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7/28/2019 Cap Budgeting 2 Risk Analysis
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INVESTMENT DECISION UNDER CONDITIONS OF
UNCERTAINTY
Introduction
Projects with Unequal Lives
Matching Lives
Equivalent Annual Value (EAV) Method Replacement Decision
Finding a Competitive Price
Capital Rationing
Profitability Index Method
Profitability Index and NPV
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PROJECT RISK ANALYSIS
TECHNIQUES TO HANDLE RISKS IN CAPITAL BUDGETING
Sensitivity Analysis Scenario Analysis
Simulation
Decision Tree Approach
Conventional ways of handling risk
Break Even Analysis
Payback Period
Risk Adjusted Discount Rate
Certainty Equivalent Approach
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PROJECTS OF UNEQUAL LIVES It would be wrong to compare the NPVs of two
projects having different economic lives and
selecting the one with higher NPV.
One way of handling such decision is to extend thecash flows of each technology for a number of
periods till the lives of the two competing
equipment match. This is rather tedious.
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PROJECTS OF UNEQUAL LIVES
An alternative approach is to compare the cost of each technology based on annual costs.
For this purpose we make use of annuity tables andtranslate the present values of cost for equivalent
annualised value (EAV).
The technology with lower EAV of cost is chosen.
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R EPLACEMENT DECISION
Relates to a policy of how often the old equipment
needs to be replaced.
Some firms continue with the existing assets till they
last. The decision to replace is not made by them butis forced on them by the asset when it breaks down
completely.
Such a philosophy is not prudent as firms keepincurring large costs without realising that by early
replacement the scope to save cost exists.
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REPLACEMENT DECISION
Determination of such policy is based on the
principles of mutually exclusive option with different
lives.
The policy of how often the replacement is made is
based on equivalent annualised value.
The policy that gives the largest equivalent annualised
value is adopted.
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FINDING COMPETITIVE PRICE
Third situation that is often faced by businessenterprises is to find a minimum price that must be
quoted for long contracts for high volumes.
Help from EXCEL programme utilising Goal Seek function is handy in finding a quick solution. The
method can also be used for target increase in value
of the firm.
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CAPITAL R ATIONING
This situation refers to limited funds that inhibitsacceptance of all positive NPV projects.
The firm has to make the best use of the capitalavailable.
It must focus on maximization of addition of presentvalues of inflows per unit of initial investment.
This is akin to marginal efficiency of capital.
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PROFITABILITY INDEX
The method to be adopted under conditions of capital rationing is the profitability index (PI).
PI is the present values of inflow per unit of capitaloutlay. Projects with higher PI are preferred over
those with lower PI.
However, guiding principle remains maximization of NPV.
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INVESTMENT APPRAISAL : R ISK ANALYSIS
Objectives:
Discuss the relationship between risk and return
Evaluate investment projects in the conditions of
uncertainty
Discuss the techniques used to evaluate investment
projects under conditions of uncertainty
Discuss risk analysis in practice
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RISK IN INVESTMENT APPRAISAL
Risk: refers to a situation where the future is unclear and there ismore than one possible outcomes.
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TECHNIQUES FOR DEALING WITH RISK
The techniques for dealing with risk include:
a) the expected NPV rule;
b) the risk-adjusted discount rate approach;
c) sensitivity analysis
d) Simulation
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R ISK IN CAPITAL BUDGETING
Capital budgeting exercise is based on the futurecash flows that are estimated which are uncertain.
Capital budgeting exercise assumes the cash flows
to be certain and hence the decision made iscorrect.
Capital budgeting decision must incorporate the risk
emanating from the changes in the cash flows.
There are various ways to assess risk in capital
budgeting decisions.
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WAYS OF ESTIMATING RISK Sensitivity Analysis
Scenario Analysis Simulation
Decision Tree Analysis
CONVENTIONAL WAYS
BEP Analysis
Payback Period
Risk-adjusted Discount Rate
Certainty Equivalent
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SENSITIVITY ANALYSIS
Sensitivity analysis relates to finding out the critical
variables in the assumptions of cash flow.
Then find the change in NPV of the project with a
given change in the each of the critical variables.
More often than not the critical determinants of the
cash flows are
selling price and
proportions of variable cost.
Only one variable is assumed to change at a time.
15
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SCENARIO ANALYSIS
Scenario analysis is similar to sensitivity analysis in
approach.
It recognises that because of the interrelationships
several variables change simultaneously.
Each case classified as scenario, we find the change
in NPV for simultaneous change in several
variables.
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SCENARIO ANALYSIS
Each scenario is assigned a probability.
NPV is calculated for all scenarios and we arrive at
expected NPV,
its variance and standard deviations.
This forms the basis of decision making.
Risk assessment is not done on a single variable
basis.
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SIMULATION
Scenario analysis suffers from disadvantage thatsufficiently large scenarios may not be available
for reliable decision making
Simulation overcomes the problem of scenarioanalysis
It is possible to simulate large number of
scenarios and find out the NPVs under each so asto make statistical data dependable and relevant
for decision making.
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DECISION TREE ANALYSIS
Decision tree analysis handles the issues of risk in adifferent manner.
