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What is risk

Risk is the term used when the degree of variation from an expected outcome can be quantified. This is normally done by using probabilities.


What is uncertainty

Uncertainty is the term used when the degree of variation from an expected outcome cannot be quantified.


What are the methods of dealing with risk and uncertainty

• Expected value
• Simulation
• Discounted payback
• Risk adjusted discount rate

Uncertainty= • Sensitivity analysis


What is expected value

Mean/average/ Mew/-is the weighted average of all the possible outcome.

The expected value can be calculated by multiplying the possible outcomes by their corresponding probabilities.

This will allow an expected NPV to be determined.

E(X) = Σpx
X= cash flow from each outcome


What are the advantages of expected value

▪ Deals with multiple outcomes (cause you can put them all into one average)

▪ Quantifies probabilities

▪ Simple & straight forward


What are the disadvantages of expected value

▪ By asking for a series of forecasts the whole forecasting procedure is complicated. Inaccurate forecasting is already a major weakness in project evaluation.

▪ The EV gives no indication of the dispersion of possible outcomes about the EV. The more widely spread out the possible results are, the more risky the investment is usually seen to be. The EV ignores this aspect of the probability distribution.

In ignoring risk, the EV technique also ignores the investor's attitude to risk. Some investors are more likely to take risks than others.

▪ Expected values will never occur ( It'll only be one of the possibilities not the probability ) BECAUSE it *is* an average (therefore only appropriate for when we make a decision time and time again (repetitively) e.g. making sandwiches every week and therefore over time you will be in the average position. As an average, EV is based on the idea that a project is repeated many times. So if it is for a one off decision, its not very appropriate.

▪ Assigning probabilities is highly subjective

▪ Expected values do not evaluate the range of possible NPV outcomes. It's a risk neutral approach therefore ignores the investors attitude to risk because it ignores the range of possible outcomes

Only appropriate for where we make decisions repetitively


What is sensitivity analysis?

It deals with uncertainty

Sensitivity analysis assesses the extent to which the net present value (NPV) of an investment project responds to changes in project variables.

Sensitivity analysis measures the amount of change in a variable that could arise before the decision to accept or reject the project changes. The decision to accept or reject the project changes if the NPV changes from being positive to being negative


How do you calculate sensitivity of any cash

Step 1 – Calculate the NPV of the project

Step 2 – Calculate the PV of the cash flows under consideration using the ANNUITY FACTOR at company's COST OF CAPITAL

Step 3 – Apply to the following formula:

Sensitivity= NPV of project ÷ PV of CF under consideration


How do you calculate sensitivity to a change in discount rate (cost of capital)

Step 1 – Calculate the NPV of the project
Step 2 – Calculate the IRR of the project
Step 3 – Apply to the following formula:

Sensitivity= (IRR-Original Discount rate)÷ Original Discount rate


What are the advantages of sensitivity analysis

▪ Simple to calculate and understand
▪ Identifies critical estimates
▪ Allows managers to make better judgements by providing them with information as to the critical estimates


What are the disadvantages of sensitivity analysis

▪ Assumes variables change independently of one another e.g. assumes selling price has no impact on sales volume

▪ Sensitivity does not examine/assess the probability/chance of a variable changing

While sensitivity analysis can indicate the critical variables of an investment project, however, sensitivity analysis does not give any indication of the probability of a change in any critical variable.

▪ It does not provide a decision. This is dependent upon the management attitude to risk


What is simulation?

This is an advanced form of sensitivity analysis. it looks at the impact of many variables changing at the same time. An example of this might be that a 1% reduction in the selling price might be expected to result in a 0.5% increase in the volume of sales.

It uses a mathematical model to produce a distribution of the possible outcomes from the project and allows their probabilities to be calculated:

- The NPV is then calculated based on a large number of simulations or what if’s?

- The range of NPV results is therefore plotted on a graph and the range of results is likely to follow the pattern of a normal distribution.

-The normal distribution can be used to assess the level of risk. If might, for example be possible to determine that there is a 5% chance of the NPV being negative.

