Cr.
2 Annual unit sales 5 Cr.
3 Selling price per unit ` 100
4 Variable cost per unit ` 50
5 Fixed costs per year ` 50 Cr.
6 Discount Rate 6%
Required:
1. Calculate the NPV of the project.
2. Compute the impact on the project’s NPV considering a 2.5 per cent adverse variance in each
variable. Which variable is having maximum effect?
Consider Life of the project as 3 years.

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Solution
1. Calculation of Net Cash Inflow per year

Particulars Amount (`)

A Selling price per unit 100
B Variable cost per unit 50
C Contribution per unit (A - B) 50
D Number of units sold per year 5 Cr.
E Total Contribution (C × D) ` 250 Cr.
F Fixed cost per year ` 50 Cr.
G Net cash inflow per year (E - F) ` 200 Cr.

Calculation of Net Present Value (NPV) of the Project

Year Year Cash Flow PV factor @ 6% Present Value (PV)

(` in Cr.) (` in Cr.)
0 (400.00) 1.000 (400.00)
1 200.00 0.943 188.60
2 200.00 0.890 178.00
3 200.00 0.840 168.00
Net Present Value 134.60

Here, NPV represent the most likely outcomes and not the actual outcomes. The actual
outcome can be lower or higher than the expected outcome.
2. Sensitivity Analysis considering 2.5 % Adverse Variance in each variable

Particulars Base Initial Selling Variable Fixed Cost Units

capital Price per Cost Per Per Unit sold per
cost Unit Unit increased year
increased Reduced increased to reduced
to ` 410 to ` 97.5 to ` 51.25 ` 51.25 to 4.875
crore crore
(`) (`) (`) (`) (`) (`)
A Selling price per 100 100 97.5 100 100 100
unit

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B Variable cost per 50 50 50 51.25 50 50

unit
C Contribution per unit 50 50 47.5 48.75 50 50
(A - B)
(` in Cr.) (` in Cr.) (` in Cr.) (` in Cr.) (` in Cr.) (` in Cr.)
D Number of units 5 5 5 5 5 4.875
sold per year
(units in Crores)
E Total Contribution 250 250 237.5 243.75 250 243.75
(C × D)
F Fixed cost per year 50 50 50 50 51.25 50
G Net Cash Inflow per 200 200 187.5 193.75 198.75 193.75
year
(E - F)
H PV of Net cash 534.60 534.60 501.19 517.89 531.26 517.89
Inflow per year (G ×
2.673)
I Initial capital cost 400 410 400 400 400 400
J NPV (H - I) 134.60 124.60 101.19 117.89 131.26 117.89
K Percentage Change - -7.43% -24.82% -12.41% -2.48% -12.41%
in NPV
The above table shows that by changing one variable at a time by 2.5% (adverse) while keeping the
others constant, the impact in percentage terms on the NPV of the project can be calculated. Thus,
the change in selling price has the maximum effect on the NPV by 24.82%.
Advantages of Sensitivity Analysis:
Following are the main advantages of Sensitivity Analysis:
(1) Critical Issues: This analysis identifies critical factors that impinge on a project’s success or
failure.
(2) Simplicity: It is a simple technique.

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Disadvantage of Sensitivity Analysis

Following are the main disadvantages of Sensitivity Analysis:
(1) Assumption of Independence: This analysis assumes that all variables are independent i.e.
they are not related to each other, which is unlikely in real life.
(2) Ignore probability: This analysis does not look to the probability of changes in the variables.
4.3.2 Scenario Analysis
Although sensitivity analysis is probably the most widely used risk analysis technique, it does have
limitations. Therefore, we need to extend sensitivity analysis to deal with the probability distributions
of the inputs. In addition, it would be useful to vary more than one variable at a time so we could see
the combined effects of changes in the variables.

Scenario analysis provides answer to these situations of extensions. This analysis brings in the
probabilities of changes in key variables and also allows us to change more than one variable at a
time.

This analysis begins with base case or most likely set of values for the input variables. Then, go for
worst case scenario (low unit sales, low sale price, high variable cost, etc.) and best case scenario
(high unit sales, high sale price, low variable cost, etc.). Alternatively, Scenarios analysis is possible
where some factors are changed positively and some factors are changed negatively.
So, in a nutshell Scenario analysis examine the risk of investment, to analyse the impact of
alternative combinations of variables, on the project’s NPV (or IRR).
Illustration 10
XYZ Ltd. is considering a project “A” with an initial outlay of ` 14,00,000 and the possible three cash
inflow attached with the project as follows:

Particulars Year 1 Year 2 Year 3

Worst case 450 400 700
Most likely 550 450 800
Best case 650 500 900
Assuming the cost of capital as 9%, determine NPV in each scenario. If XYZ Ltd is certain about the
most likely result in first two years but uncertain about the third year’s cash flow, analyze what will
be the NPV expecting worst scenario in the third year.

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Solution
The possible outcomes will be as follows:
Year PVF Worst Case Most likely Best case
@ 9% Cash PV Cash PV Cash PV
Flow Flow Flow
(` ‘000) (` ‘000) (` ‘000) (` ‘000) (` ‘000) (` ‘000)
0 1 (1,400) (1,400) (1,400) (1,400) (1,400) (1,400)
1 0.917 450 412.65 550 504.35 650 596.05
2 0.842 400 336.80 450 378.90 500 421.00
3 0.772 700 540.40 800 617.60 900 694.80
NPV -110.15 100.85 311.85

If XYZ Ltd. is certain about the most likely result in first two years but uncertain about the third year’s
cash flow, then, NPV expecting worst case scenario is expected in the third year will be as follows:
` 5,50,000 ` 4,50,000 ` 7,00,000
= − ` 14,00,000 + + +
(1+0.09) (1+0.09)2 (1+0.09)3

= − ` 14,00,000 + ` 5,04,587 + ` 3,78,756 + ` 5,40,528 = ` 23,871

Scenario Analysis Vs Sensitivity Analysis
 Sensitivity analysis and Scenario analysis both help to understand the impact of the change
in input variable on the outcome of the project. However, there are certain basic differences
between the two.
 Sensitivity analysis calculates the impact of the change of a single input variable on the
outcome of the project viz., NPV or IRR. The sensitivity analysis thus enables to identify that
single critical variable which can impact the outcome in a huge way and the range of
outcomes of the project given the change in the input variable.
 Scenario analysis, on the other hand, is based on a scenario. The scenario may be recession
or a boom wherein depending on the scenario, all input variables change. Scenario Analysis
calculates the outcome of the project considering this scenario where the variables have
changed simultaneously. Similarly, the outcome of the project would also be considered for
the normal and recessionary situation. The variability in the outcome under the three different
scenarios would help the management to assess the risk a project carries. Higher deviation
in the outcome can be assessed as higher risk and lower to medium deviation can be
assessed accordingly.

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 Scenario analysis is far more complex than sensitivity analysis because in scenario analysis
all inputs are changed simultaneously, considering the situation in hand while in sensitivity
analysis, only one input is changed and others are kept constant.
4.3.3 Simulation Analysis (Monte Carlo)
Simulation is the exact replica of the actual situation. To simulate an actual situation, a model shall
be prepared. The simulation Analysis is a technique, in which infinite calculations are made to obtain
the possible outcomes and probabilities for any given action.
Monte Carlo simulation ties together sensitivities and probability distributions. The method came out
of the work of first nuclear bomb and was so named because it was based on mathematics of Casino
gambling. Fundamental appeal of this analysis is that it provides decision makers with a probability
distribution of NPVs rather than a single point estimates of the expected NPV.
This analysis starts with carrying out a simulation exercise to model the investment project. It
involves identifying the key factors affecting the project and their inter relationships. It involves
modelling of cash flows to reveal the key factors influencing both cash receipt and payments and
their inter relationship.
This analysis specifies a range for a probability distribution of potential outcomes for each of model’s
assumptions.
4.3.3.1 Steps for Simulation Analysis:
1. Modelling the project: The model shows the relationship of NPV with parameters and
exogenous variables. (Parameters are input variables specified by decision maker and held
constant over all simulation runs. Exogenous variables are input variables, which are
stochastic in nature and outside the control of the decision maker).
2. Specify values of parameters and probability distributions of exogenous variables.
3. Select a value at random from probability distribution of each of the exogenous variables.
4. Determine NPV corresponding to the randomly generated value of exogenous variables and
pre-specified parameter variables.
5. Repeat steps (3) & (4) a large number of times to get a large number of simulated NPVs.
6. Plot probability distribution of NPVs and compute a mean and Standard Deviation of returns
to gauge the project’s level of risk.
Example: Uncertainty associated with two aspects of the project: Annual Net Cash Flow & Life of
the project. NPV model for the project is

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∑ [CFt /(1 + i) t ] - I
t =1

Where i Risk free interest rate, I initial investment are parameters, CF = Annual Cash Flow
With i = 10%, I = ` 1,30,000, CFt & n stochastic exogenous variables with the following distribution
will be as under:
Annual Cash Flow Project Life
Value (`) Probability Value (Year) Probability
10,000 0.02 3 0.05
15,000 0.03 4 0.10
20,000 0.15 5 0.30
25,000 0.15 6 0.25
30,000 0.30 7 0.15
35,000 0.20 8 0.10
40,000 0.15 9 0.03
10 0.02

Ten manual simulation runs are performed for the project. To perform this operation, values are
generated at random for the two exogenous variables viz., Annual Cash Flow and Project Life. For
this purpose, we take following steps
(1) set up correspondence between values of exogenous variables and random numbers
(2) choose some random number generating device.
Correspondence between Values of Exogenous Variables and two Digit Random Numbers:

Annual Cash Flow Project Life

Value Probability Cumulative Two Value Probability Cumulative Two
(`) Probability Digit (Year) Probability Digit
Random Random
No. No.
10,000 0.02 0.02 00 – 01 3 0.05 0.05 00 – 04
15,000 0.03 0.05 02 – 04 4 0.10 0.15 05 – 14
20,000 0.15 0.20 05 – 19 5 0.30 0.45 15 – 44
25,000 0.15 0.35 20 – 34 6 0.25 0.70 45 – 69
30,000 0.30 0.65 35 – 64 7 0.15 0.85 70 – 84

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35,000 0.20 0.85 65 – 84 8 0.10 0.95 85 – 94

40,000 0.15 1.00 85 - 99 9 0.03 0.98 95 – 97
10 0.02 1.00 98 - 99
Random Number
53479 81115 98036 12217 59526
97344 70328 58116 91964 26240
66023 38277 74523 71118 84892
99776 75723 03172 43112 83086
30176 48979 92153 38416 42436
81874 83339 14988 99937 13213
19839 90630 71863 95053 55532
09337 33435 53869 52769 18801
31151 58295 40823 41330 21093
67619 52515 03037 81699 17106
For random numbers, we can begin from any-where taking at random from the table and read any
pair of adjacent columns, column/row wise. For the first simulation run we need two digit random
numbers (1) For Annual Cash Flow (2) For Project Life. The numbers are 53 & 97 and corresponding
value of Annual Cash Flow and Project Life are ` 3,000 and 9 years respectively.

Simulation Results
Annual Cash Flow Project Life
Run Random Corres. Value Random Corres. Value PVAF NPV
No. of Annual No. of Project @ 10% (1)x(2) –
Cash Flow (1) Life (2) 1,30,000
1 53 30,000 97 9 5.759 42,770
2 66 35,000 99 10 6.145 85,075
3 30 25,000 81 7 4.868 (8,300)
4 19 20,000 09 4 3.170 (66,600)
5 31 25,000 67 6 4.355 (21,125)
6 81 35,000 70 7 4.868 40,380
7 38 30,000 75 7 4.868 16,040
8 48 30,000 83 7 4.868 16,040
9 90 40,000 33 5 3.791 21,640
10 58 30,000 52 6 4.355 650

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4.3.3.2. Advantages of Simulation Analysis: Strength lies in Variability.

(1) We can predict all type of bad market situation beforehand.

