ACCA paper f9 financial management study materials F9FM session07 d08

1.2 Sources of risk in projects The major risks to the success of an investment project will be the variability of the future cash flows.. The cash flows, probabilities, or cost of capi

OVERVIEW

Objective

Ü To appraise investment projects where the outcome is not certain

RISK AND UNCERTAINTY

STATISTICAL MEASURES

SENSITIVITY

ANALYSIS

Ü Definition

Ü Method

Ü Advantages

Ü Limitations

SIMULATION

Ü Use

Ü Stages

Ü Advantages

Ü Limitations

Ü Expected values

Ü Standard deviation

Ü Definitions

Ü Sources of risk REDUCTION OF RISK

1 RISK AND UNCERTAINTY

1.1 Definition

1.1.1 Risk

A condition in which several possible outcomes exist, the probabilities of

which can be quantified from historical data

1.1.2 Uncertainty

The inability to predict possible outcomes due to a lack of historical data

being available for quantification

1.2 Sources of risk in projects

The major risks to the success of an investment project will be the variability of the future cash flows This could be the variability of income streams or the variability of cost cash flows or a combination of both

Definition

The analysis of changes made to significant variables in order to determine

their effect on a planned course of action

The cash flows, probabilities, or cost of capital are varied until the decision changes, i.e the NPV becomes zero This will show the sensitivity of the decision to changes in those

elements

Therefore the estimation of IRR is an example if sensitivity analysis, in this case on the cost

of capital

Sensitivity analysis can also be referred to as “what if?” analysis

2.1 Method

Step 1 Calculate the NPV of the project on the basis of best estimates

Step 2 For each element of the decision (cash flows, cost of capital)

calculate the change necessary for the NPV to fall to zero

The sensitivity can be expressed as a % change

For an individual cash flow in the computation

Sensitivity = 100%

considered flow

of PV

Commentary

For change in sales volume, the factor to consider is contribution This may involve

combining a number of flows

Example 1

Williams has just set up a company, JPR Manufacturing Ltd, and estimates its

cost of capital to be 15% His first project involves investing in $150,000 of

equipment with a life of 15 years and a final scrap value of $15,000

The equipment will be used to produce 15,000 deluxe pairs of rugby boots per

annum generating a contribution of $2.75 per pair He estimates that annual

fixed costs will be $15,000 per annum

Required:

(a) Determine, on the basis of the above figures, whether the project is

worthwhile

(b) Calculate what percentage changes in the factors would cause your

decision in (a) change

(i) initial investment

(ii) volume

(iii) fixed costs

(iv) scrap value

(v) cost of capital

Comment on your results

Ignore tax

Solution

(a) Time Cash flow DF @ 15% PV

0

1 − 15

1 − 15

15

Initial cost Contribution Fixed costs Scrap value

_

_

(b) The sensitivity of the decision in (a) can be calculated by expressing the

NPV as a percentage of the various factors

(i) Initial investment

Sensitivity =

(ii) Volume

The PV figure of contribution is directly proportional to volume

Sensitivity =

(iii) Fixed costs

Sensitivity =

(iv) Scrap value

Sensitivity =

(v) Sensitivity to cost of capital

This can be found by calculating the project’s IRR:

Year Cash flow factor Present value

0

1-15

15

(150,000) 26,250 15,000

1

_

IRR = r

NPV NPV

NPV

1 2 2 1

−

=

2.2 Advantages of sensitivity analysis

X It gives an idea of how sensitive the project is to changes in any of the original estimates

X It directs management attention to checking the quality of data for the most sensitive variables

X It identifies the Critical Success Factors for the project and directs project management

X It can be easily adapted for use in spreadsheet packages

2.3 Limitations

W Although it can be adapted to deal with multi-variable changes, sensitivity is normally only used to examine what happens when one variable changes and others remain constant

W Assumes data for all other variables is accurate

W Without a computer it can be time-consuming

W Probability of changes is not considered.

3.1 Use of simulation

Simulation is a technique which allows more than one variable to change at the same time One example of simulation is the “Monte Carlo” method Calculations will not be required

in the exam, an awareness of the stages is sufficient

3.2 Stages in a Monte Carlo simulation

(1) Specify the major variables

(2) Specify the relationship between the variables

(3) Attach probability distributions to each variable and assign random numbers to reflect the distribution

(4) Simulate the environment by generating random numbers

(5) Record the outcome of each simulation

(6) Repeat simulation many times to obtain a probability distribution of the likely outcomes

3.3 Advantages

X It gives more information about the possible outcomes and their relative probabilities

X It is useful for problems which cannot be solved analytically

3.4 Limitations

W It is not a technique for making a decision, only for obtaining more information about the possible outcomes

W It can be very time-consuming without a computer

W It could prove expensive in designing and running the simulation, even on a computer

W Simulations are only as good as the probabilities, assumptions and estimates made

4.1 Expected values

The quantitative result of weighting uncertain events by the probability of their occurrence

4.1.1 Calculation

Expected value = weighted arithmetic mean of possible outcomes

=∑x p(x)