It DOES NOT asses the likelihood of a variable changing as well as not directly pointing to the correct investment decision


What is discounted payback (or adjusted pay back)?

This is the same technique as payback except that the cash flows are discounted before the payback period is calculated. You can build risk into a discount rate

The discount rate used can be adjusted to reflect the risk involved. The shorter the discounted payback period the less risk is attached to a project and the higher the discount rate, the higher the risk that we can use to evaluate the project.

The discounted payback period has the same advantages and disadvantages as traditional payback except that it has an additional advantage of taking into account the time value of money.


What is risk adjusted discount rate?

how is the risk incorporated? mention the two ways

The discount rate used to determine the NPV of a project will reflect the time value of money. The discount rate can, however, be adjusted to reflect the risk of the project. If risk is higher the discount rate will be increased. A higher discount rate results in a lower NPV.

A risk adjusted discount rate can be found using the CAPM

Increase the discount rates by adding a risk premiym OR use the CAPM with a risk appropriate beta factor


When is expected value appropriate- give 3 reasons

* If there is a reasonable basis for making the forecasts and estimates
* the decision and risk are small in relation to the business
* the decision is a common one for the business i.e. repetative


What can expected value also be used to- give 3 reasons

* calculating the worst possible outcome and it's probability
* calculating the probability that the project will fail
* assessing the standard deviation of the outcomes


What are the advantages of simulation

▪ It includes all possible outcomes in the decision making process
▪ Easily understood techniques
▪ It has a wide variety of applications (inventory control, component replacement, corporate models, etc.).

▪ Works in complex situations which are difficult to model mathematically in other way


What are the disadvantages of simulation

▪ Models can become extremely complex
▪ Time and costs involved in their construction can be more than is gained from the improved decision
▪ Probability distributions may be difficult to formulate


Standard deviation is a measure of?

Standard deviation is a measure of the variability/dispersal of a distribution (NPV) around it's mean/average/expected value


When considering standard deviation as a statistical measure,

the tighter the distritbution..?

the tighter the distribution, the lower the standard deviation


What is the weighted average of all the possible outcomes in a standard deviation

It is the expected value that is the weighted average of all the possible outcome

NOT the standard deviation,


what is sensitivity of volume?

Look at contribution because it affects both sales, rev and vc by the same proportions. so we need to look at contribution to look at volume


what is expected value in comparison to standard deviation and the disadvantage in comparison to SD

The expected value of the NPV, for example, is a mean or average value of a number of possible NPVs, while standard deviation is a measure of dispersal of possible NPVs about the expected (mean) NPV. In reality, many investment projects cannot be repeated and so only one of the possible outcomes will actually occur. The expected (mean) value will not actually occur, causing difficulties in applying and interpreting the NPV decision rule when using probability analysis.


explain the use of probability analysis (using probability) in incorporating risk into investment appraisal.

probability analysis can be used to
- calculate the values of possible outcomes and their probability distribution,

-the value of the worst possible outcome and its probability,

-the probability that an investment will generate a positive NPV,

-the standard deviation of the possible outcomes and the expected value (mean value) of the NPV.

Probability analysis in investment appraisal in the first instance involves calcualtion of an expected net present value where a weighted average of the possible outcomes is used.

Probability analysis also allows us to consider risk by calculating the NPV for each possible outcome. This then allows us to: condsidering the worst case possible outcome and its probability.


What is the another disadvantage of Expected value with regards to assessing and calculating

another difficulty with probability analysis is the question of how the probabilities of possible outcomes are assessed and calculated. One method of determining probabilities is by considering and analysing the outcomes of similar investment projects from the past. However, this approach relies on the weak assumption that the past is an acceptable guide to the future. Assessing probabilities this way is also likely to be a very subjective process


what is the general formula for the sensitivity analysis

Sensitivity= NPV of project ÷ PV of CF under consideration


It assesses the likelihood of a variable changing

is this true or false of simulation



It points directly to the correct investment decision

is this true or false of simulation