(2) Handle problems characterised by:

(a) numerous exogenous variables following any kind of distribution.
(b) complex inter-relationships among parameters, exogenous variables and endogenous
variables. Such problems defy capabilities of analytical methods.
(c) compels decision maker to explicitly consider the inter-dependencies and
uncertainties featuring the project.
4.3.3.3 Shortcomings
(1) Difficult to model the project and specify probability distribution of exogenous variables.
(2) Simulation is inherently imprecise. Provides rough approximation of probability distribution of
NPV Due to its imprecision, simulation probability distribution may be misleading when a tail
of distribution is critical.
(3) Realistic simulation model being likely to be complex would probably be constructed by
management expert and not by the decision maker. Decision maker lacking understanding of
the model may not use it.
(4) Determine NPV in simulation run, risk free discount rate is used. It is done to avoid pre-
judging risk, which is reflected in the dispersion of the distribution of N.P.V. This derived
measure of NPV takes a different meaning from its original value, and, therefore, is difficult
to interpret.
4.3.4. Decision Tree Analysis
Till now we have discussed simple accept-or-reject decisions which view current investments in
isolation of subsequent decisions. However, practically investment decisions may have implications
for future or further investment decisions and may also impact future decision and events. Such
situation can be handled by taking a sequence of decisions over a period. The technique to handle
this type of sequential decisions is done through “Decision Tree” technique.
Basically, decision tree is a graphic display of the relationship between a present decision and future
events, future decision, and their consequences.

This approach assumes that there are only two types of situations that a finance manager has to
face. The first situation is where the manager has control or power to determine what happens next.
This is known as “Decision”, as he can do what he desires to do.

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2.34 ADVANCED FINANCIAL MANAGEMENT

The second situation is where finance manager has no control over what happens next. This is
known as “Event”. Since the outcome of the events is not known, a probability distribution needs to
be assigned to the various outcomes or consequences. It should, however, be noted when a finance
manager faced with a decision situation, he is assumed to act rationally. For example, in a
commercial business, he will choose the most profitable course of action and in non-profit
organization, the lowest cost may be rational choice.
Steps involved in Decision Tree analysis:
Step 1- Define Investment: Decision tree analysis can be applied to a variety of business decision-
making scenarios. Normally it includes following types of decisions.
• Whether or not to launch a new product, if so, whether this launch should be local,
national, or international.
• Whether extra production requirement should be met by extending the factory or by
outsourcing it to an external supplier.

• Whether to dig for oil or not if so, upto what height and continue to dig even after finding
no oil upto a certain depth.
Step 2- Identification of Decision Alternatives: It is very essential to clearly identity decision
alternatives. For example if a company is planning to introduce a new product, it may be local launch,
national launch or international launch.
Step 3- Drawing a Decision Tree: After identifying decision alternatives, at the relevant data such
as the projected cash flows, probability distribution expected present value etc. should be put in
diagrammatic form called decision tree.
While drawing a decision tree, it should be noted that NPVs etc. should be placed on the branches
of decision tree, coming out of the decisions identified.
While drawing a decision tree, it should be noted that the:-
• The decision point (traditionally represented by square) is the option available for
manager to take or not to take - in other words action at these points.
• The event or chance or outcome (traditionally represented by circle) which are dependent
on chance process, along with the probabilities thereof, and monetary value associated
with them.
• This diagram is drawn from left to right.

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Step 4- Evaluating the Alternatives: After drawing out the decision the next step is the evaluation
of alternatives. The various alternatives can be evaluated as follows:

(i) This procedure is carried out from the last decision in the sequence (extreme right) and goes
on working back to the first (left) for each of the possible decision.
(ii) At each final stage decision point, select the alternative which has the highest NPV and
truncate the other alternatives. Each decision point is assigned a value equal to the NPV of
the alternative selected at the decision point.
(iii) Proceed backward in the same manner calculating the NPV at chance or event or outcome
points ( ) selecting the decisions alternative which has highest NPV at various decision
points [ ] rejecting the inferior decision option, assigning NPV to the decision point, till the
first decision point is reached.
In Capital Budgeting, the decision taker has to identify and find out the various alternatives available
to an investment decision. By drawing a decision tree, the alternatives are highlighted through a
diagram, giving the range of possible outcomes. The stages set for drawing a decision tree is based
on the following rules.
1. It begins with a decision point, also known as decision node, represented by a rectangle while
the outcome point, also known as chance node, denoted by a circle.

2. Decision alternatives are shown by a straight line starting from the decision node.
3. The Decision Tree Diagram is drawn from left to right. Rectangles and circles have to be
sequentially numbered.
4. Values and Probabilities for each branch are to be incorporated next.
The Value of each circle and each rectangle is computed by evaluating from right to left. This
procedure is carried out from the last decision in the sequence and goes on working back to the first
for each of the possible decisions. The following rules have been set for such evaluation.
(a) The expected monetary value (EMV) at the chance node with branches emanating from a
circle is the aggregate of the expected values of the various branches that emanate from the
chance node.
(b) The expected value at a decision node with branches emanating from a rectangle is the
highest amongst the expected values of the various branches that emanate from the decision
node.

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X 1 Decision node
22 Y
2 and 3 Chance node
Z
1 X,Y and Z Possible Outcomes

33

Illustration 11
L & R Limited wishes to develop new virus-cleaner software. The cost of the pilot project would be
` 2,40,000. Presently, the chances of the product being successfully launched on a commercial
scale are rated at 50%. In case it does succeed. L&R can invest a sum of ` 20 lacs to market the
product. Such an effort can generate perpetually, an annual net after tax cash income of ` 4 lacs.
Even if the commercial launch fails, they can make an investment of a smaller amount of ` 12 lacs
with the hope of gaining perpetually a sum of ` 1 lac. Evaluate the proposal, adopting decision tree
approach. The discount rate is 10%.
Solution
Decision tree diagram is given below:

Evaluation
At Decision Point C: The choice is between investing ` 20 lacs for a perpetual benefit of ` 4 lacs
and not to invest. The preferred choice is to invest, since the capitalized value of benefit of ` 4 lacs
(at 10%) adjusted for the investment of ` 20 lacs, yields a net benefit of ` 20 lacs.

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At Decision Point D: The choice is between investing ` 12 lacs, for a similar perpetual benefit of
` 1 lac. and not to invest. Here the invested amount is greater than capitalized value of benefit at
` 10 lacs. There is a negative benefit of ` 2 lacs. Therefore, it would not be prudent to invest.
At Outcome Point B: Evaluation of EMV is as under (` in lacs).
Outcome Amount (`) Probability Result (`)
Success 20.00 0.50 10.00
Failure 0.00 0.50 00.00
Net result 10.00
EMV at B is, therefore, `10 lacs.
At A: Decision is to be taken based on preferences between two alternatives. The first is to test, by
investing ` 2,40,000 and reap a benefit of ` 10 lacs. The second is not to test, and thereby losing
the opportunity of a possible gain.
The preferred choice is, therefore, investing a sum of ` 2,40,000 and undertaking the test.

5. REPLACEMENT DECISION
Capital budgeting refers to the process we use to make decisions concerning investments in the
long-term assets of the firm. The general idea is that the capital, or long-term funds, raised by the
firms are used to invest in assets that will enable the firm to generate revenues several years into
the future. Often the funds raised to invest in such assets are not unrestricted, or infinitely available;
thus the firm must budget how these funds are invested. Among various capital budgeting decision,
Replacement decision is one of the most important classifications of capital budgeting. The
replacement decision can be divided into following two types of decisions:

5.1 Replacement of Existing Machine

This is a decision concerning whether an existing asset should be replaced by a newer version of
the same machine or even a different type of machine that has the same functionality as the existing
machine. Such replacements are generally made to maintain existing levels of operations, although
profitability might change due to changes in expenses (that is, the new machine might be either
more expensive or cheaper to operate than the existing machine).
Evaluation of replacement projects is slightly more complicated comparing expansion projects
because an existing asset is being replaced. When identifying the cash flows for replacement
projects, keep in mind that the cash flows associated with the existing (replaced) asset will no longer
exist if the new asset is purchased. Therefore, we must not only determine the cash flows that the

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new asset will generate, but we must also determine the effect of eliminating the cash flows
generated by the replaced asset. For example, if a new asset that will produce cash sales equal to
` 100,000 per year is purchased to replace an existing asset that is generating cash sales equal to
` 75,000, then the incremental, or marginal, cash flow related to sales is ` 25,000. Likewise, if the
asset that is replaced can be sold for ` 350,000, then the purchase price of the new asset effectively
is ` 350,000 less than its invoice price. In other words, for replacement decisions, we must determine
the overall net effect of purchasing a new asset to replace an existing asset—the cash flows
associated with the old asset will be replaced with the cash flows associated with the new asset.
Two items that you must remember to include when determining the incremental cash flows are
depreciation — not because it is a cash flow, but because it affects cash flows through taxes and
taxes — both of which generally change when an older asset is replaced with a newer asset.
Therefore analysis of replacement decision follows certain steps:
Step I. Net cash outflow (assumed at current time /[Present value of cost]):
a. (Book value of old equipment - market value of old equipment) × Tax Rate = Tax payable/
savings from sale
b. Cost of new equipment – [Tax payable/savings from sale + market value of old equipment] =
Net cash outflow
Step II. Estimate change in cash flow per year, if replacement decision is implemented.
Change in cash flow = [(Change in sales ± Change in operating costs) – Change in depreciation]
(1 – tax rate) + Change in depreciation
Step III. Present value of benefits = Present value of yearly cash flows + Present value of estimated
salvage of new system
Step IV. Net present value = Present value of benefits – Present value of costs
Step V. Decision rule. Accept when present value of benefits > present value of costs.
Reject when the opposite is true.
Illustration 12
A Company named Roby’s cube decided to replace the existing Computer system of their
organisation. Original cost of old system was ` 25,000 and it was installed 5 years ago. Current
market value of old system is ` 5,000. Depreciation of the old system was charged with life of 10
years with Estimated Salvage value as Nil. Depreciation of the new system will be charged with life
over 5 years. Present cost of the new system is ` 50,000. Estimated Salvage value of the new
system is ` 1,000. Estimated cost savings with new system is ` 5,000 per year. Increase in sales

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with new system is assumed at 10% per year based on original total sales of ` 10,00,000. Company
follows straight line method of depreciation. Cost of capital of the company is 10% whereas tax rate
is 30%.
Solution
Step I. Net cash outflow (assumed at current time) [Present values of cost]:
a. (Book value of old system – market value of old system) × Tax Rate
= Tax payable/savings from sale
= [(` 25,000 – 5 × ` 2,500) – ` 5,000] × 0.30 = ` 7,500 × 0.30
= ` 2,250
b. Cost of new system – [Tax payable/savings from sale + Market value of old system]
= Net cash outflow
Or, ` 50,000 – [` 2,250 + ` 5,000] = `42,750
Step II. Estimated change in cash flows per year if replacement decision is implemented.
Change in cash flow = [(Change in sales ± Change in operating costs)-Change in depreciation)] (1-
tax rate) + Change in depreciation
= [` 1,00,000 × 0.1 + ` 5,000 – (` 49,000/5 – ` 25,000/10)] (1-0.30) + (` 49,000/5 –
` 25000/10)]
= ` 12,690

Step III. Present value of benefits = Present value of yearly cash flows + Present value of estimated
salvage of new system
= ` 12,690 × PVIFA (10%, 5) + ` 1,000 × PVIF (10%, 5)
= ` 48,723
Step IV. Net present value = Present value of benefits - Present value of costs
= ` 48,723 – ` 42,750

= ` 5,973
Step V. Decision rule: Since NPV is positive we should accept the proposal to replace the machine.

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5.2 Optimum Replacement Cycle

Case discussed above is a simple example replacement decision based on NPV. This decision was
based on assumption that the projects do not form part of continuous replacement cycle.

However, sometimes, project may involve continuous replacement cycle. In such cases NPV
decision rules needs modification. To determine optimal replacement cycle, concept of Equivalent
Annual Cost (EAC), discussed at Intermediate (IPC) Level is used.

The formula to compute EAC is as follows:

PV of Cash Outflow
PVAF

This decision is based on assumption that as the machine (asset) becomes older its efficiency
decreases and leading to increase in operating cost and reduction in resale value.
Illustration 13
X Ltd. is a taxi operator. Each taxi cost to company ` 4,00,000 and has a useful life of 3 years. The
taxi’s operating cost for each of 3 years and salvage value at the end of year is as follows:
Year 1 Year 2 Year 3
Operating Cost ` 1,80,000 ` 2,10,000 ` 2,38,000
Resale Value ` 2,80,000 ` 2,30,000 ` 1,68,000

You are required to determine the optimal replacement period of taxi if cost of capital of X Ltd. is
10%.
Solution
NPV if taxi is kept for 1 Year
= – ` 4,00,000 - ` 1,80,000 (0.909) + ` 2,80,000 (0.909)
= – ` 3,09,100
NPV if taxi is kept for 2 Year
= – ` 4,00,000 – ` 1,80,000 x 0.909 + ` 20,000 x 0.826
= – ` 5,47,100
NPV if taxi is kept for 3 Year
= – ` 4,00,000 – ` 1,80,000 x 0.909 – ` 2,10,000 x 0.826 – ` 70,000 x 0.751
= – ` 7,89,650

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Since above NPV figures relate to different periods, there are not comparable. to make them
comparable we shall use concept of EAC as follows:

EAC of 1 year
3,09,100
= ` 3,40,044
0.909
EAC of 2 year
5,47,100
= ` 3,15,331
1.735
EAC of 3 year
7,89,650
= ` 3,17,639
2.486
Since lowest EAC incur if taxi for 2 year; Hence the optimum replacement cycle to replace taxi in 2
years.

