project on simulation

8/6/2019 Project on Simulation

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SENSITIVITY ANALYSIS

The NPV of a project is based upon the series of cash flows and the discount

factor. both these determinants depends upon so many variables such as sales

revenue, input cost, competition etc .given the level of all these variables therewill be a set series of cash flows and hence there will be a NPV of the proposal. If

any of these variables changes the value of the NPV will also change. It means

that the value of NPV is sensitive to all these variables. However the value of NPV

will not change in the same proportion for a given change in any one of these

variables. For some variables the NPV may be less sensitive while for others the

NPV may be more sensitive. The sensitivity analysis deals with the consideration

of sensitivity of the NPV in relation to different variables contributing to the NPV.

The following steps are required to apply the SA to capital budgeting proposal:

a) Based on the expectations for the future, the cash flows are estimated inrespect of the proposal. NPV of the proposal is calculated on the basis of

these cash flows.

b) To identify the variables which have a bearing on the cash flows of aproposal .For example some of these variables may be the selling price,

cost of inputs, market share, market growth rate etc.

c) To find out the effect of change in any of these variables on the value ofNPV. This exercise should be performed for all the factors individually. For

example in case of a project involving the product sale, the effect of change

in different variables such as number of units sold, selling price, discount

rate etc. can be taken up on the NPV or IRR of the project. This information

can be used in conjunction with the basic capital budgeting analysis to

decide whether or not to take up the project.

Example

ABC and CO. is evaluating two proposals A1 and A2 both having cash out flow of

Rs 30,000 each. However these alternatives proposals may result in different cash

inflows depending upon different economic condition i.e good average and poor.

The following information is available-


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A1 A2

ECONOMIC LIFE 10 YEARS 15 YEARS

CASH INFLOWS(ANNUAL)

GOOD ECO.CONDITION RS 8000 RS6000

AVERAGE

ECO.CONDITION RS 6000 RS 5500

POOR ECO.CONDITION RS 4500 RS 4500

Evaluate the proposals and advise the firm given that the minimum required rate

of return of the firm is 10%.

Solution:

As the three estimates of cash flows are given for different economic condition

the NPV of the proposals should also be calculated under all the three conditions.

Further the cash flows are in the form of annuity of 10 years for proposal A1and

for 15 Years for proposal A2. The relevant PVAF(10%,10y) and PVAF(10%,15y)are

6.145 and 7.606 respectively. The present values of the cash flows may be

calculated as follows:

Proposal A1 Proposal A2

CF PVAF PV CF PVAF PV

Good Condition 8,000 6.145 49,160 6,000 7.606 45,636

Average Condition 6,000 6.145 36,870 5,500 7.606 41,833

Poor Condition 4,500 6.145 27,653 4,500 7.606 34,227


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Calculation of NPV of proposals:

Proposal A1 Proposal A2

Pv outflow NPV pv outflow NPV

Good Condition 49,160 30,000 19,160 45,636 30,000 15,636

Average Condition 36,870 30,000 6,870 41,833 30,000 11,833

Poor Condition 27,653 30,000 (2,347) 34,227 30,000 4,227

The proposal A2 is better and hence should be selected. The proposal A2is having

positive NPV under all the three types of economic conditions, whereas theproposalA1may have a negative NPV in case the economic conditions become

poor. so, the proposal A1is risky as compared to proposal A2.

In the example 9.1 the situation was over simplified by taking effect of cash flows

on the value of the NPV. However the same procedure can be extended and the

effect of change in different variables on the value of NPV can be identified .The

sensitivity of a capital budgeting proposal in general may be analyzed with

reference to (1) level of revenues (2) The expected growth rate in revenues (3)the

operating margin and (4) the working capital requirements as a percentage of

revenue etc. with each such variable the NPV and IRR of a proposal may be

ascertained by keeping the other variables unchanged. Example 2 illustrates this

point.

EXAMPLE 2

The following forecast are made about a proposal which is being evaluated by a

firm.

Initial outlay RS.12, 000 cash inflows RS. 4,500(annual)

Life 4 years ke 14%

PVAF (14%, 4Y) =2.9137PVAF (14%,3Y) = 2.3216


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SOLUTION

The NPV of the project is

NPV =-12,000 +4,500 x (2.9137)

= RS 1,112

Now the sensitivity of different variables with respect to this value of NPV (RS

1,112) may be analyzed as follows:

1. Sensitivity with respect to initial outlay:Since NPV is RS 1,112 therefore the outlay can increase from RS 12000 to

RS 13,112 i.e RS 12000 RS 1,112 before the NPV becomes zero. Therefore

there is a margin of RS 1,112 or 9.4% of the initial outlay.

Margin for initial outlay =(1,112/12000) x 100 =9.4%

2. Sensitivity with respect to annual cash inflows:The PVF(14%,4Y) = 2.9137

Therefore 12000 =Annual inflows x 2.9137

Therefore Annual inflows =4,118.

There the annual cash inflows can decrease from the present level of RS. 4,

500 to RS. 4,118 before the NPV becomes 0. So the annual cash inflows

have a margin of RS 382(i.e RS 4,500 RS 4,118) or 8.5%(i.e 382/4,500 x

100)

3. Sensitivity with respect to discount rate:say the discount rate at which the NPV is 0,is x

Therefore RS 12000 = 4,500xx

Therefore, x =2.667

The PVAF of 2.667 for 4 years period is approximately found in 18% column

in the PV AF table. The discount rate can increase from the present level of

14 % to 18%before the NPV becomes negative. Therefore there is a margin

of 4%(i.e 18% -14%) or 29%(i.e 4/14 x 100).


