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Capital Budgeting Final Paper 2: Strategic Financial Management,

Chapter 2: Capital Budgeting, Part 3 CA. Anurag Singal

Learning Objectives

Sensitivity Analysis

Scenario Analysis

Simulation Analysis

Decision Tree Analysis

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Known as "What if” Analysis.

Can be applied to a variety of planning activities not just to capital budgeting decisions.

Determines how the distribution of possible NPV or internal rate of return for a project under consideration is affected consequent to a change in one particular input variable

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Sensitivity Analysis - 2

Done by changing one variable at one time, while keeping other variables (factors) unchanged.

Begins with the base-case situation which is developed using the expected values for each input.

It provides the decision maker with the answers to a whole range of “what if” question.

This analysis can also be used to compute Break-even points.

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Example of Sensitivity Analysis

What is NPV, if the selling price falls by 10%?

What will be IRR if project’s life is only 3 years instead of expected 5 years?

What shall be the revenue required to meet costs (i.e., break-even level of volume) in net present value terms?

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Steps of Sensitivity Analysis

Step 1 • each variable is changed by several percentage points above and

below the expected value, holding all other variables constant.

Step 2 • a new NPV is calculated using each of these values.

Step 3 • the set of NPVs is plotted on graph to show how sensitive NPV is

to the change in each variable.

Step 4 • the slope of lines in the graph shows how sensitive NPV is to the

change in each of input.

Step 5 • The steeper the slope, the more sensitive the NPV is to a change

in a variable.

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Advantages of Sensitivity Analysis

• This analysis identifies critical factors that impinge on a project’s success or failure.

Critical Issues

• This analysis is quite simple. Simplicity

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Disadvantage of Sensitivity Analysis

• This analysis assumes that all variables are independent i.e. they are not related to each other, which is unlikely in real life.

Assumption of Independence

• This analysis does not look to the probability of changes in the variables. Ignore

probability • This analysis provides information on the

basis of which decisions can be made but does not point directly to the correct decision. Not so reliable

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Illustration : Initial Investment 1,25,000

Selling price per Unit 100

Variable costs per unit 30

Fixed costs for the period 1,00,000

Sales volume 2000

Life 5 years

Discount rate 10%

Required: Project’s NPV and show how sensitive the results are to various input factors.

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Solution S

ellin

g P

rice ●125,000 = [(P - 30)

2,000 - 100,000] X 3.791 ●32,973 = 2,000P - 60,000 - 100,000 ●P = 96.49 ●i.e. fall of 3.51% before NPV is zero.

●Var

iabl

e C

ost ●125,000 = [(100 - v)

2,000 - 100,000] X 3.791 ●32,973 = 200,000 - 2000V - 100,000 ●V = 33.51 ●i.e. increase of 11.71% before NPV is zero.

Volu

me ●125,000 =[(100 - 30)

q - 100,000] X 3.791 ●32,973=70q - 100,000 ●q = 1,900 ●in fall of 5.02% before NPV is zero

NPV = -125,000 + [(100 - 30) 2,000 - 100,000] X 3.791 = 26,640

Sensitivity to change to :

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Solution - 2

Life ●125,000 = 40,000 x AFn @

10% ●3.125 =AFn @ 10% ●AF for 4 years at 10% is 3.17 ●i.e. life can fall to

approximately 4 years before NPV is zero.

Fixed Cost ●125,000 = [(100 - 30) 2,000 -

F] X 3.791 ●32,973 =140,000 – F ●F =107,027 ●i.e. an increase of 7.03% before NPV is zero

Initial Cost

●(125,000 + 26,640) = 151,640 (PV of Cash Inflows) ●i.e. Increase of 21.31% before NPV is zero.

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Scenario Analysis

Analysis brings in the probabilities of changes in key variables

Allows to change more than one variable at a time.

Analysis begins with base case or most likely set of values for the input variables.

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Scenario Analysis contd..

Then goes for worst case scenario (low unit sales, low sale price, high variable cost and so on) and best case scenario.

Analysis seek to establish ‘worst and best’ scenarios so that whole range of possible outcomes can be considered.

Scenario analysis answers the question “How bad could the project look”.

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Critical components:

Step 1 • The first component involves determining the factors around which the scenarios will be built. These

factors can range from the state of economy to the response of competitors on any action of the firm

Step 2 • Second component is determining the number of scenarios to analysis for each factor. Normally three

scenarios are considered in general i.e. a best case, an average and a worst case. However, they may vary on long range.