Where x = value of an outcome, p(x) = probability of that outcome , ∑ = sum

Example 2

State of market Diminishing Static Expanding

Figures represent the net present value of projects under each market state in

$m

Required:

Determine which is the best project based on expected values

Solution

Project 1 Expected value =

Project 2 Expected value =

Project 3 Expected value =

The best project based on expected values is

4.1.2 Advantages

X It reduces the information to one number for each choice

X The idea of an average is readily understood

4.1.3 Limitations

W The probabilities of the different possible outcomes may be difficult to estimate

W The average may not correspond to any of the possible outcomes

W Unless the same decision has to be made many times, the average will not be achieved;

it is therefore not a valid way of making a decision in “one-off” situations

W The average gives no indication of the spread of possible results, i.e it ignores risk

4.2 Standard deviation

A measure of variation of numerical values from a mean value

A measure of spread i.e it indicates the likely level of variation from an expected value

Exam questions are more likely to provide standard deviation for interpretation, rather than

to require its calculation

4.2.1 Calculation

σ = standard deviation = ∑(x−x)2 prob( x)

Prob (x) = probability of each observation

Note that variance = σ2

Example 3

Using the information from Example 2, calculate the standard deviation for

each project

Solution

Project 1

Project 2

Project 3

4.2.2 Advantages

X It gives an idea of the spread of possible results around the average

X It can be used in further mathematical analysis, in particularly using Normal

Distributions.”

4.2.3 Limitations

W The calculation of standard deviation can be difficult

W The exact meaning is not widely understood by non-financial managers

Ways of reducing project risk:

Ü Setting a maximum payback period

Ü Use of a higher discount rate − therefore reducing the influence of distant cash flows

Ü Select projects with a combination of low standard deviation and acceptable average predicted outcome

Ü More effort directed to Critical Success Factors indicated by sensitivity analysis

Key points

ÐExam calculations on project risk are likely to focus on sensitivity analysis

i.e finding the value of key variables at which NPV = 0

ÐAdjusting the discount rate to reflect a project’s risk is dealt with later in

the session on the Capital Asset Pricing Model (CAPM)

FOCUS

You should now be able to:

Ü distinguish between risk and uncertainty;

Ü evaluate the sensitivity of project NPV to changes in key variables;

Ü explain the role of simulation in generating a probability distribution for the NPV of a project;

Ü apply the probability approach to calculating expected NPV of a project and the

associated standard deviation

EXAMPLE SOLUTIONS

Solution 1 — Sensitivity analysis

(a) Time Cash flow DF @ 15% PV

0

1 − 15

1 − 15

15

Initial cost Contribution Fixed costs Scrap value

(150,000) 41,250 (15,000) 15,000

1 5.847 5.847 0.123

(150,000) 241,189 (87,705) 1,845 _

5,329 _

The project is worthwhile as NPV is positive

(b) The sensitivity of the decision in (a) can be calculated by expressing

the NPV as a percentage of the various factors

(i) Initial investment

If the initial investment rises by more than $5,329, the project would be

rejected

Sensitivity =

000 , 150

329 ,

5 × 100 = 3.6%

(ii) Volume

The PV figure of contribution $241,189 is directly proportional to

volume If this PV is reduced by more than $5,329, the project would

be rejected

Sensitivity =

189 , 241

329 ,

5 × 100 = 2.2%

(iii) Fixed costs

Sensitivity =

705 , 87

329 ,

5 × 100 = 6.1%

(iv) Scrap value

Sensitivity =

845 , 1

329 ,

5 × 100 = 289%

From the above calculations the decision to accept the project is

extremely sensitive to most of the figures given in the question The

project will be rejected in the event of small rises in the initial

investment or fixed cost figures or falls in contribution or volume It

could be seen, for instance, that the project just breaks even if fixed

costs become $15,000 × 1.06 = $15,900

The scrap value is relatively irrelevant to the investment decision – we

would have to pay to have the plant taken away before the project

would be rejected

(v) Sensitivity to cost of capital

This can be found by calculating the project’s IRR, which is probably

only marginally above 15%

Year Cash flow 16% factor Present value

0

1-15

15

(150,000) 26,250 15,000

1 5.575 0.108

(150,000) 146,344 1,620

(2,036) _

IRR = r

2 1

NPV NPV

−

2,036 + 5,329

= 15.7%

If the cost of capital rises from 15% to more than 15.7% the project

would be rejected

Solution 2 — Expected values

Project 1 Expected value = 100 × 0.4 + 200 × 0.3 + 1,000 × 0.3 = 400

Project 2 Expected value = 0 × 0.4 + 500 × 0.3 + 600 × 0.3 = 330

Project 3 Expected value = 180 × 0.4 + 190 × 0.3 + 200 × 0.3 = 189

Therefore, based on expected values, Project 1 should be adopted

Solution 3 — Standard deviation

Project 1 (100−400)2×0.4+(200−400)2×0.3+(1,000−400)2×3

= 156,000 = 395 Project 2 (0−330)2×0.4+(500−330)2×0.3+(600−330)2×0.2

= 74,100 = 272

Project 3 (180−189)2×0.4+(190−189)2×0.3+(200−189)2 ×0.3

= 69 = 8.3