It recognises that business decisions are taken insequential manner where past governs the future
actions.
Decision tree is applied to the big decisions that canbe broken into a chain of smaller decisions, each of which faces some risk represented as chance event.
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DECISION TREE ANALYSIS
It is a systematic depiction of all the alternatives
available.
Alternatives are displayed in a structure that
resembles a tree, depicting the decision points
followed by chance events.
Starting from the rear in roll-back manner at each
decision point NPV is computed.
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DECISION TREE ANALYSIS
The decision at any point is based on the NPV and
branches with lower NPVs are dropped. As we proceed from backwards the size of the
decision tree truncates with clear decision made ateach decision point till we reach the first decision
point.
All decisions are made on pragmatic basis of maximising the NPV.
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CONVENTIONAL WAYS OF HANDLING R ISK
Conventional tools of assessing risk include
computation of break-even point: Lower the
break-even point to the safer is the project. and
finding the payback period: Faster the project
pays back the original investment safer it is.
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CONVENTIONAL WAYS OF HANDLING R ISK
Two other techniques that build in the risk in thedecision making process itself are
Risk-adjusted Discount Rate and
Certainty Equivalent Approach.
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R ISK ADJUSTED DISCOUNT R ATE
It is based on the premise that uncertain cash flows
need to offer a greater return to become attractiveenough for acceptance. Therefore more risky cash
flows must be assessed against a greater hurdle
rate.
This is easily achieved by increasing the discount
rate by adding a suitable premium commensurate
with the risk of the cash flows being evaluated.
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R ISK ADJUSTED DISCOUNT R ATE
Discount rate must be consistent with the quality of
cash flows. Though fundamentally sound, appealing
and convenient it suffers from limitation of
compounding the risk with time.
If discounted at higher rate the distant cash flows erode in
value extremely fast as compared to near cash flows.
Distant cash flows are more risky and must be valued less
but compounding decrease in value seems unwarranted.
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CERTAINTY EQUIVALENT
Certainty equivalent approach
replaces the risky cash flows with equivalent certain cash
flows, and then
discounting them at risk free rate.
The approach handles riskiness in the cash flow and
then matches them with an appropriate discount rate.
It eliminates compounding of risk with time.
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EXPECTED NET PRESENT VALUE
The expected NPV rule (ENPV):EV of a project is the mean value which will be obtained if
the project was repeated many times over
EV is not the most likely value of the project.
It is only the weighted average of all the possible
outcomes
EV is calculated by multiplying the each possible outcome
by its probability of occurrence and then add them up
EXAMPLE 1
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EXAMPLE 1
NIITM Ltd needs to purchase a machine to manufacture a newproduct. The choice lies between two machines (A and B). Each
machine has an estimated life of three years with no scrapvalue.
Machine A will cost Rs30,000 and machine B will cost Rs40,000,payable immediately in each case. The total variable cost of manufacture of each unit are Rs2 if made on machine A, but only
Rs1.00 if made on machine B. This is because machine B is moresophisticated and requires less labour to operate it.
The product will sell for Rs8 each.
The demand for the product is uncertain but is estimated at
2,000 units for each year, 3,000 units for each year or 5,000 unitsfor each year. (Note that whatever sales level actually occurs,that level will apply to each year.)
The sales manager has placed probabilities on the level of demand as follows:
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NIITM LTD: EXAMPLE 1
Annual demand Probability of occurrence
2000 0.2
3000 0.6
5000 0.2
Presume that both taxation and fixed costs will beunaffected by any decision made.
NIITM Ltd’s cost of capital is 6% p.a.
a) Calculate the NPV for each of the three activity levels foreach machine A and B and state your conclusion.
b) Calculate the expected NPV for each machine and state yourconclusion.
NIITM LTD: EXAMPLE 1
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NIITM LTD: EXAMPLE 1Machine A
2000 3000 5000
Demand Demand Demand
Rs. Rs. Rs.
Year 0 (30,000) (30,000) (30,000)
1 ( Rs.8- Rs.2)/unit 12,000 18,000 30,000
2 12,000 18,000 30,000
3 12,000 18,000 30,000
Discounted : Factor
Rs. Rs. Rs.
Year0 (1.00) (30,000) (30,000) (30,000)
1 (0.94) 11,280 16,920 28,200
2 (0 .89) 10,680 16,020 26,700
3 (0.84) 10,080 15,120 25,200
Rs.2,040 Rs.8,060 Rs.50,100
Expected value
= (0.2 x 2,040) + (0.6 x 18,060) + (0.2 x 50,100) = Rs.21,264
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SOLUTION 4.1Different cash flows of Machine B
Units 2000 3000 5000
demand demand demand
Rs. Rs. Rs.
Year 0 40,000 40,000 40,000
1(Rs.8-Rs.1)/unit 14,000 21,000 35,000
2 14,000 21,000 35,000
3 14,000 21,000 35,000
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SOLUTION 12000 3000 5000
Discounted : Factor Rs. Rs. Rs.