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The above analysis shows that the project is so sensitive to the annual cash

inflows and even a change of 8.5%in the cash inflows can make the project

as unviable.

It may be tempting to change each & every variable in order to analyze the

sensitivity of the proposal, however it may be relevant to focus only on two

sets of variables in particular i.e (1)those that matter the most in terms of

affecting the cash flows (2)those that matter the most for uncertainty e.g

the operating margin.

SA helps in identifying the different variables having effect on the NPV of a

proposal. It helps in establishing the sensitivity or vulnerability of the

proposal to a given variable and showing areas where additional analysis

may be under taken before a proposal is finally selected. The final decision

on whether or not to take the proposal will be based on the regular capital

budgeting analysis and the information generated by the sensitivity

analysis. It is entirely possible that a decision maker, when faced with the

results from the SA might decide to override a proposal originally approved

by capital budgeting analysis. He may point out that a small change in any

one variable makes the proposal unacceptable.

Limitations of sensitivity analysis:

1)

It may be observed that the SA is neither a risk measuring nor a riskreducing technique. It does not provide any clear cut decision rule.

2)Moreover the study of effect of variations in one variable by keepingother variables constant may not be very effective as the variable

may be interdependent. In a practical situations the variables are

often related and move together e.g the selling price and the

expected sales volume are interrelated.

3) The analysis present results for a range of values, without providingany sense of the likelihood of these values occurring.


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CAPITAL BUDGETING AND OPTIMUM REPLACEMENT TIMING

Sometimes a firm may be engaged with taking a very particular capital

budgeting decision dealing with timing of replacement on an asset. A

firm might be having an asset which is a must for its operations andrequires to be replaced frequently. Otherwise , the repair and

maintenance cost will be to high or the normal operation will be

unnecessarily affected. For example, a cold drink bottling plant supplies

the product to the shopkeepers through specially designed and

fabricated delivery vans or a firm manufacturing consumer durable e.g

fridge etc. provides two wheelers to its service engineers who have to

visit the customers for attending complaints. In these cases the delivery

van or the two wheelers scooters must be replaced periodicallyotherwise (1)either the cost of maintenance will be too high or (2)the

normal working will be hampered . Even before the periodical

replacement. The cost of repairs and maintenance goes on increasing.

So the question before the firm may be to decide whether to replace the

asset only periodically or should it be replaced even earlier in view of

the mounting maintenance cost. To put it differently the firm has to

decide the optimum replacement timing.

Example1

A delivery van must be replaced every four years and the related cash

flows are as follows:

Figures in

Rs'000

Age of Van in years

Yr. 0 Yr. 1 Yr. 2 Yr. 3 Yr. 4

cost of van 1,5oo - - - -maintenance cost - 400 450 500 500

repairs - - 100 200 400

scrap value - 800 600 400 200

The firm is faced with the decision : should the van be kept for four years and

then scrapped away for RS 2,00,000? Or should it be replaced earlier?


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Solution:

It may be noted that the van can be replaced after 1 year or 2 years or 3 years. So

each replacement option will cover a different time period. The decision

regarding optimum replacement timing can be taken on the basis of EAM.

Since the cash flows are given in terms of cash outflows only i.e in terms of cost

only, the decision can be taken on the basis of minimizing the EA of the cost.

option 1- replacement cycle 4 years: if the firm decides to replace the van only at

the end of 4th

year, then the cost will be:

Figures in RS 000

years

Net out

flows PVF15%,n PV Amount0 1,500 1.000 1,500

1 400 0.870 348

2 550 0.756 416

3 700 0.658 461

4 700 0.572 400

Total 3,125

Therefore the present value of cost is Rs 31,25,000.

The EA of cost =PV of cost/ PVAF (15%, 4Y)

=Rs 31,25,000/2.855 =Rs 10,94,571

So if the firm replaces the van after 4 years , it is meeting an annual cost of Rs

1o,94,571.

OPTION II Replacement cycle 3 years: If the firm decides to replace the van at

the end of 3rd

year then the cost will be:


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The EA of cost = PV of cost/ PVAF (15%, 3Y)

=Rs 24, 61, 000/2.283 = Rs 10,77,968.

So if the firm replaces the van after every 3 years, it is meeting an annual cost of

Rs 10,77968.

OPTION III REPLACEMENT CYCLE 2 YEARS: If the firm decides to replace the van

at the end of 2nd

year then the cost will be:

FIGURES IN RS 000

YEARNET OUTFLOW PVF(15%,n)

PVAMOUNT

0 1,500 1.000 1,500

1 400 0.870 348

2 50 0.756 38

TOTAL 1,810


The EA of cost = PV of cost/ PVAF (15%, 2Y )

=Rs 18,10,000/1.626 =Rs 11,13,161

So if the firm replaces the van after every 2 years, it is meeting an annual cost of

Rs 11,13, 161.

FIGURES IN RS OOO

YEAR

NET OUT

FLOW PVF15%,n PV AMOUNT

0 1,500 1.000 1,500

1 400 0.870 3482 550 0.756 416

3 300 0.658 197

Total 2,461


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The firm is having a minimum of EA cost when the replacement cycle is 3 years.

Therefore it is the most beneficial for the firm to replace the van every 3 years

and not to wait till 4 years.

The above procedure to find out the optimum replacement cycle is based upontwo assumptions:

1) That the asset will be replaced indefinitely and it will be replaced by anidentical asset with same cash flows.

2) Revenues (i.e cash inflows) are not affected by the age of the asset.However this is not a necessary assumption. If there is an expectations of

decrease in revenues after some years then this decrease can also be taken

as outflow of that year.


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