Cap Budgeting 2 Risk Analysis

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



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



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.



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.



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.



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.



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.



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.



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.



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



RISK IN INVESTMENT APPRAISAL

Risk: refers to a situation where the future is unclear and there ismore than one possible outcomes.



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



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.



WAYS OF ESTIMATING RISK Sensitivity Analysis

Scenario Analysis Simulation

Decision Tree Analysis

CONVENTIONAL WAYS

BEP Analysis

Payback Period

Risk-adjusted Discount Rate

Certainty Equivalent



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



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.



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.



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.



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.




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.




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.



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.



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.



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.



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.



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.



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



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:



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



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



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



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



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.



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.



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.




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




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.




Identifying the key or critical variablei.e. Those with short margin of safety.




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



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




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




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




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



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



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



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



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

Cap Budgeting 2 Risk Analysis

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