6. ADJUSTED PRESENT VALUE

As we are well aware that to evaluate a capital project we discount the expected cash flows by
overall Cost of Capital i.e. WACC. Further, as discussed earlier to incorporate risk in the evaluation
of any project we can adjust the same discount rate.
However instead of adjusting the cost of capital we can use an alternative approach called Adjusted
Present Value (APV) Method. This approach separates the investment decision and financing
decision.

Following formula is used to evaluate a project as per this approach:

Base Case NPV + PV of Tax Benefit on Interest
Base Case NPV is calculated using cost of equity assuming the company is unlevered i.e., all equity
financed. Now question arises how to calculate the Unlevered Cost of Equity. It has been discussed
in the chapter of Business Valuation of this Study Material.
Since viability of the project is partly dependent on how project is financed the PV of Tax Benefits
on Interest payment allows for such adjustment. Thus, this method provides a broader view to
evaluate a project considering the benefit of increased use of debt in financing of any project.

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TEST YOUR KNOWLEDGE

Theoretical Questions
1. Write short note on Certainty Equivalent Approach.
2. What is the sensitivity analysis in Capital Budgeting?
3. Write a note on project appraisal under inflationary conditions.
4. Explain the steps involved in Simulation Analysis.

Practical Questions
1. Skylark Airways is planning to acquire a light commercial aircraft for flying class clients at an
investment of ` 50,00,000. The expected cash flow after tax for the next three years is as
follows: (`)
Year 1 Year 2 Year 3
CFAT Probability CFAT Probability CFAT Probability
14,00,000 0.1 15,00,000 0.1 18,00,000 0.2
18,00,000 0.2 20,00,000 0.3 25,00,000 0.5
25,00,000 0.4 32,00,000 0.4 35,00,000 0.2
40,00,000 0.3 45,00,000 0.2 48,00,000 0.1

The Company wishes to take into consideration all possible risk factors relating to airline
operations. The company wants to know:
(i) The expected NPV of this venture assuming independent probability distribution with
6 per cent risk free rate of interest.
(ii) The possible deviation in the expected value.

(iii) How would standard deviation of the present value distribution help in Capital
Budgeting decisions?
2. Cyber Company is considering two mutually exclusive projects. Investment outlay of both the
projects is ` 5,00,000 and each is expected to have a life of 5 years. Under three possible
situations their annual cash flows and probabilities are as under:

Cash Flow (`)

Situation Probabilities Project A ProjectB
Good 0.3 6,00,000 5,00,000

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Normal 0.4 4,00,000 4,00,000

Worse 0.3 2,00,000 3,00,000
The cost of capital is 7 per cent, which project should be accepted? Explain with workings.
3. A company is considering Projects X and Y with following information:
Project Expected NPV (`) Standard deviation
X 1,22,000 90,000
Y 2,25,000 1,20,000

(i) Which project will you recommend based on the above data?
(ii) Explain whether your opinion will change, if you use coefficient of variation as a
measure of risk.
(iii) Which measure is more appropriate in this situation and why?
4. KLM Ltd., is considering taking up one of the two projects-Project-K and Project-So Both the
projects having same life require equal investment of ` 80 lakhs each. Both are estimated to
have almost the same yield. As the company is new to this type of business, the cash flow
arising from the projects cannot be estimated with certainty. An attempt was therefore, made
to use probability to analyse the pattern of cash flow from other projects during the first year
of operations. This pattern is likely to continue during the life of these projects. The results of
the analysis are as follows:
Project K Project S
Cash Flow (in `) Probability Cash Flow (in `) Probability
11 0.10 09 0.10
13 0.20 13 0.25
15 0.40 17 0.30
17 0.20 21 0.25
19 0.10 25 0.10

Required:

(i) Calculate variance, standard deviation and co-efficient of variance for both the
projects.
(ii) Which of the two projects is riskier?

5. Project X and Project Y are under the evaluation of XY Co. The estimated cash flows and
their probabilities are as below:

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Project X : Investment (year 0) ` 70 lakhs

Probability weights 0.30 0.40 0.30
Years ` lakhs ` lakhs ` lakhs
1 30 50 65
2 30 40 55
3 30 40 45
Project Y: Investment (year 0) ` 80 lakhs.
Probability weighted Annual cash flows through life
` lakhs
0.20 40
0.50 45
0.30 50

(a) Which project is better based on NPV, criterion with a discount rate of 10%?
(b) Compute the standard deviation of the present value distribution and analyse the
inherent risk of the projects.
6. Shivam Ltd. is considering two mutually exclusive projects A and B. Project A costs ` 36,000
and project B ` 30,000. You have been given below the net present value probability
distribution for each project.
Project A Project B
NPV estimates (`) Probability NPV estimates (`) Probability
15,000 0.2 15,000 0.1
12,000 0.3 12,000 0.4
6,000 0.3 6,000 0.4
3,000 0.2 3,000 0.1
(i) Compute the expected net present values of projects A and B.
(ii) Compute the risk attached to each project i.e. standard deviation of each probability
distribution.

(iii) Compute the profitability index of each project.

(iv) Which project do you recommend? State with reasons.
7. Following are the estimates of the net cash flows and probability of a new project of M/s X
Ltd.:

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Year P = 0.3 P = 0.5 P = 0.2

Initial investment 0 4,00,000 4,00,000 4,00,000
Estimated net after tax cash inflows per year 1 to 5 1,00,000 1,10,000 1,20,000
Estimated salvage value (after tax) 5 20,000 50,000 60,000
Required rate of return from the project is 10%. Find:
(i) The expected NPV of the project.
(ii) The best case and the worst case NPVs.

(iii) The probability of occurrence of the worst case if the cash flows are perfectly
dependent overtime and independent overtime.
(iv) Standard deviation and coefficient of variation assuming that there are only three
streams of cash flow, which are represented by each column of the table with the given
probabilities.
(v) Coefficient of variation of X Ltd. on its average project which is in the range of 0.95 to
1.0. If the coefficient of variation of the project is found to be less risky than average,
100 basis points are deducted from the Company’s cost of Capital
Should the project be accepted by X Ltd?
8. XY Ltd. has under its consideration a project with an initial investment of ` 1,00,000. Three
probable cash inflow scenarios with their probabilities of occurrence have been estimated as
below:
Annual cash inflow (`) 20,000 30,000 40,000
Probability 0.1 0.7 0.2
The project life is 5 years and the desired rate of return is 20%. The estimated terminal values
for the project assets under the three probability alternatives, respectively, are ` 0, 20,000
and 30,000.
You are required to:
(i) Find the probable NPV;
(ii) Find the worst-case NPV and the best-case NPV; and
(iii) State the probability occurrence of the worst case, if the cash flows are perfectly
positively correlated over time.

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9. XYZ Ltd. is considering a project for which the following estimates are available:

`
Initial Cost of the project 10,00,000
Sales price/unit 60
Cost/unit 40
Sales volumes
Year 1 20000 units
Year 2 30000 units
Year 3 30000 units
Discount rate is 10% p.a.
You are required to measure the sensitivity of the project in relation to each of the following
parameters:
(a) Sales Price/unit
(b) Unit cost
(c) Sales volume
(d) Initial outlay and
(e) Project lifetime
Taxation may be ignored.
10. From the following details relating to a project, analyse the sensitivity of the project to
changes in initial project cost, annual cash inflow and cost of capital:

Initial Project Cost (`) 1,20,000

Annual Cash Inflow (`) 45,000
Project Life (Years) 4
Cost of Capital 10%
To which of the three factors, the project is most sensitive? (Use annuity factors: for 10%
3.169 and 11% 3.103).

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11. Red Ltd. is considering a project with the following Cash flows:
`
Years Cost of Plant Recurring Cost Savings
0 10,000
1 4,000 12,000
2 5,000 14,000
The cost of capital is 9%. Measure the sensitivity of the project to changes in the levels of
plant value, running cost and savings (considering each factor at a time) such that the NPV
becomes zero. The P.V. factor at 9% are as under:
Year Factor
0 1
1 0.917
2 0.842
Which factor is the most sensitive to affect the acceptability of the project?
12. The Easygoing Company Limited is considering a new project with initial investment, for a
product “Survival”. It is estimated that IRR of the project is 16% having an estimated life of 5
years.

Financial Manager has studied that project with sensitivity analysis and informed that annual
fixed cost sensitivity is 7.8416%, whereas cost of capital (discount rate) sensitivity is 60%.
Other information available are:

Profit Volume Ratio (P/V) is 70%,

Variable cost ` 60/- per unit
Annual Cash Flow ` 57,500/-
Ignore Depreciation on initial investment and impact of taxation.
Calculate
(i) Initial Investment of the Project

(ii) Net Present Value of the Project

(iii) Annual Fixed Cost
(iv) Estimated annual unit of sales

(v) Break Even Units

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Cumulative Discounting Factor for 5 years

8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18%
3.993 3.890 3.791 3.696 3.605 3.517 3.433 3.352 3.274 3.199 3.127

13. Unnat Ltd. is considering investing ` 50,00,000 in a new machine. The expected life of
machine is five years and has no scrap value. It is expected that 2,00,000 units will be
produced and sold each year at a selling price of ` 30.00 per unit. It is expected that the
variable costs to be ` 16.50 per unit and fixed costs to be ` 10,00,000 per year. The cost of
capital of Unnat Ltd. is 12% and acceptable level of risk is 20%.
You are required to measure the sensitivity of the project’s net present value to a change in
the following project variables:
(a) sale price;

(b) sales volume;

(c) variable cost;
(d) On further investigation it is found that there is a significant chance that the expected
sales volume of 2,00,000 units per year will not be achieved. The sales manager of
Unnat Ltd. suggests that sales volumes could depend on expected economic states
which could be assigned the following probabilities:

State of Economy Annual Sales (in Units) Prob.

Poor 1,75000 0·30
Normal 2,00,000 0·60
Good 2,25,000 0·10
Calculate expected net present value of the project and give your decision whether company
should accept the project or not.
14. The Textile Manufacturing Company Ltd., is considering one of two mutually exclusive
proposals, Projects M and N, which require cash outlays of ` 8,50,000 and ` 8,25,000
respectively. The certainty-equivalent (C.E) approach is used in incorporating risk in capital
budgeting decisions. The current yield on government bonds is 6% and this is used as the
risk free rate. The expected net cash flows and their certainty equivalents are as follows:
Project M Project N
Year-end Cash Flow ` C.E. Cash Flow ` C.E.
1 4,50,000 0.8 4,50,000 0.9

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2 5,00,000 0.7 4,50,000 0.8

3 5,00,000 0.5 5,00,000 0.7
Present value factors of ` 1 discounted at 6% at the end of year 1, 2 and 3 are 0.943, 0.890
and 0.840 respectively.
Required:
(i) Which project should be accepted?
(ii) If risk adjusted discount rate method is used, which project would be appraised with a
higher rate and why?
15. Determine the risk adjusted net present value of the following projects:

X Y Z
Net cash outlays (`) 2,10,000 1,20,000 1,00,000
Project life 5 years 5 years 5 years
Annual Cash inflow (`) 70,000 42,000 30,000
Coefficient of variation 1.2 0.8 0.4

The Company selects the risk-adjusted rate of discount on the basis of the coefficient of
variation:
Coefficient of Risk-Adjusted Rate of P.V. Factor 1 to 5 years At risk
Variation Return adjusted rate of discount
0.0 10% 3.791
0.4 12% 3.605
0.8 14% 3.433
1.2 16% 3.274
1.6 18% 3.127
2.0 22% 2.864
More than 2.0 25% 2.689

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16. New Projects Ltd. is evaluating 3 projects, P-I, P-II, P-III. Following information is available
in respect of these projects:
P-I P-II P-III
Cost ` 15,00,000 ` 11,00,000 ` 19,00,000
Inflows-Year 1 6,00,000 6,00,000 4,00,000
Year 2 6,00,000 4,00,000 6,00,000
Year 3 6,00,000 5,00,000 8,00,000
Year 4 6,00,000 2,00,000 12,00,000
Risk Index 1.80 1.00 0.60
Minimum required rate of return of the firm is 15% and applicable tax rate is 40%. The risk
free interest rate is 10%.
Required:
(i) Find out the risk-adjusted discount rate (RADR) for these projects.
(ii) Which project is the best?
17. A firm has projected the following cash flows from a project under evaluation:
Year ` lakhs
0 (70)
1 30
2 40
3 30
The above cash flows have been made at expected prices after recognizing inflation. The
firm’s cost of capital is 10%. The expected annual rate of inflation is 5%.
Show how the viability of the project is to be evaluated.
18. Shashi Co. Ltd has projected the following cash flows from a project under evaluation:

Year 0 1 2 3
` (in lakhs) (72) 30 40 30
The above cash flows have been made at expected prices after recognizing inflation. The firm’s
cost of capital is 10%. The expected annual rate of inflation is 5%. Show how the viability of the
project is to be evaluated. PVF at 10% for 1-3 years are 0.909, 0.826 and 0.751.
19. KLM Ltd. requires ` 15,00,000 for a new project.
Useful life of project is 3 years.
Salvage value - NIL.
Depreciation is ` 5,00,000 p.a.

