Risk When is more than one possibleoutcome 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
The break-even NPV •Initial investment A rise of £56,500 will leave NPV at zero. A percentage increase of: £56,500 ––––––––– ×100 = 7.06% £800,000 •Sales price The cash flow per unit (after costs), c, can fall to 28pence before break-even is reached: 800,000 = c × 1,000,000 × 2.855 800,000 c = ––––––––––––––––– = 0.2802 2.855 ×1,000,000
The break-even NPV (continued) •Material cost If the cash flow per unit can fall to 28 pence before break-evenis reached 2 pence can be added to the price of materials beforethe project produces a negative net present value. Material costcan rise by 5 per cent ((2 ÷ 40) ×100) before break-even isreached. •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£800,000 300,000 ×after discounting.800,000 annuity factor = 800,000Annuity 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. 18.5 - 15 × 100 = 23.3 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
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.