Step 3 • Third component is to place focus on critical factors and build relatively few scenarios for each factor

Step 4 • Fourth component is the assignment of probabilities to each scenarios. This assignment may be based

on the macro factors e.g. exchange rates, interest rates etc. and micro factors e.g. competitor’s reactions etc.

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Illustration

XYZ Ltd. is considering a project “A” with an initial outlay of Rs 14,00,000 and the possible three cash inflow attached with the project in Rs ‘000 as follows

Rs’000 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 whether project should be accepted or not.

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Solution The Possible outcomes will be as follows:-

Year PVF@ 9%

Worst Case Most Likely Best Case

Cash Flow ’000

PV ‘000

Cash Flow ’000

PV ‘000

Cash Flow ’000

PV ‘000

0 1 (1400) (1400) (1400) (1400) (1400) (1400)

1 0.917 450 412.65 550 504.35 650 596.05

2 0.842 400 336.80 450 378.90 500 421

3 0.772 700 540.40 800 617.60 900 694.80

NPV (110.15) 100.85 311.85

Contd.. 16

Solution - 2

Now suppose that CEO of XYZ Ltd. is bit confident about the estimates in the first two years, but not sure about the third year’s high cash inflow. He is interested in knowing what will happen to traditional NPV if 3rd year turn out the bad contrary to his optimism.

The NPV in such case will be as follows: -1,400,000 +550000 + 450000 + 700000 (1+0.09) (1+0.09)2 (1+0.09)3

−1400000+ 504587 + 378756 + 540528.44 =23871.44

Thus, CEO’s concern is well founded that, as a worst case in the third year alone yield a marginally positive NPV.

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Simulation Analysis( Monte Carlo)

Monte Caro simulation ties together sensitivities and probability distributions

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.

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Previous Examination Question

Step-1

•Modeling the project

Step-2

•Specify values of parameters and probability distributions of exogenous variables.

Step-3

•Select a value at random from probability distribution of each of the exogenous variables.

Step-4

•Determine N.P.V. corresponding to the randomly generated value of exogenous variables and pre-specified parameter variables.

Step-5

•Repeat steps (3) & (4) a large number of times to get a large number of simulated NPVs.

Step-6

•Plot probability distribution of NPVs and compute a mean and Standard Deviation of returns to gauge the project’s level of risk.

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Steps for Simulation Analysis - 4 marks (May 2011)

Example

Uncertainty associated with two aspects of the project: Annual Net Cash Flow & Life of the project. N.P.V. model for the project is

n Σt=1 [CFt / (1+i)t] - I

Where Risk free interest rate, initial investment are parameters.

With i = 10%, I = Rs 13,000, CFt & n stochastic exogenous variables with the following

distribution will be as under:

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Illustration-Probability-Project Life

Project Life Value (yrs) Probability

3 0.05

4 0.10

5 0.30

6 0.25

7 0.15

8 0.10

9 0.03

10 0.02

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Probability-Cash Flow

Annual Cash Flow Value (Rs) Probability

1000 0.02

1500 0.03

2000 0.15

2500 0.15

3000 0.30

3500 0.20

4000 0.15

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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 (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:

Question (Contd.)

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Correspondence between Values of Annual Cash Flow and two Digit Random Numbers

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Cash Flow Value (Rs)

Probability Cumulative Probability

Two Digit Random No.

1,000 0.02 0.02 00 – 01

1,500 0.03 0.05 02 – 04

2,000 0.15 0.20 05 – 19

2,500 0.15 0.35 20 – 34

3,000 0.30 0.65 35 – 64

3,500 0.20 0.85 65 – 84

4,000 0.15 1.00 85 - 99

Correspondence between Values of Project Life and two Digit Random Numbers

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Project Life Value (Year)

Probability Cumulative Probability

Two Digit Random No.