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Given below are projected revenues and costs (excluding depreciation) ignoring inflation:

Year → 1 2 3
Revenues in ` 10,00,000 13,00,000 14,00,000
Costs in ` 5,00,000 6,00,000 6,50,000

Applicable tax rate is 35%. Assume nominal cost of capital to be 14% (after tax). The inflation
rates for revenues and costs are as under:
Year Revenues % Costs %
1 9 10
2 8 9
3 6 7

PVF at 14%, for 3 years = 0.877, 0.769 and 0.675

Show amount to the nearest rupee in calculations.
You are required to calculate net present value of the project.
20. A firm has an investment proposal, requiring an outlay of ` 80,000. The investment proposal
is expected to have two years economic life with no salvage value. In year 1, there is a 0.4
probability that cash inflow after tax will be ` 50,000 and 0.6 probability that cash inflow after
tax will be ` 60,000. The probability assigned to cash inflow after tax for the year 2 is as
follows:
The cash inflow year 1 ` 50,000 ` 60,000
The cash inflow year 2 Probability Probability
` 24,000 0.2 ` 40,000 0.4
` 32,000 0.3 ` 50,000 0.5
` 44,000 0.5 ` 60,000 0.1

The firm uses a 10% discount rate for this type of investment.
Required:
(i) Construct a decision tree for the proposed investment project and calculate the
expected net present value (NPV).
(ii) What net present value will the project yield, if worst outcome is realized? What is the
probability of occurrence of this NPV?

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(iii) What will be the best outcome and the probability of that occurrence?
(iv) Will the project be accepted?
(Note: 10% discount factor 1 year 0.909; 2 year 0.826)
21. Jumble Consultancy Group has determined relative utilities of cash flows of two forthcoming
projects of its client company as follows:

Cash Flow in ` -15000 -10000 -4000 0 15000 10000 5000 1000

Utilities -100 -60 -3 0 40 30 20 10

The distribution of cash flows of project A and Project B are as follows:

Project A
Cash Flow (`) -15000 - 10000 15000 10000 5000
Probability 0.10 0.20 0.40 0.20 0.10
Project B
Cash Flow (`) - 10000 -4000 15000 5000 10000
Probability 0.10 0.15 0.40 0.25 0.10

Which project should be selected and why ?

22. A & Co. is contemplating whether to replace an existing machine or to spend money on
overhauling it. A & Co. currently pays no taxes. The replacement machine costs ` 90,000
now and requires maintenance of ` 10,000 at the end of every year for eight years. At the
end of eight years it would have a salvage value of ` 20,000 and would be sold. The existing
machine requires increasing amounts of maintenance each year and its salvage value falls
each year as follows:
Year Maintenance Salvage
(`) (`)
Present 0 40,000
1 10,000 25,000
2 20,000 15,000
3 30,000 10,000
4 40,000 0
The opportunity cost of capital for A & Co. is 15%.

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 ADVANCED CAPITAL BUDGETING DECISIONS 3.53
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Required:
When should the company replace the machine?
(Notes: Present value of an annuity of Re. 1 per period for 8 years at interest rate of 15% :
4.4873; present value of Re. 1 to be received after 8 years at interest rate of 15% : 0.3269).
23. A company has an old machine having book value zero – which can be sold for ` 50,000.
The company is thinking to choose one from following two alternatives:
(i) To incur additional cost of ` 10,00,000 to upgrade the old existing machine.
(ii) To replace old machine with a new machine costing ` 20,00,000 plus installation cost
` 50,000.
Both above proposals envisage useful life to be five years with salvage value to be nil.
The expected after tax profits for the above three alternatives are as under :
Year Old existing Upgraded Machine New Machine
Machine (`) (`) (`)
1 5,00,000 5,50,000 6,00,000
2 5,40,000 5,90,000 6,40,000
3 5,80,000 6,10,000 6,90,000
4 6,20,000 6,50,000 7,40,000
5 6,60,000 7,00,000 8,00,000
The tax rate is 40 per cent.
The company follows straight line method of depreciation. Assume cost of capital to be 15
per cent.
P.V.F. of 15%, 5 = 0.870, 0.756, 0.658, 0.572 and 0.497. You are required to advise the
company as to which alternative is to be adopted.
24. Company X is forced to choose between two machines A and B. The two machines are
designed differently but have identical capacity and do exactly the same job. Machine A costs
` 1,50,000 and will last for 3 years. It costs ` 40,000 per year to run. Machine B is an
‘economy’ model costing only ` 1,00,000, but will last only for 2 years, and costs ` 60,000
per year to run. These are real cash flows. The costs are forecasted in rupees of constant
purchasing power. Ignore tax. Opportunity cost of capital is 10 per cent. Which machine
company X should buy?

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25. Company Y is operating an elderly machine that is expected to produce a net cash inflow of
` 40,000 in the coming year and ` 40,000 next year. Current salvage value is
` 80,000 and next year’s value is ` 70,000. The machine can be replaced now with a new
machine, which costs ` 1,50,000, but is much more efficient and will provide a cash inflow of
` 80,000 a year for 3 years. Company Y wants to know whether it should replace the
equipment now or wait a year with the clear understanding that the new machine is the best
of the available alternatives and that it in turn be replaced at the optimal point. Ignore tax.
Take opportunity cost of capital as 10 per cent. Advise with reasons.

26. A machine used on a production line must be replaced at least every four years. Costs
incurred to run the machine according to its age are:
Age of the Machine (years)
0 1 2 3 4
Purchase price (in `) 60,000
Maintenance (in `) 16,000 18,000 20,000 20,000
Repair (in `) 0 4,000 8,000 16,000
Scrap Value (in `) 32,000 24,000 16,000 8,000
Future replacement will be with identical machine with same cost. Revenue is unaffected by
the age of the machine. Ignoring inflation and tax, determine the optimum replacement cycle.
PV factors of the cost of capital of 15% for the respective four years are 0.8696, 0.7561,
0.6575 and 0.5718.
27. Trouble Free Solutions (TFS) is an authorized service center of a reputed domestic air
conditioner manufacturing company. All complaints/service related matters of Air conditioner
are attended by this service center. The service center employs a large number of mechanics,
each of whom is provided with a motor bike to attend the complaints. Each mechanic travels
approximately 40000 kms per annuam. TFS decides to continue its present policy of always
buying a new bike for its mechanics but wonders whether the present policy of replacing the
bike every three year is optimal or not. It is of believe that as new models are entering into
market on yearly basis, it wishes to consider whether a replacement of either one year or two
years would be better option than present three year period. The fleet of bike is due for
replacement shortly in near future.
The purchase price of latest model bike is ` 55,000. Resale value of used bike at current
prices in market is as follows:

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Period `
1 Year old 35,000
2 Year old 21,000
3 Year old 9,000
Running and Maintenance expenses (excluding depreciation) are as follows:

Year Road Taxes Insurance etc. Petrol Repair Maintenance etc.

(`) (`)

1 3,000 30,000
2 3,000 35,000
3 3,000 43,000

Using opportunity cost of capital as 10% you are required to determine optimal replacement
period of bike.

ANSWERS/ SOLUTIONS
Answers to Theoretical Questions
1. This approach recognizes risk in capital budgeting analysis by adjusting estimated cash flows
and employs risk free rate to discount the adjusted cash-flows. Under this method, the
expected cash flows of the project are converted to equivalent riskless amounts. The greater
the risk of an expected cash flow, the smaller the certainty equivalent values for receipts and
longer the CE value for payment. This approach is superior to the risk adjusted discounted
approach as it can measure risk more accurately.

This is yet another approach for dealing with risk in capital budgeting to reduce the forecasts
of cash flows to some conservative levels. In certainty Equivalent approach we incorporate
risk to adjust the cash flows of a proposal so as to reflect the risk element. The certainty
Equivalent approach adjusts future cash flows rather than discount rates. This approach
explicitly recognizes risk, but the procedure for reducing the forecasts of cash flows is implicit
and likely to be inconsistent from one investment to another.

2. Sensitivity analysis is used in Capital budgeting for more precisely measuring the risk. It helps
in assessing information as to how sensitive are the estimated parameters of the project such
as cash flows, discount rate, and the project life to the estimation errors. Future being always
uncertain and estimations are always subject to error, sensitivity analysis takes care of
estimation errors by using a number of possible outcomes in evaluating a project. The

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methodology adopted in sensitivity analysis is to evaluate a project by using a number of

estimated cash flows so as to provide to the decision maker an insight into the variability of
outcome. Thus, it is a technique of risk analysis which studies the responsiveness of a
criterion of merit like NPV or IRR to variation in underlying factors like selling price, quantity
sold, returns from an investment etc.
Sensitivity analysis answers questions like,
(i) What happens to the present value (or some other criterion of merit) if flows are, say
` 50,000 than the expected ` 80,000?
(ii) What will happen to NPV if the economic life of the project is only 3 years rather than
expected 5 years?
Therefore, wherever there is an uncertainty, of whatever type, the sensitivity analysis plays
a crucial role. However, it should not be viewed as the method to remove the risk or
uncertainty, it is only a tool to analyse and measure the risk and uncertainty. In terms of
capital budgeting the possible cash flows are based on three assumptions:

(a) Cash flows may be worst (pessimistic)

(b) Cash flows may be most likely.
(c) Cash flows may be most optimistic.
Sensitivity analysis involves three steps
(1) Identification of all those variables having an influence on the project’s NPV or IRR.
(2) Definition of the underlying quantitative relationship among the variables.
(3) Analysis of the impact of the changes in each of the variables on the NPV of the
project.
The decision maker, in sensitivity analysis always asks himself the question – what if?
3. Project Appraisal normally involves feasibility evaluation from technical, commercial,
economic and financial aspects. It is generally an exercise in measurement and analysis of
cash flows expected to occur over the life of the project. The project cash outflows usually
occur initially and inflows come in the future.
During inflationary conditions, the project cost increases on all heads viz. labour, raw
material, fixed assets such as equipments, plant and machinery, building material,
remuneration of technicians and managerial personnel etc. Beside this, inflationary conditions

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erode purchasing power of consumers and affect the demand pattern. Thus, not only cost of
production but also the projected statement of profitability and cash flows are affected by the
change in demand pattern. Even financial institutions and banks may revise their lending
rates resulting in escalation in financing cost during inflationary conditions. Under such
circumstances, project appraisal has to be done generally keeping in view the following
guidelines which are usually followed by government agencies, banks and financial
institutions.
(i) It is always advisable to make provisions for cost escalation on all heads of cost,
keeping in view the rate of inflation during likely period of delay in project
implementation.
(ii) The various sources of finance should be carefully scrutinized with reference to
probable revision in the rate of interest by the lenders and the revision which could be
affected in the interest-bearing securities to be issued. All these factors will push up
the cost of funds for the organization.
(iii) Adjustments should be made in profitability and cash flow projections to take care of
the inflationary pressures affecting future projections.
(iv) It is also advisable to examine the financial viability of the project at the revised rates
and assess the same with reference to economic justification of the project. The
appropriate measure for this aspect is the economic rate of return for the project which
will equate the present value of capital expenditures to net cash flows over the life of
the projects. The rate of return should be acceptable which also accommodates the
rate of inflation per annum.
(v) In an inflationary situation, projects having early payback periods should be preferred
because projects with long payback period are riskier.
Under conditions of inflation, the project cost estimates that are relevant for a future date will
suffer escalation. Inflationary conditions will tend to initiate the measurement of future cash
flows. Either of the following two approaches may be used while appraising projects under
such conditions:
(a) Adjust each year's cash flows to an inflation index, recognizing selling price increases
and cost increases annually; or
(b) Adjust the 'Acceptance Rate' (cut-off) suitably retaining cash flow projections at
current price levels.

