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# Npvrisk

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### Npvrisk

1. 1. Risk When is more than one possibleoutcome for an investment there is risk.
2. 2. 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
3. 3.  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
4. 4. Objective Probabilities
5. 5. Frequency distribution of supermarket profitability
6. 6. Sensitivity analysis Acmart plc•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
7. 7. Acmarts plc (continued) •Required rate of return on a project of this riskclass is 15 per cent •Expected net present value:
8. 8. Sensitivity graph for Marts
9. 9. 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
10. 10. 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
11. 11. 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
12. 12. Scenario analysis: Acmart Acmart plc:
13. 13. Acmart plc
14. 14. 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.
15. 15. 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.