Risk

When is more than one possible outcome for an investment there is risk.

Risk and project appraisal

•Presenting a more realistic and rounded view of a project’s prospects by incorporating risk in an

appraisal

•Presenting a sensitivity graph and discuss break-even NPV

•Undertake scenario analysis

•Adjusting for risk by varying the discount rate

Three types of expectations about the future: 1 Certainty 2 Risk 3. Uncertainty

Objective probabilities Estimated from historical data E.g. a supermarket chain has 100 existing supermarkets what

is the probability of a new one being profitable.Subjective

Objective Probabilities

Frequency distribution of supermarket profitability

Sensitivity analysis

•Acmart plc has developed a new product line called Marts

•Likely demand for Marts is 1,000,000 per year, at a price of £1, for the four-year life of the project

Acmart plc

Acmarts plc (continued)

•Required rate of return on a project of this risk class is 15 per cent

•Expected net present value:

Sensitivity graph for Marts

The break-even NPV

•Initial investment

A rise of £56,500 will leave NPV at zero. A percentage increase of:

•Sales price The cash flow per unit (after costs), c, can fall to 28 pence before break-even is reached:

800,000 c = ––––––––––––––––– = 0.2802 2.855 ×1,000,000

800,000 = c × 1,000,000 × 2.855

£56,500 ––––––––– ×100 = 7.06% £800,000

The break-even NPV (continued)•Material cost

If the cash flow per unit can fall to 28 pence before break-even is reached 2 pence can be added to the price of materials before the project produces a negative net present value. Material cost can rise by 5 per cent ((2 ÷ 40) ×100) before break-even is reached.

•Discount rate We need to calculate the annuity factor that will lead to the four

annual inflows of £300,000 equalling the initial outflow of £800,000 after discounting.300,000 × annuity factor = 800,000

800,000 Annuity factor (four-year annuity) = ––––––– = 2.667

300,000

The interest rate corresponding to a four-year annuity factor of 2.667 is approximately 18.5 per cent. This is a percentage rise of 23.3 per cent.

× 100 = 23.318.5 - 15

15

Advantages and disadvantages of using sensitivity analysis

•Advantages

– Information for decision making: at least you know what the margins for error are.

– You know which factors the success of the project is most sensitive to.

– To make contingency plans: if you know the value of a project is sensitive to a particular input you can plan make alternative arrangements if the price of that input increases.

•Drawbacks

– The absence of any formal assignment of probabilities to the variations of the parameters

– Each variable is changed in isolation while all other factors remain constant

Scenario analysis: Acmart

Acmart plc:

Acmart plc

Adjusting for risk through the discount rate

Assume investors are risk averse Investors demand higher rates of return to take

on additional risk. →The cost of capital is higher for risky projects.

How do we estimate the risk premium?

We need to know how investors price risk in the market.

As a first step we need to understand how investors manage the risk of their investments.