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An example of approach (ii) above can be as follows:

Normal Acceptance Rate : 15.0%
Expected Annual Inflation : 5.0%
Adjusted Discount Rate : 15.0 × 1.05 or 15.75%
It must be noted that measurement of inflation has no standard approach nor is easy. This
makes the job of appraisal a difficult one under such conditions.
4. Please refer paragraph 4.3.3

Answers to the Practical Questions

1. (i) Expected NPV
(` in lakhs)
Year I Year II Year III
CFAT P CF×P CFAT P CF×P CFAT P CF×P
14 0.1 1.4 15 0.1 1.5 18 0.2 3.6
18 0.2 3.6 20 0.3 6.0 25 0.5 12.5
25 0.4 10.0 32 0.4 12.8 35 0.2 7.0
40 0.3 12.0 45 0.2 9 48 0.1 4.8
x or CF 27.0 x or CF 29.3 x or CF 27.9

NPV PV factor @ 6% Total PV

27 0.943 25.461
29.3 0.890 26.077
27.9 0.840 23.436
PV of cash inflow 74.974
Less: Cash outflow 50.000
NPV 24.974

(ii) Possible deviation in the expected value

Year I
X- X X- X (X - X ) 2 P1 (X - X ) 2 P1
14 – 27 -13 169 0.1 16.9
18 – 27 -9 81 0.2 16.2

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25 – 27 -2 4 0.4 1.6
40 – 27 13 169 0.3 50.7
85.4

σ1 = 85.4 = 9.241

Year II
X- X X- X (X - X ) 2 P2 (X - X ) 2 ×P2
15-29.3 -14.3 204.49 0.1 20.449
20-29.3 -9.3 86.49 0.3 25.947
32-29.3 2.7 7.29 0.4 2.916
45-29.3 15.7 246.49 0.2 49.298
98.61

σ 2 = 98.61 = 9.930

Year III
X- X X- X (X - X ) 2 P3 (X - X ) 2 × P3
18-27.9 -9.9 98.01 0.2 19.602
25-27.9 -2.9 8.41 0.5 4.205
35-27.9 7.1 50.41 0.2 10.082
48-27.9 20.1 404.01 0.1 40.401
74.29

σ = 74.29 = 8.619
3

Standard deviation about the expected value:

85.4 98.61 74.29
σ= + + = 14.3696
2
(1.06 ) (1.06 ) (1.06 )6
4

(iii) Standard deviation is a statistical measure of dispersion; it measures the deviation

from a central number i.e. the mean.
In the context of capital budgeting decisions especially where we take up two or more
projects giving somewhat similar mean cash flows, by calculating standard deviation
in such cases, we can measure in each case the extent of variation. It can then be
used to identify which of the projects is least risky in terms of variability of cash flows.

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A project, which has a lower coefficient of variation will be preferred if sizes are
heterogeneous.

Besides this, if we assume that probability distribution is approximately normal we are

able to calculate the probability of a capital budgeting project generating a net present
value less than or more than a specified amount.

2. Project A
Expected Net Cash flow (ENCF)
0.3 (6,00,000) + 0.4 (4,00,000) + 0.3 (2,00,000) = 4,00,000

σ2=0.3 (6,00,000– 4,00,000)2 + 0.4 (4,00,000 – 4,00,000)2 + 0.3 (2,00,000 – 4,00,000)2

σ= 24,00,00,00,000

σ = 1,54,919.33
Present Value of Expected Cash Inflows = 4,00,000 × 4.100 = 16,40,000
NPV = 16,40,000 – 5,00,000 = 11,40,000
Project B
ENCF = 0.3 (5,00,000) + 0.4 (4,00,000) + 0.3 (3,00,000) = 4,00,000
σ2=0.3 (5,00,000 – 4,00,000)2 + 0.4 (4,00,000 – 4,00,000)2 + 0.3 (3,00,000 – 4,00,000)2
σ= 6,00,00,00,000

σ = 77,459.66
Present Value of Expected Cash Inflows = 4,00,000 × 4.100 = 16,40,000
NPV = 16,40,000 – 5,00,000 = 11,40,000
Recommendation: NPV in both projects being the same, the project should be decided on
the basis of standard deviation and hence project ‘B’ should be accepted having lower
standard deviation, means less risky.
3. (i) On the basis of standard deviation project X be chosen because it is less risky than
Project Y having higher standard deviation.
SD 90,000
(ii) CVx = = = 0.738
ENPV 1,22,000

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1,20,000
CVy = = 0.533
2,25,000

On the basis of Co-efficient of Variation (C.V.) Project X appears to be riskier and

hence Y should be accepted.
(iii) However, the NPV method in such conflicting situation is best because the NPV
method is in compatibility of the objective of wealth maximisation in terms of time
value.
4. Calculation of Variance and Standard Deviation
Project K

Expected Net Cash Flow

= (0.10 x 11) + (0.20 x13) + (0.40 x 15) + (0.20 x 17) + (0.10 x 19)
= 1.1 + 2.6 + 6 + 3.4 + 1.9 = 15
2 2 2 2 2
σ 2 = 0.10 (11 – 15 ) + 0.20 (13 – 15 ) + 0.40 (15 – 15 ) + 0.20 (17 – 15 ) + 0.10 (19 – 15 )

= 1.6 + 0.8 + 0 + 0.8 + 1.6 = 4.8

σ= 4.8 = 2.19

Project S
Expected Net Cash Flow
= (0.10 X 9) + (0.25 X 13) + (0.30 X 17) + (0.25 X 21) + (0.10 X 25)

= 0.9 + 3.25 + 5.1 + 5.25 + 2.5 = 17

2 2 2 2 2 2
σ = 0.1 ( 9 – 17 ) + 0.25 (13 – 17 ) + 0.30 (17 – 17 ) + 0.25 ( 21 – 17 ) + 0.10 ( 25 – 17 )

= 6.4 + 4 + 0 + 4 + 6.4 = 20.8

σ = 20.8 = 4.56

Calculation of Coefficient of Variation

Standard Deviation
Coefficient of Variation =
Mean
2.19
Project K = = 0.146
15

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4.56
Project S = = 0.268
17
Project S is riskier as it has higher Coefficient of Variation.

5. (a) Calculation of NPV of XY Co.:

Project X Cash flow PVF PV
Year
1 (30 × 0.3) + (50 × 0.4) + (65 × 0.3) 48.5 0.909 44.09
2 (30 × 0.3) + (40 × 0.4) + (55 × 0.3) 41.5 0.826 34.28
3 (30 × 0.3) + (40 × 0.4) + (45 × 0.3) 38.5 0.751 28.91
107.28
NPV: (107.28 – 70.00) = (+) 37.28
Project Y (For 1-3 Years)
1-3 (40 × 0.2) + (45 × 0.5) + (50 × 0.3) 45.5 2.487 113.16
NPV (113.16 – 80.00) (+) 33.16

(b) Calculation of Standard deviation σ

As per Hiller’s model

n
M= ∑ (1+r)-1 Mi
i=0

n
σ 2 = ∑ (1+r)-2i σ i2
i=0

Hence

Project X

Year

1 (30 - 48.5)2 0.30 + (50 - 48.5)2 0.40 + (65 - 48.5)2 0.30 = 185.25 =13.61

2 (30 - 41.5)2 0.30 + (40 - 41.5)2 0.40 + (55 - 41.5)2 0.30 = 95.25 = 9.76

3 (30 - 38.5)2 0.30 + (40 - 38.5)2 0.40 + (45 - 38.5)2 0.30 = 35.25 = 5.94

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Standard Deviation about the expected value

185.25 95.25 35.25
= 2 + 4 +
(1 + 0.10) (1 + 0.10) (1 + 0.10) 6

185.25 95.25 35.25

= + + = 153.10+65.06+19.90
1.21 1.4641 1.7716
= 238.06 = 15.43

Project Y (For 1-3 Years)

(40 - 45.5)2 0.20 + (45 - 45.5)2 0.50 + (50 - 45.5)2 0.30 = 12.25 = 3.50

Standard Deviation about the expected value

12.25 12.25 12.25

= 2 + 4 +
(1 + 0.10) (1 + 0.10) (1 + 0.10) 6

12.25 12.25 12.25

= + + = 10.12+8.37+6.91
1.21 1.4641 1.7716

= 25.4 = 5.03

Analysis: Project Y is less risky as its Standard Deviation is less than Project X.
6. (i) Statement showing computation of expected net present value of Projects A and B:
Project A Project B
NPV Probability Expected NPV Probability Expected
Estimate Value Estimate Value
(`)
15,000 0.2 3,000 15,000 0.1 1,500
12,000 0.3 3,600 12,000 0.4 4,800
6,000 0.3 1,800 6,000 0.4 2,400
3,000 0.2 600 3,000 0.1 300
1.0 EV = 9,000 1.0 EV = 9,000

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(ii) Computation of Standard deviation of each project

Project A

P X (X – EV) P (X - EV)²
0.2 15,000 6,000 72,00,000
0.3 12,000 3,000 27,00,000
0.3 6,000 - 3,000 27,00,000
0.2 3,000 - 6,000 72,00,000
Variance = 1,98,00,000
Standard Deviation of Project A = 1,98,00,000 = ` 4,450

Project B
P X (X – EV) P (X - EV)²
0.1 15,000 6,000 36,00,000
0.4 12,000 3,000 36,00,000
0.4 6,000 - 3,000 36,00,000
0.1 3,000 - 6,000 36,00,000
Variance = 1,44,00,000

Standard Deviation of Project A = 1,44,00,000 = ` 3,795

(iii) Computation of profitability of each project

Profitability index = Discount cash inflow / Initial outlay
9,000 + 36,000 45,000
In case of Project A : PI = = = 1.25
36,000 36,000

9,000 + 30,000 39,000

In case of Project B : PI = = = 1.30
30,000 30,000

(iv) Measurement of risk is made by the possible variation of outcomes around the
expected value and the decision will be taken in view of the variation in the expected
value where two projects have the same expected value, the decision will be the
project which has smaller variation in expected value. In the selection of one of the
two projects A and B, Project B is preferable because the possible profit which may
occur is subject to less variation (or dispersion). Much higher risk is lying with
project A.

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7. (a) (i) Expected cash flows:-

Year Net cash P.V. PV. @
flows 10%
0 (4,00,000 x 1) = (-)4,00,000 1.000 (-)4,00,000
1 to 4 (1,00,000x0.3+1,10,000x0.5 = 1,09,000 3.170 3,45,530
+ 1,20,000 x 0.2)
5 [1,09,000 + (20,000 x 0.3 + = 1,52,000 0.621 94,392
50,000 x 0.5 + 60,000 x 0.2)]
NPV = 39,922

(ii) ENPV of the worst case

1,00,000 x 3.790 = ` 3,79,000 (Students may have 3.791 also the values will
change accordingly)
20,000 x 0.621 = ` 12,420/-

ENPV = (-) 4,00,000 + 3,79,000 + 12,420 = (-) ` 8,580/-

ENPV of the best case
ENPV = (-) 4,00,000 + 1,20,000 x 3.790 + 60,000 x 0.621 = ` 92,060/-.

(iii) (a) Required probability = 0.3

(b) Required probability = (0.3)5 = 0.00243
(iv) The base case NPV = (-) 4,00,000 + (1,10,000 x 3.79) + (50,000 x 0.621)

= ` 47,950/-
ENPV = 0.30 x (-) 8580 + 0.5 x 47950 + 92060 x 0.20 = ` 39,813/-
Therefore,

σΕNPV = 0.3( −8580 − 39,813) 2 + 0.5( 47950 − 39813) 2 + 0.2(92,060 − 39,813) 2

= ` 35,800/-
Therefore, CV = 35,800/39,813 = 0.90

© The Institute of Chartered Accountants of India

 3.66
2.66 ADVANCED FINANCIAL MANAGEMENT

(v) Risk adjusted out of cost of capital of X Ltd. = 10% - 1% = 9%.