3 0.05 0.05 00 – 04

4 0.10 0.15 05 – 14

5 0.30 0.45 15 – 44

6 0.25 0.70 45 – 69

7 0.15 0.85 70 – 84

8 0.10 0.95 85 – 94

9 0.03 0.98 95 – 97

10 0.02 1.00 98 - 99

Random Number Table

Random Number

53479 81115 98036 12217 5952697344 70328 58116 91964 2624066023 38277 74523 71118 8489299776 75723 3172 43112 8308630176 48979 92153 38416 4243681874 83339 14988 99937 1321319839 90630 71863 95053 555329337 33435 53869 52769 1880131151 58295 40823 41330 2109367619 52515 3037 81699 17106

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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 Result- Annual Cash Flow

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Run Random No. Corres. Value of Annual

Cash Flow 1 53 3,000 2 66 3,500 3 30 2,500 4 19 2,000 5 31 2,500 6 81 3,500 7 38 3,000 8 48 3,000 9 90 4,000

10 58 3,000

Simulation Result- Project Life

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Run Random No.

Corres. Value of Project Life

1 97 9 2 99 10 3 81 7 4 09 4 5 67 6 6 70 7 7 75 7 8 83 7 9 33 5

10 52 6

Simulation Result- NPV

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Run Random No.

Corres. Value of Annual

Cash Flow

Random No.

Corres. Value of Project Life

N.P.V.

1 53 3,000 97 9 4277 2 66 3,500 99 10 8507 3 30 2,500 81 7 830 4 19 2,000 09 4 (6660)

5 31 2,500 67 6 (2112)

6 81 3,500 70 7 4038 7 38 3,000 75 7 1604 8 48 3,000 83 7 1604 9 90 4,000 33 5 2164

10 58 3,000 52 6 65

Advantages of Simulation Analysis

Strength lies in Variability.

Handle problems characterised by numerous exogenous variables following any kind of distribution.

Complex inter-relationships among parameters, exogenous variables and endogenous variables. Such problems defy capabilities of analytical methods.

Compels decision maker to explicitly consider the inter-dependencies and uncertainties featuring the project.

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Shortcomings

Difficult to model the project and specify probability distribution of exogenous variables.

Determine N.P.V. in simulation run, risk free discount rate is used .This measure of N.P.V. takes a different meaning from its original value, and, therefore, is difficult to interpret.

Realistic simulation model being likely to be complex would probably be constructed by management expert and not by the decision maker.

Simulation is inherently imprecise.

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Decision tree is a graphic display of the relationship between a present decision and future events, future decision and their consequences.

Assumes that there are only two types of

situation that a finance manager has

to face.

A probability distribution needs to be assigned to the

various outcomes or consequences ,since the outcome of the events is not known

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Steps involved in decision tree analysis

Define investment

Identification of Decision Alternatives

Drawing a decision tree

Evaluating the

alternatives

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Rules for Drawing a Decision Ttree

1 • Begins with a decision point, also known as decision node,

represented by a rectangle while

2 • The outcome point, also known as chance node, denoted by a

circle.

3 • Decision alternatives are shown by a straight line starting from

the decision node.

4 • The Decision Tree Diagram is drawn from left to right.

Rectangles and circles have to be sequentially numbered.

5 • Values and Probabilities for each branch are to be incorporated

next.

Contd.. 34

Decision Tree Rules - 2

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6 • The Value of each circle and each rectangle is computed by evaluating from right to

left

7 • The 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.

8 • 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.

9 • 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.

Diagrammatic Presentation

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Illustration

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%.

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Solution

B

C

D

Invest 20 lac

Income 4lac perpetuity

Not to Invest Invest 12 lac Income 1 lac perpetuity

Not to Invest

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Evaluation

At C: The choice is between investing Rs 20 lacs for a perpetual benefit of Rs 4 lacs and not to invest.

The preferred choice is to invest, since the capitalized value of benefit of Rs 4 lacs (at 10%) adjusted for the investment of Rs 20 lacs, yields a net benefit of Rs 20 lacs.

At D: The choice is between investing Rs 12 lacs, for a similar perpetual benefit of Rs 1 lac. and not to invest.

Here the invested amount is greater than capitalized value of benefit at Rs 10 lacs. There is a negative benefit of Rs 2 lacs. Therefore, it would not be prudent to invest.

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Evaluation 2

At B: Evaluation of EMV is as under (Rs in lacs). Outcome Amount (Rs) Probability Result (Rs) Success 20.00 0.50 10.00 Failure 0.00 0.50 00.00 Net result 10.00 EMV at B is, therefore, Rs 10 lacs.

At A: Decision is to be taken based on preferences between two

alternatives. The first is to test, by investing Rs, 2,40,000 and reap a benefit of Rs 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 Rs 2,40,000/- and undertaking the test.