Year0 (1.00) (40,000) (40,000) (40,000)
1 (0.94) 13,160 19,740 32,900
2 (0.89) 12,460 18,690 31,1503 (0.84) 11,760 17,640 29,400
(Rs.2,620) Rs.16,070 Rs.53,450
Expected value
= (0.2 x 2,620) + (0.6 x 16,070) + (0.2 x 53,450)
= Rs.19,808
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THE RISK ADJUSTED DISCOUNT RATE
This approach to investment decision making process is an attempt to
deal with risk in a manner that takes account of the attitudes of the
decision maker.
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THE RISK ADJUSTED DISCOUNT RATE
Example 2 Before any investments are considered, the decision
maker should begin by determining an appropriate
discount rate for risk-free investments.
Suppose that the rate on such bonds issued by the
government is currently 7%. This figure should be
used as the base from which discount rates are
calculated for risky investments.
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THE RISK ADJUSTED DISCOUNT RATE Class of Risk Example of Risk Premium Discount rate
type of project
Very low Buying a bond 1% 8%
Low Improvement in
Existing factory 3% 10%
Medium Increased in existing
Output 5% 12%
High Launch a new product 8% 15%
Very high Research on areas
Related to current activity 11% 18%
The use of risk-adjusted discount rate approach to investment appraisal is indeed, acommon sense approach. However, it is subjective, particularly, the choice of the riskpremiums and the assignment of projects to particular risk classes is based onpersonal judgement.
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SENSITIVITY ANALYSIS
Sensitivity analysis: is a procedure that calculates the changes in the
net present value given a change in one of the
cash flow elements such as product price.
With sensitivity analysis each of the figures used
in the NPV is examined in turn, to determine
how variations from the estimated figures
impact on the NPV
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SENSITIVITY ANALYSIS
Sensitivity analysis helps managers to gain betterunderstanding of the nature and degree of risk
associated with a project;
because it reveals the margin of safety
associated with each key variable relating to a
particular project.
It is a form of break even analysis. The point at
which NPV is equal to zero is the break-evenpoint.
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SENSITIVITY ANALYSIS
Identifying the key or critical variablei.e. Those with short margin of safety.
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SENSITIVITY ANALYSIS
Example 3
S Ltd, which has a cost of capital of 12 per cent, is considering theinvestment of Rs.7m in an improved moulding machine project witha life of four years. The garden ornaments produced will retail atRs.9.20 each and cost Rs.6 each to make. It is expected that 800,000
ornaments will be sold each year. What are the key variables for theproject?
S 3
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SOLUTION 3
NPV of the project can be expressed in terms of theproject variables as follows:
NPV = ( (S -VC) X CPVF.) – I0
Where: S = Selling price per unitVC = Variable cost per unit
N = No of units sold per year
I0 = initial investment
CPVF. = Cumulative present value factor for four yearsat 12%
S
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SENSITIVITY ANALYSIS
Inserting the information given in the question and finding the
cumulative PV factor from annuity table, we have:
(9.20 - 6.00) X800,000X 3.037)-7,000,000 = 0
S
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SENSITIVITY ANALYSIS
a) Initial investment. Find the value of I0
that makes the NPV zero
I0 = (9.20 -6.00) x 800,000 x 3.037) = Rs.7,774,720
This is an increase of Rs.774,720 or 11.1 per cent on the planned
initial investment
S
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SENSITIVITY ANALYSIS
b) Sales price
S = 6.00 + (7,000,000 / (800,000 x 3.037) ) = Rs.8.88
This is a decrease of 32 paise or 3.5 per cent of planned sales price.
c) Variable cost
As a decrease of 32 paise in sales price makes the
NPV zero, an increase of 32 paise or 5.3 per cent in
variable cost will have the same effect.
E 1
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EXERCISE 1
c) Try to calculate the 32 paise or 5.3% by using thegeneral equation above
d). Sales volume
N = 700,000 / (9.20 - 6.00) x 3.037) = 720,283
This is a decrease of 79,717 units or 10 per cent on
the planned sales volume.
) D
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E) DISCOUNT RATE
CPVF = 7,000,000 / (9.20 –
6.00) X 800,000) = 2.734 Using the annuity tables 2.743 corresponds to the
discount rate of almost exactly 17 per cent. An
increase of 5 per cent in absolute terms or 42 per
cent on the current project discount rate.
S
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SENSITIVITY ANALYSIS- SUMMARY
Sensitivity analysis of the proposed investment by Swift Ltd
Variable Original est. B/E point Difference Dif. as % Sensitivity
Sales Volume 800,000 720,283 (79,717) 10% Low
Sales price Rs.9.20 Rs.8.88 (Rs.0.32) 3.5% High
Variable cost Rs.6.00 Rs.6.32 Rs.0.32. 5.3% High
Discount rate 12% 17% 5% 42% Very Low
Initial Inv Rs.7,000,000 Rs.7,774,720 Rs.774,720 11.1% Low
A D
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ADVANTAGES AND DISADVANTAGES
Advantages
Useful in directing the attention of managers to the most sensitive
variables of the project
Disadvantages
Does not formally quantify risk
Does not clearly provide any clear-cut decision rule
Recommended