NPV
Year Expected net cash flow PV @ 9%
0 (-) 4,00,000 1.000 (-) 4,00,000
1 to 4 1,09,000 3.240 3,53,160
5 1,52,000 0.650 98,800
ENPV = 51,960
Therefore, the project should be accepted.
8. The expected cash flows of the project are as follows:
Year Pr = 0.1 Pr = 0.7 Pr = 0.2 Total
` ` ` `
0 -10,000 -70,000 -20,000 -1,00,000
1 2,000 21,000 8,000 31,000
2 2,000 21,000 8,000 31,000
3 2,000 21,000 8,000 31,000
4 2,000 21,000 8,000 31,000
5 2,000 21,000 8,000 31,000
5 0 14,000 6,000 20,000

(i) NPV based on expected cash flows would be as follows:

` 31,000 ` 31,000 ` 31,000 ` 31,000 ` 31,000 ` 20,000
=-` 1,00,000 + + + + + +
(1 + 0.20 )1 (1 + 0.20 )2 (1 + 0.20 )3 (1 + 0.20 )4 (1 + 0.20 )5 (1 + 0.20 )5
= - ` 1,00,000 + ` 25,833.33 + ` 21,527.78 + ` 17,939.81 + ` 14,949.85+ ` 12,458.20
+ ` 8,037.55
NPV = ` 746.52
(ii) For the worst case, the cash flows from the cash flow column farthest on the left are
used to calculate NPV

= - ` 100,000 + ` 20,000 + ` 20,000 + ` 20,000 + ` 20,000 + ` 20,000

5
(1 + 0.20 )1 (1 + 0.20 )2 (1 + 0.20 )3 (1 + 0.20 )4 (1 + 0.20 )
= - ` 100,000 + ` 16,666.67+ ` 13,888.89 + ` 11,574.07 + ` 9,645.06+ ` 8037.76

NPV = - ` 40,187.76

© The Institute of Chartered Accountants of India

 ADVANCED CAPITAL BUDGETING DECISIONS 3.67
2.67

For the best case, the cash flows from the cash flow column farthest on the right are
used to calculated NPV
` 40,000 ` 40,000 ` 40,000 ` 40,000 ` 40,000 ` 30,000
= - ` 100,000 + + + + + +
(1 + 0.20)1 (1 + 0.20) 2 (1 + 0.20) 3 (1 + 0.20) 4 (1 + 0.20) 5 (1 + 0.20) 5
= - ` 1,00,000 + ` 33,333.33+ ` 27,777.78 + ` 23,148.15+ ` 19,290.12 + ` 16,075.10 +
` 12,056.33
NPV = ` 31,680.81
(iii) If the cash flows are perfectly dependent, then the low cash flow in the first year will
mean a low cash flow in every year. Thus, the possibility of the worst case occurring
is the probability of getting ` 20,000 net cash flow in year 1 is 10%.
9. Calculation of NPV
20,000 × 20 30,000 × 20 30,000 x 20
NPV = - 10,00,000 + + +
1.1 1.21 1.331

= - ` 10,00,000 + ` 3,63,636 + ` 4,95,868 + ` 4,50,789

= ` 13,10,293 – ` 10,00,000
= ` 3,10,293
Measurement of sensitivity is as follows:

(a) Sales Price:-

Let the sale price/Unit be S so that the project would break even with 0 NPV.
20,000 × (S − 40) 30,000 × (S − 40) 30,000 (S − 40)
∴ 10,00,000 = + +
1.1 1.21 1.331

S – 40 = ` 10,00,000/` 65,514
S – 40 = ` 15.26
S = ` 55.26 which represents a fall of (60-55.26)/60

Or 0.079 or 7.9%

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 3.68
2.68 ADVANCED FINANCIAL MANAGEMENT

Alternative Method
10,00,000 x 20
= ` 15.26
13,10,293

S= ` 40 + ` 15.26
= ` 55.26

Alternative Solution
If sale Price decreased by say 10%, then NPV (at Sale Price of ` 60 – ` 6 = ` 54)
20000 × 14 30000 × 14 30000 × 14
NPV = -10,00,000 + + +
(1.1)1 (1.1) 2 (1.1) 3

= -` 10,00,000 + ` 2,54,545 + ` 3,47,107 + ` 3,15,552

= - ` 82,796
3,10,293 - (- 82,796)
NPV decrease (%) = X 100 = 126.68%
3,10,293

(b) Unit Cost:-

If sales price = ` 60 the cost price required to give a margin of ` 15.26 is (` 60 – `
 44.74 − 40 
15.26) or ` 44.74 which would represent a rise of 11.85% i.e.,  × 100 
 40 

Alternative Solution
If unit cost increased by say 10%. The new NPV will be as follows:
20000 × 16 30000 × 16 30000 × 16
NPV = -10,00,000 + + +
(1.1)1 (1.1) 2 (1.1) 3

= -` 10,00,000 + ` 2,90,909 + ` 3,96,694 + ` 3,60,631

= ` 48,234
3,10,293 - ( 48,234)
NPV decrease (%) = X 100 = 84.46%
3,10,293

(c) Sales volume:-

The requisite percentage fall is:-
3,10,293/13,10,293 × 100 = 23.68%

© The Institute of Chartered Accountants of India

 ADVANCED CAPITAL BUDGETING DECISIONS 3.69
2.69

Alternative Solution
If sale volume decreased by say 10%. The new NPV will be as follows:
18000 × 20 27000 × 20 27000 × 20
NPV = -10,00,000 + + +
(1.1)1 (1.1) 2 (1.1) 3

= - ` 10,00,000 + ` 3,27,272 + ` 4,46,281 + ` 4,05,710

= ` 1,79,263
3,10,293 - 1,79,263
NPV decrease (%) = X 100 = 42.22%
3,10,293

(d) Since PV of inflows remains at `13,10,293 the initial outlay must also be the
same.

∴ Percentage rise = 3,10,293/10,00,000 × 100 = 31.03%.

Alternative Solution

If initial outlay increased by say 10%. The new NPV will be as follows:
20000 × 20 30000 × 20 30000 × 20
NPV = - ` 11,00,000 + + +
(1.1)1 (1.1) 2 (1.1) 3

= - ` 11,00,000 + ` 3,63,636 + ` 4,95,868 + ` 4,50,789 = ` 2,10,293

3,10,293 - 2,10,293
NPV decrease (%) = X 100 = 32.22%
3,10,293

(e) Present value for 1st two years.

= - ` 10,00,000 + ` 4,00,000 x 0.909 + ` 6,00,000 x 0.826
= - ` 10,00,000 + ` 3,63,600 + ` 4,95,600
= - ` 10,00,000 + ` 8,59,200
= - ` 1,40,800

∴ The project needs to run for some part of the third year so that the present value
of return is ` 1,40,800. It can be computed as follows:
(i) 30,000 units x ` 20 x 0.751 = ` 4,50,600

(ii) Per day Production in (`) assuming a year of 360 days =

© The Institute of Chartered Accountants of India

 3.70
2.70 ADVANCED FINANCIAL MANAGEMENT

` 4,50,600
= ` 1,252
360
` 1,40,800
(iii) Days needed to recover `1,40,800 = = 112
` 1,252

Thus, if the project runs for 2 years and 112 days then break even would
(3 - 2.311)
be achieved representing a fall of × 100 = 22.97%.
3

10. CALCULATION OF NPV

`
PV of cash inflows (` 45,000 x 3.169) 1,42,605
Initial Project Cost 1,20,000
NPV 22,605
If initial project cost is varied adversely by 10%*
NPV (Revised) (` 1,42,605 - ` 1,32,000) ` 10,605
Change in NPV (` 22,605 – ` 10,605)/ ` 22,605 i.e. 53.08 %
If annual cash inflow is varied adversely by 10%*
Revised annual inflow ` 40,500
NPV (Revised) (` 40,500 x 3.169) – (` 1,20,000) (+) ` 8,345
Change in NPV (` 22,605 – ` 8,345) / ` 22,605 63.08 %
If cost of capital is varied adversely by 10%*
NPV (Revised) (` 45,000 x 3.103) – ` 1,20,000 (+) ` 19,635
Change in NPV (` 22,605 – ` 19,635) / ` 22,605 13.14 %
Conclusion: Project is most sensitive to ‘annual cash inflow’.
*Note: Students may please note that they may assume any other percentage rate other than
10 % say 15%, 20 % 25 % etc.
11. P.V. of Cash Flows
Year 1 Running Cost ` 4,000 x 0.917 = (` 3,668)
Savings ` 12,000 x 0.917 = ` 11,004
Year 2 Running Cost ` 5,000 x 0.842 = (` 4,210)
Savings ` 14,000 x 0.842 = ` 11,788
` 14,914
Year 0 Less: P.V. of Cash Outflow ` 10,000 x 1 ` 10,000
NPV ` 4,914

© The Institute of Chartered Accountants of India

 ADVANCED CAPITAL BUDGETING DECISIONS 3.71
2.71

Sensitivity Analysis
(i) Increase of Plant Value by ` 4,914
4,914
∴ x 100 = 49.14%
10,000

(ii) Increase in PV of Running Cost by ` 4,914

4,914 4,914
= x 100 = 62.38%
3,668 + 4,210 7,878

(iii) Fall in PV of Saving by ` 4,914

4,914 4,914
= x 100 = 21.56%
11,004 + 11,788 22,792

Hence, savings factor is the most sensitive to affect the acceptability of the project as in
comparison of other two factors a slight % change in this fact shall more affect the NPV than
others.
Alternative Solution
P.V. of Cash Flows
Year 1 Running Cost ` 4,000 x 0.917 = (` 3,668)
Savings ` 12,000 x 0.917 = ` 11,004
Year 2 Running Cost ` 5,000 x 0.842 = (` 4,210)
Savings ` 14,000 x 0.842 = ` 11,788
` 14,914
Year 0 Less: P.V. of Cash Outflow ` 10,000 x 1 ` 10,000
NPV ` 4,914
Sensitivity Analysis
(i) If the initial project cost is varied adversely by say 10%*.
NPV (Revised) (` 4,914 – ` 1,000) = ` 3,914
` 4,914 −` 3,914
Change in NPV = 20.35%
` 4,914

(ii) If Annual Running Cost is varied by say 10%*.

NPV (Revised) (` 4,914 – ` 400 X 0.917 – ` 500 X 0.842)

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 3.72
2.72 ADVANCED FINANCIAL MANAGEMENT

= ` 4,914 – ` 367 – ` 421= ` 4,126

` 4,914 −` 4,126
Change in NPV = 16.04%
` 4,914

(iii) If Saving is varied by say 10%*.

NPV (Revised) (` 4,914 – ` 1,200 X 0.917 – ` 1,400 X 0.842)
= ` 4,914 – ` 1,100 – ` 1,179 = ` 2,635
4,914 - 2,635
Change in NPV = 46.38%
4,914

Hence, savings factor is the most sensitive to affect the acceptability of the project.
* Any percentage of variation other than 10% can also be assumed.
12. (i) Initial Investment
IRR = 16% (Given)
At IRR, NPV shall be zero, therefore
Initial Cost of Investment = PVAF (16%,5) x Cash Flow (Annual)
= 3.274 x ` 57,500
= ` 1,88,255
(ii) Net Present Value (NPV)
16 - X
Let Cost of Capital be X, then = 60% X = 10%
X
Thus NPV of the project
= Annual Cash Flow x PVAF (10%, 5) – Initial Investment
= ` 57,500 x 3.791 – ` 1,88,255

= ` 2,17,982.50 – ` 1,88,255 = ` 29,727.50

(iii) Annual Fixed Cost
Let change in the Fixed Cost which makes NPV zero is X. Then,

` 29,727.50 – 3.791X = 0
Thus X = ` 7,841.60

© The Institute of Chartered Accountants of India

 ADVANCED CAPITAL BUDGETING DECISIONS 3.73
2.73

Let original Fixed Cost be Y then,

Y × 7.8416% = ` 7,841.60
Y = ` 1,00,000
Thus Fixed Cost is equal to ` 1,00,000
(iv) Estimated Annual Units of Sales
` 60
Selling Price per unit = = ` 200
100% - 70%
Annual Cash Flow + Fixed Cost
=Sales Value
P/V Ratio

` 57,500 + ` 1,00,000
= ` 2,25,000
0.70
` 2,25,000
Sales in Units = =1,125 units
` 200
(v) Break Even Units
Fixed Cost 1,00,000
= = 714.285 units
ContributionPer Unit 140

13. Calculation of NPV

= - ` 50,00,000 + [2,00,000 (` 30 – ` 16.50) – ` 10,00,000] PVIAF (12%,5)
= - ` 50,00,000 + [2,00,000 (` 13.50) – ` 10,00,000] 3.605
= - ` 50,00,000 + [` 27,00,000 – ` 10,00,000] 3.605

= - ` 50,00,000 + ` 61,28,500 = ` 11,28,500

Measurement of Sensitivity Analysis
(a) Sales Price:-

Let the sale price/Unit be S so that the project would break even with 0 NPV.
∴` 50,00,000 = [2,00,000 (S – ` 16.50) – ` 10,00,000] PVIAF (12%,5)
` 50,00,000 = [2,00,000S – ` 33,00,000 – ` 10,00,000] 3.605

` 50,00,000 = [2,00,000S – ` 43,00,000] 3.605

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 3.74
2.74 ADVANCED FINANCIAL MANAGEMENT

` 13,86,963 = 2,00,000S – ` 43,00,000

` 56,86,963 = 2,00,000S
S = ` 28.43 which represents a fall of (30 - 28.43)/30 or 0.0523 or 5.23%
(b) Sales volume:-
Let V be the sale volume so that the project would break even with 0 NPV.
` 50,00,000 = [V (` 30 – ` 16.50) – ` 10,00,000] PVIAF (12%,5)
` 50,00,000 = [V (` 13.50) – ` 10,00,000] PVIAF (12%,5)
` 50,00,000 = [` 13.50V – ` 10,00,000] 3.605
` 13,86,963 = ` 13.50V – ` 10,00,000
` 23,86,963 = ` 13.50V
V = 1,76,812 which represents a fall of (2,00,000 - 1,76,812)/2,00,000 or 0.1159 or
11.59%
(c) Variable Cost:
Let the variable cost be V so that the project would break even with 0 NPV.

