Risk Analysis and Decision Making in Project Evaluation

The effect of risk on the value of a project is included in the required rate of return.

However, many assumptions are made in forecasting cash flows.

How do we factor in variability of these forecasts?

• –  sensitivity analysis

• –  Scenario analysis

• –  break-even analysis

• –  simulation techniques

• –  decision tree analysis

  Sensitivity analysis
  Analyses effect of changing one or more input variables (one variable at a time) to observe

  the effects on the results (similar to ‘what if we changed ...?’).

  Steps:

  Benefits

• –  It shows which areas may require further analysis to resolve estimation doubt. Drawbacks

• –  Judgment is required. e.g. What is a ‘pessimistic’ estimate?

• –  This particular approach treats each variable in isolation.

  Note: Simulation is just another form of sensitivity analysis which considers the effect of combinations of possible events on the project’s NPV (see later).

1. Make pessimistic, optimistic and expected estimates for each variable.

2. For each variable, calculate NPV using the optimistic estimate of this variable

   while keeping other variables at their expected values. Repeat this calculation

   using the pessimistic estimate of this variable.

3. Calculate difference between pessimistic and optimistic NPV for each variable.

– This type of analysis provides us with an indication of the ‘reliability’ of the initial expected NPV calculation and our ‘decision confidence’.

Example

Consider a three-year project which requires an initial cash outlay of $40,000, has an opportunity cost of capital of 10% p.a. and has had the following variable estimates:

Solution Annual profit=

Selling price:

Variable costs:

Sales volume:

With respect to which variable is the project’s success most sensitive to?

Variable Selling price Variable costs Sales volume

Range

$49,737 $29,843

$9,948

What actions could be taken now that we know this information?

• Gathering more information on the selling price and variable costs.

• The project is still acceptable based on pessimistic values of variable costs and sale

  volume.

§ A variation on sensitivity analysis is scenario analysis. – Allow the interrelationships between variables.

• For example, the following scenario:
– The next few years each have heavy cold seasons, and sales exceed expectations,

but labor costs skyrocket.

Break-even analysis Break-even analysis involves:

• –  measuring the sensitivity of the profitability of a project to variation in one variable (e.g. sales), as similar to the sensitivity analysis.

• –  calculating value of the input variable (e.g. sales), at which the present values of the project’s cash inflows and outflows are equal, such that the project’s net present value is zero. Break-even is where NPV =0.

• Note: It involves a similar concept to ‘accounting profit’ break-even analysis, but here, cash flows are the focus, not accrual accounting.

– for example, predicting minimum sales required for the project to be profitable—the break-even point.

Example – cont.
Capex is $500,000 and cost of capital is 10%

Simulation Analysis
Simulation allows us to consider the effect of changing more than one variable at a time.

3 Steps:

§ Identify relevant variables and specify the probability distribution of each variable. § Specify any inter-relationships between the variables.

§ Use a computer to:
(a)Randomly select values for each variable from their specified probability distribution. (b)Calculate a NPV given those values selected.
(c)Repeat steps (a) and (b) many times until a probability distribution for NPV is generated.

Distribution of profits

Probability

-$60,000 $45,000 $150,000 $255,000 $360,000 NPV ($)

Limitations

• Only as good as the input data and the specified inter-relationships.

• Does not provide a definitive answer to accept or reject.

  Decision-tree analysis
  o Used to evaluate a sequence of decisions relating to an investment in a risky project.

  o The decision-tree approach takes into account the probability of various events occurring and the effect of those events on the expected NPV of a project.

  o Useful when a limited number of contingencies are possible at different stages, otherwise it becomes too complex.

Example

Solar Electronics Corporation (SEC) has developed the technology for a solar-powered jet engine.

The marketing department propose that SEC develop some prototypes and conduct marketing test of the engine (The first decision). This test will cost $100 million and there is a 75% chance that market testing will prove successful.

After completion of the marketing tests, SEC will decide whether to engage in full-scale production, necessitating the investment of $1,500 million (The second decision).
If the solar-powered jet engine can work well (pass the market test), the full-scale production can generate a positive NPV of $1,518 million at year 1 (with annual CF of $900 million from year 2 to year 6). However, if the solar-powered jet engine cannot pass the market test, the full- scale production can generate a negative NPV of -$3,611 million. Cost of capital is 15%.

Should the firm test the market for solar-powered jet engine?

If the test is successful, NPV1 = $1,518 million If the test is not successful, NPV1 = 0