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Illustration:

Big Oil is wondering whether to drill for oil in Westchester Country. The prospects are as follows:

Draw a decision tree showing the successive drilling decisions to be made by Big Oil. How deep should it be prepared to drill?

Depth of Well Feet

Total Cost Millions of Dollars

Cumulative Probability of Finding Oil

PV of Oil (If found) Millions of Dollars

2,000 4 0.5 10

4,000 5 0.6 9

6,000 6 0.7 8

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Solution:

The given data is easily represented by the following decision tree diagram:

D1 D2

D3

PV of Oil =10 mn –Cost of 4 mn= 6 mn dollars

Cost of 4 million dollars

9-5=4 million of dollars



8-6=2 millions of dollars

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Solution - 2

There are three decision points in the tree indicated by D1, D2 and D3.

Using rolling back technique, we shall take the decision at decision point D3 first and then use it to arrive decision at a decisions point D2 and then use it to arrive decision at a decision point D1.

Statement showing the evaluation of decision at Decision Point D3

Decision Event Probability PV of Oil(if found) (Millions in $)

Expected PV of Oil (Millions in $)

1. Drill upto 6000 Feet Finding Oil Dry (Refer Working Notes)

0.25 0.75

+2 -6

0.50 -4.50 -------- -4.00

2. Do not Drill -5.00

Since the Expected P.V. of Oil (if found) on drilling upto 6,000 feet - 4 millions of dollars is greater than the cost of not drilling - 5 millions of dollars. Therefore, Big Oil should drill upto 6,000 feet.

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Solution - 3





0.20 0.80

+4 -4

0.80 -3.20 --------- -2.40

2. Do not Drill -4.00

Since the Expected P.V. of Oil (if found) on drilling upto 4,000 feet - 2.4 millions of dollars is greater than the cost of not drilling - 4 millions of dollars. Therefore, Big Oil should drill upto 4,000 feet.

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Solution - 4





0.50 0.50

+6 -2.40

3.00 -1.20 --------- +1.8

2. Do not Drill NIL

Since the Expected P.V. of Oil (if found) on drilling upto 2,000 feet is 1.8 millions of dollars (positive), Big Oil should drill upto 2,000 feet.

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Working Notes:

Let x be the event of not finding oil at 2,000 feet and y be the event of not finding oil at 4,000 feet and z be the event of not finding oil at 6,000 feet.

We know, that, P (x ∩ y) = P (x) × P(y/x) Where, P(x ∩ y) is the joint probability of not finding oil at 2,000 feet and 4,000 feet, P(x) is the probability of not

finding oil at 2,000 feet and P(y/x) is the probability of not finding oil at 4,000 feet, if the event x has already occurred. P (x ∩ y) = 1 - Cumulative probability of finding oil at 4,000 feet

= 1 - 0.6 = 0.4

P(x) = 1 - Probability of finding oil at 2,000 feet = 1 - 0.5 = 0.5

Hence, P(y/x) = P(x∩y) = 0.40 = 0.80 P(x) 0.50 Therefore, probability of finding oil between 2,000 feet to 4,000 feet = 1 - 0.8 = 0.2

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Working Notes - 2

We know that

P (x ∩ y ∩ z)= P (x) × p (y/x) × p (z/x ∩ y)

Where P (x ∩ y ∩ z) is the joint probability of not finding oil at 2,000 feet, 4,000 feet and 6,000 feet, P(x) and P(y/x) are as explained earlier and P(z/x ∩ y) is the probability of not finding oil at 6,000 feet if the

event x and y has already occurred.

P (x ∩ y ∩ z) = 1 - Cumulative probability of finding oil at 6,000 feet = 1- 0.7 = 0.3

P(x∩y∩z) 0.30 0.30 P(z/x ∩ y = P(x) x P(y/z) = 0.5 x 0.8 = 0.40 = 0.75 Therefore, probability of finding oil between 4,000 feet to 6,000 feet = 1 - 0.75 = 0.25

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Evaluation

At 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

At 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.

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Evaluation - 2

At B: Evaluation of EMV is as under (Rs in lacs).

Outcome Amount (Rs) 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 Rs, 2,40,000 and reap a benefit of Rs 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.

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Lesson Summary


Scenario Analysis

Simulation Analysis


50

Thank You

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