∴ ` 50,00,000 = [2,00,000(` 30 – V) – ` 10,00,000] PVIAF(12%,5)

` 50,00,000 = [` 60,00,000 – 2,00,000 V – ` 10,00,000] 3.605

` 50,00,000 = [` 50,00,000 – 2,00,000 V] 3.605
` 13,86,963 = ` 50,00,000 – 2,00,000 V
` 36,13,037 = 2,00,000V
V = ` 18.07 which represents a fall of (18.07 – 16.50)/16.50 or 0.0951 or 9.51%
(d) Expected Net Present Value
(1,75,000 X 0.30) + (2,00,000 X 0.60) + (2,25,000 X 0.10) =1,95,000
NPV = [1,95,000 X ` 13.50 – ` 10,00,000] 3.605 – ` 50,00,000 = ` 8,85,163
Further NPV in worst and best cases will be as follows:
Worst Case:
[1,75,000 X ` 13.50 – ` 10,00,000] 3.605 – ` 50,00,000 = - ` 88,188

© The Institute of Chartered Accountants of India

 ADVANCED CAPITAL BUDGETING DECISIONS 3.75
2.75

Best Case:
[2,25,000 X ` 13.50 – ` 10,00,000] 3.605 – ` 50,00,000 = ` 23,45,188
Thus, there are 30% chances that the rise will be a negative NPV and 70% chances
of positive NPV. Since acceptable level of risk of Unnat Ltd. is 20% and there are 30%
chances of negative NPV hence project should not be accepted.
14. (i) Statement Showing the Net Present Value of Project M
Year Cash Flow C.E. Adjusted Cash Present Total Present
end ( `) (b) flow (`) value factor value (`)
(a) (c) = (a) × (b) at 6% (e) = (c) ×
(d) (d)
1 4,50,000 0.8 3,60,000 0.943 3,39,480
2 5,00,000 0.7 3,50,000 0.890 3,11,500
3 5,00,000 0.5 2,50,000 0.840 2,10,000
8,60,980
Less: Initial Investment 8,50,000
Net Present Value 10,980

Statement Showing the Net Present Value of Project N

Year Cash C.E. Adjusted Cash Present Total Present
end Flow (`) flow (`) value factor value (`)
(a) (b) (c) = (a) × (b) (d) (e) = (c) × (d)
1 4,50,000 0.9 4,05,000 0.943 3,81,915
2 4,50,000 0.8 3,60,000 0.890 3,20,400
3 5,00,000 0.7 3,50,000 0.840 2,94,000
9,96,315
Less: Initial Investment 8,25,000
Net Present Value 1,71,315
Decision: Since the net present value of Project N is higher, so the project N should
be accepted.

(ii) Certainty - Equivalent (C.E.) Co-efficient of Project M (2.0) is lower than Project N
(2.4). This means Project M is riskier than Project N as "higher the riskiness of a cash
flow, the lower will be the CE factor". If risk adjusted discount rate (RADR) method is
used, Project M would be analysed with a higher rate.

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 3.76
2.76 ADVANCED FINANCIAL MANAGEMENT

RADR is based on the premise that riskiness of a proposal may be taken care of, by
adjusting the discount rate. The cash flows from a more risky proposal should be
discounted at a relatively higher discount rate as compared to other proposals whose
cash flows are less risky. Any investor is basically risk averse. However, he may be
ready to take risk provided he is rewarded for undertaking risk by higher returns. So,
more risky the investment is, the greater would be the expected return. The expected
return is expressed in terms of discount rate which is also the minimum required rate
of return generated by a proposal if it is to be accepted. Therefore, there is a positive
correlation between risk of a proposal and the discount rate.
15. Statement showing the determination of the risk adjusted net present value
Projects Net Coefficient Risk Annual PV factor Discounted Net present
cash of adjusted cash 1-5 years cash inflow value
outlays variation discount inflow
rate
` ` ` `
(i) (ii) (iii) (iv) (v) (vi) (vii) = (v) × (viii) = (vii) −
(vi) (ii)
X 2,10,000 1.20 16% 70,000 3.274 2,29,180 19,180
Y 1,20,000 0.80 14% 42,000 3.433 1,44,186 24,186
Z 1,00,000 0.40 12% 30,000 3.605 1,08,150 8,150
16. (i) The risk free rate of interest and risk factor for each of the projects are given. The risk
adjusted discount rate (RADR) for different projects can be found on the basis of
CAPM as follows:
Required Rate of Return = IRf + (ko - IRF ) Risk Factor
For P-I : RADR = 0.10 + (0.15 – 0.10 ) 1.80 = 19%
For P-II : RADR = 0.10 + (0.15 – 0.10 ) 1.00 = 15 %
For P-III : RADR = 0.10 + (0.15 – 0.10) 0.60 = 13 %
(ii) The three projects can now be evaluated at 19%, 15% and 13% discount rate as
follows:
Project P-I
Annual Inflows ` 6,00,000
PVAF (19 %, 4) 2.639
PV of Inflows (` 6,00,000 x 2.639) ` 15,83,400

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 ADVANCED CAPITAL BUDGETING DECISIONS 3.77
2.77

Less: Cost of Investment ` 15,00,000

Net Present Value ` 83,400
Project P-II
Year Cash PVF (15%,n) PV (`)
Inflow (`)
1 6,00,000 0.870 5,22,000
2 4,00,000 0.756 3,02,400
3 5,00,000 0.658 3,29,000
4 2,00,000 0.572 1,14,400
Total Present Value 12,67,800
Less: Cost of Investment 11,00,000
Net Present Value 1,67,800

Project P-III
Year Cash Inflow (`) PVF (13%,n) PV (`)
1 4,00,000 0.885 3,54,000
2 6,00,000 0.783 4,69,800
3 8,00,000 0.693 5,54,400
4 12,00,000 0.613 7,35,600
Total Present Value 21,13,800
Less: Cost of Investment 19,00,000
Net Present Value 2,13,800
Project P-III has highest NPV. So, it should be accepted by the firm
17. It is stated that the cash flows have been adjusted for inflation; hence they are “nominal”. The
cost of capital or discount rate is “real”. In order to be compatible, the cash flows should be
converted into “real flow”. This is done as below:
Year Nominal Adjusted Real cash PVF @ 10% PV of cash
cash flows Inflation* factor flows flows
0 (70) − (70) 1.000 (70)
1 30 0.952 28.56 0.909 25.96
2 40 0.907 36.28 0.826 29.97

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 3.78
2.78 ADVANCED FINANCIAL MANAGEMENT

3 30 0.864 25.92 0.751 19.47

Total 75.40
Less: Cash out flow 70.00
NPV (+) 5.40

* 1/1.05; 1/(1.05)2 ; 1/(1.05)3;

Advise: With positive NPV, the project is financially viable.
Alternatively, instead of converting cash flows into real terms, the discount rate can be
converted into nominal rate. Result will be the same.
An alternative solution is presented herewith
Alternative solution:
Year Nominal cash flows PVF @ 15.50% adjusted by PV of cash flows
the inflation factor i.e. 5%*
1 30 0.866 25.98
2 40 0.749 29.96
3 30 0.649 19.47
Cash inflow 75.41
Less: Cash out flow 70.00
Net present value 5.41
0.909 0.826 0.751
* = 0.866, = 0.749, = 0.649
1.05 1.1025 1.1576

Advise: With positive NPV, the project is financially viable.

18. Here the given cash flows have to be adjusted for inflation. Alternatively, the discount rate
can be converted into nominal rate, as follows:-
0.909 0.826 0.826
Year 1 = = 0.866; Year 2 = or = 0.749
1.05 (1.05 ) 1.1025
2

0.751 0.751
Year 3 = = = 0.649
(1.05 ) 1.1576
3

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 ADVANCED CAPITAL BUDGETING DECISIONS 3.79
2.79

Year Nominal Cash Adjusted PVF PV of Cash Flows

Flows (` in lakhs) as above (` in lakhs)
1 30 0.866 25.98
2 40 0.749 29.96
3 30 0.649 19.47
Cash Inflow 75.41
Less: Cash Outflow 72.00
Net Present Value 3.41

With positive NPV, the project is financially viable.

Alternative Solution
Assumption: The cost of capital given in the question is “Real’.
Nominal cost of capital = (1.10) (1.05) -1 = 0.155 =15.50%
DCF Analysis of the project
(` Lakhs)
Period PVF @15.50% CF PV
Investment 0 1 -72 -72.00
Operation 1 0.866 30 +25.98
---do--- 2 0.750 40 +30.00
---do--- 3 0.649 30 +19.47
NPV +3.45

The proposal may be accepted as the NPV is positive.

19. (i) Inflation adjusted Revenues
Year Revenues (`) Revenues (Inflation Adjusted) (`)
1 10,00,000 10,00,000(1.09) = 10,90,000
2 13,00,000 13,00,000(1.09) (1.08) = 15,30,360
3 14,00,000 14,00,000(1.09) (1.08)(1.06) = 17,46,965

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 3.80
2.80 ADVANCED FINANCIAL MANAGEMENT

(ii) Inflation adjusted Costs

Year Costs (`) Costs (Inflation Adjusted) (`)
1 5,00,000 5,00,000(1.10) = 5,50,000
2 6,00,000 6,00,000(1.10)(1.09) = 7,19,400
3 6,50,000 6,50,000(1.10)(1.09)(1.07) = 8,33,905
(iii) Tax Benefit on Depreciation = ` 5,00,000 x 0.35 = ` 1,75,000

(iv) Net Profit after Tax

Year Revenues Costs Net Profit Tax Profit
(Inflation (Inflation (`) (`) after Tax
Adjusted) Adjusted) (3) =(1) -(2) (4) = 35% (`)
(`) (`) of (3) (3) - (4)
(1) (2)
1 10,90,000 5,50,000 5,40,000 1,89,000 3,51,000
2 15,30,360 7,19,400 8,10,960 2,83,836 5,27,124
3 17,46,965 8,33,905 9,13,060 3,19,571 5,93,489
(v) Present Value of Cash Inflows
Year Net Tax Benefit on Cash PVF@ PV
Profit Depreciation Inflow (`) 14% (`)
after tax (`)
(`)
1 3,51,000 1,75,000 5,26,000 0.877 4,61,302
2 5,27,124 1,75,000 7,02,124 0.769 5,39,933
3 5,93,489 1,75,000 7,68,489 0.675 5,18,730
15,19,965
NPV = ` 15,19,965 – ` 15,00,000 = ` 19,965
20. (i) The decision tree diagram is presented in the chart, identifying various paths and
outcomes, and the computation of various paths/outcomes and NPV of each path are
presented in the following tables:

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 ADVANCED CAPITAL BUDGETING DECISIONS 3.81
2.81

The Net Present Value (NPV) of each path at 10% discount rate is given below:
Path Year 1 Cash Flows Year 2 Cash Flows Total Cash Inflows NPV
Cash
(`) (`) Inflows (`) (`)
(PV)
(`)
1 50,000×.909 = 45,450 24,000×.826 = 19,824 65,274 80,000 (―) 14,726
2 45,450 32,000×.826 = 26,432 71,882 80,000 (―) 8,118
3 45,450 44,000×.826 = 36,344 81,794 80,000 1,794
4 60,000×.909 = 54,540 40,000×.826 = 33,040 87,580 80,000 7,580
5 54,540 50,000×.826 = 41,300 95,840 80,000 15,840
6 54,540 60,000×.826 = 49,560 1,04,100 80,000 24,100
Statement showing Expected Net Present Value
`
z NPV (`) Joint Probability Expected NPV
1 ―14,726 0.08 ―1,178.08
2 ―8,118 0.12 ―974.16
3 1,794 0.20 358.80
4 7,580 0.24 1,819.20
5 15,840 0.30 4,752.00
6 24,100 0.06 1,446.00
6,223.76
(ii) If the worst outcome is realized the project will yield NPV of – ` 14,726. The probability
of occurrence of this NPV is 8% and a loss of ` 1,178 (path 1).

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 3.82
2.82 ADVANCED FINANCIAL MANAGEMENT

(iii) The best outcome will be path 6 when the NPV is at ` 24,100. The probability of
occurrence of this NPV is 6% and a expected profit of ` 1,446.

(iv) The project should be accepted because the expected NPV is positive at ` 6,223.76
based on joint probability.
21. Evaluation of project utilizes of Project A and Project B
Project A
Cash flow Probability Utility Utility value
(in `)
-15,000 0.10 -100 -10
-10,000 0.20 -60 -12
15,000 0.40 40 16
10,000 0.20 30 6
5,000 0.10 20 2
2

Cash flow Project B

(in `) Probability Utility Utility value
-10,000 0.10 -60 -6
-4,000 0.15 -3 -0.45
15,000 0.40 40 16
5,000 0.25 20 5
10,000 0.10 30 3
17.55

Project B should be selected as its expected utility is more.

22. A & Co.
Equivalent cost of (EAC) of new machine
`
(i) Cost of new machine now 90,000
Add: PV of annual repairs @ ` 10,000 per annum for 8 years
(` 10,000 × 4.4873) 44,873
1,34,873
Less: PV of salvage value at the end of 8 years 6,538
(`20,000×0.3269)
1,28,335
Equivalent annual cost (EAC) (` 1,28,335/4.4873) 28,600

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 ADVANCED CAPITAL BUDGETING DECISIONS 3.83
2.83

PV of cost of replacing the old machine in each of 4 years with new machine
Scenario Year Cash Flow PV @ 15% PV
(`) (`)
Replace Immediately 0 (28,600) 1.00 (28,600)
40,000 1.00 40,000
11,400
Replace in one year 1 (28,600) 0.870 (24,882)
1 (10,000) 0.870 (8,700)
1 25,000 0.870 21,750
(11,832)
Replace in two years 1 (10,000) 0.870 (8,700)
2 (28,600) 0.756 (21,622)
2 (20,000) 0.756 (15,120)
2 15,000 0.756 11,340
(34,102)
Replace in three years 1 (10,000) 0.870 (8,700)
2 (20,000) 0.756 (15,120)
3 (28,600) 0.658 (18,819)
3 (30,000) 0.658 (19,740)
3 10,000 0.658 6,580
(55,799)
Replace in four years 1 (10,000) 0.870 (8,700)
2 (20,000) 0.756 (15,120)
3 (30,000) 0.658 (19,740)
4 (28,600) 0.572 (16,359)
4 (40,000) 0.572 (22,880)
(82,799)

Advice: The company should replace the old machine immediately because the PV of cost
of replacing the old machine with new machine is least.

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 3.84
2.84 ADVANCED FINANCIAL MANAGEMENT

Alternatively, optimal replacement period can also be computed using the following
table:
Scenario Year Cashflow PV at 15% PV
Replace immediately 0 (40,000) 1 (40,000)
1 to 4 28,600 2.855 81,652
41,652

Replace after 1 year 1 10,000 0.870 8,696

1 (25,000) 0.870 (21,739)
2 to 4 28,600 1.985 56,783
43,739

Replace after 2 years 1 10,000 0.870 8,696

2 20,000 0.756 15,123
2 (15,000) 0.756 (11,342)
3 and 4 28,600 1.229 35,157
47,633
Replace after 3 years 1 10,000 0.870 8,696
2 20,000 0.756 15,123
3 30,000 0.658 19,725
3 (10,000) 0.658 (6,575)
4 28,600 0.572 16,352
53,321

Replace after 4 years 1 10,000 0.870 8,696

2 20,000 0.756 15,123
3 30,000 0.658 19,725
4 40,000 0.572 22,870
66,414

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 ADVANCED CAPITAL BUDGETING DECISIONS 3.85
2.85

23.

(A) Cash Outflow `

(i) In case machine is upgraded:
Upgradation Cost 10,00,000
(ii) In case new machine installed:
Cost 20,00,000
Add: Installation cost 50,000
Total Cost 20,50,000

Less: Disposal of old machine

` 50,000 – 40% tax 30,000
Total Cash Outflow 20,20,000

Working Note:
(i) Depreciation – in case machine is upgraded

` 10,00,000 ÷ 5 = ` 2,00,000
(ii) Depreciation – in case new machine is installed
` 20,50,000 ÷ 5 = ` 4,10,000
(iii) Old existing machine – Book Value is zero. So, no depreciation.
(B) Cash Inflows after Taxes (CFAT)

Old Existing Upgraded Machine

Machine
Year (i) (ii) (iii) (iv) = (iv)-(i)
EAT/CFAT EAT DEP CFAT Incremental
` ` ` ` CFAT `

1 5,00,000 5,50,000 2,00,000 7,50,000 2,50,000

2 5,40,000 5,90,000 2,00,000 7,90,000 2,50,000
3 5,80,000 6,10,000 2,00,000 8,10,000 2,30,000
4 6,20,000 6,50,000 2,00,000 8,50,000 2,30,000
5 6,60,000 7,00,000 2,00,000 9,00,000 2,40,000

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 3.86
2.86 ADVANCED FINANCIAL MANAGEMENT

Cash Inflow after Taxes (CFAT)

New Machine
(vi) (vii) (viii) (ix) = (viii) – (i)
Year
EAT DEP CFAT Incremental CFAT
` ` ` (` )
1 6,00,000 4,10,000 10,10,000 5,10,000
2 6,40,000 4,10,000 10,50,000 5,10,000
3 6,90,000 4,10,000 11,00,000 5,20,000
4 7,40,000 4,10,000 11,50,000 5,30,000
5 8,00,000 4,10,000 12,10,000 5,50,000

P.V. AT 15% - 5 Years – on Incremental CFAT

Upgraded Machine New Machine
Incrementa PVF Total Increment PVF Total
Year l P.V. al PV
CFAT ` CFAT `
`
1 2,50,000 0.870 2,17,500 5,10,000 0.870 4,43,700
2 2,50,000 0.756 1,89,000 5,10,000 0.756 3,85,560
3 2,30,000 0.658 1,51,340 5,20,000 0.658 3,42,160
4 2,30,000 0.572 1,31,560 5,30,000 0.572 3,03,160
5. 2,40,000 0.497 1,19,280 5,50,000 0.497 2,73,350
Total P.V. of CFAT 8,08,680 17,47,930
Less: Cash Outflows 10,00,000 20,20,000*
N.P.V. = -1,91,320 - 2,72,070

*Acquisition Cost (including installation cost) ` 20,50,000

Less: Salvage Value of existing machine net of Tax ` 30,000
` 20,20,000
As the NPV in both the new (alternative) proposals is negative, the company should
continue with the existing old Machine.

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 ADVANCED CAPITAL BUDGETING DECISIONS 3.87
2.87

24. Statement showing the evaluation of two machines

Machines A B
Purchase cost (`): (i) 1,50,000 1,00,000
Life of machines (years) 3 2
Running cost of machine per year (`): (ii) 40,000 60,000
Cumulative present value factor for 1-3 years @ 10% (iii) 2.486 −
Cumulative present value factor for 1-2 years @ 10% (iv) − 1.735
Present value of running cost of machines (`): (v) 99,440 1,04,100
[(ii) × (iii)] [(ii) × (iv)]
Cash outflow of machines (`): (vi) = (i) + (v) 2,49,440 2,04,100
Equivalent present value of annual cash outflow 1,00,338 1,17,637
[(vi) ÷ (iii)] [(vi) ÷ (iv)]

Decision: Company X should buy machine A since its equivalent cash outflow is less than
machine B.
25. Statement showing present value of cash inflow of new machine when it replaces
elderly machine now
NPV of New Machine
PV of Cash Inflow (80000 x 2.486) ` 1,98,880
Less: Purchase Cost of New Machine ` 1,50,000
` 48,880
Since NPV of New Machine is positive, it should be purchased.
Timing Decision
Replace Now

Current Realizable Value ` 80,000

NPV of New Machine ` 48,880
Total NPV ` 1,28,880

Replace after 1 Year

Cash Inflow for Year 1 ` 40000
Realisable Value of Old Machine ` 70000

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 3.88
2.88 ADVANCED FINANCIAL MANAGEMENT

NPV of New Machine ` 48,880

Total NPV after 1 Year ` 1,58,880
PV of Total NPV (158880/1.1) ` 1,44,436
Advise: Since Total NPV is higher in case of Replacement after one year Machine should be
replaced after 1 year.
26. Working Notes
First of all, we shall calculate cash flows for each replacement cycle as follows:
One Year Replacement Cycle `
Year Replacement Cost Maintenance & Repair Residual Net cash Flow
Value
0 (60,000) - - (60,000)
1 - (16,000) 32,000 16,000
Two Years Replacement Cycle `
Year Replacement Cost Maintenance & Repair Residual Net cash Flow
Value
0 (60,000) - - (60,000)
1 - (16,000) - (16,000)
2 - (22,000) 24,000 2,000

Three Years Replacement Cycle `

Year Replacement Cost Maintenance & Repair Residual Net cash Flow
Value
0 (60,000) - - (60,000)
1 - (16,000) - (16,000)
2 - (22,000) - (22,000)
3 - (28,000) 16,000 (12,000)
Four Years Replacement Cycle `
Year Replacement Cost Maintenance & Repair Residual Net cash Flow
Value
0 (60,000) - - (60,000)
1 - (16,000) - (16,000)
2 - (22,000) - (22,000)
3 - (28,000) - (28,000)
4 - (36,000) 8,000 (28,000)

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 ADVANCED CAPITAL BUDGETING DECISIONS 3.89
2.89

Now we shall calculate NPV for each replacement cycles

1 Year 2 Years 3 Years 4 Years
Year PVF@ Cash PV Cash PV Cash PV Cash PV
15% Flows Flows Flows Flows
0 1 -60,000 -60,000 -60,000 -60,000 -60,000 -60,000 -60,000 -60,000
1 0.8696 16,000 13,914 -16,000 -13,914 -16,000 -13,914 -16,000 -13,914
2 0.7561 - - 2,000 1,512 -22,000 -16,634 -22,000 -16,634
3 0.6575 - - - 0 -12,000 -7,890 -28,000 -18,410
4 0.5718 - - - 0 0 -28,000 -16,010
-46,086 -72,402 -98,438 -1,24,968

Replacement Cycles EAC (`)

1 Year 46,086 52,997
0.8696
2 Years 72,402 44,536
1.6257
3 Years 98,438 43,114
2.2832
4 Years 1,24,968 43,772
2.855

Since EAC is least in case of replacement cycle of 3 years hence machine should be replaced
after every three years.
27. In this question the effect of increasing running cost and decreasing resale value have to be
weighted upto against the purchase cost of bike. For this purpose, we shall compute
Equivalent Annual Cost (EAC) of replacement in different years shall be computed and
compared.
Year Road Petrol Total PVF PV Cumulative PV of Net
Taxes etc. (`) @10% (`) PV (`) Resale Outflow
(`) (`) Price (`) (`)

1 3,000 30,000 33,000 0.909 29,997 29,997 31,815 (1,818)

2 3,000 35,000 38,000 0.826 31,388 61,385 17,346 44,039
3 3,000 43,000 46,000 0.751 34,546 95,931 6,759 89,172

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 3.90
2.90 ADVANCED FINANCIAL MANAGEMENT

Computation of EACs
Year ∗ Purchase Net Outflow Total PVAF EAC ♣
Price of (`) Outflow @ 10% (`)
Bike (`) (`)
1 55,000 (1,818) 53,182 0.909 58,506
2 55,000 44,039 99,039 1.735 57,083
3 55,000 89,172 1,44,172 2.486 57,993

Thus, from above table it is clear that EAC is least in case of 2 years, hence bike should be
replaced every two years.

∗
Assume these periods are the periods from which bike shall be kept in use.
♣
EAC is used to bring Cash Flows occurring for different periods at one point of Time.

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