The document discusses risk in investment projects. It defines risk as the possibility of more than one outcome for an investment. It then discusses various ways to incorporate risk into a project appraisal, including sensitivity analysis, scenario analysis, and adjusting the discount rate used. Sensitivity analysis involves changing individual variables to see the impact on NPV, while scenario analysis considers the joint impact of changes to multiple variables simultaneously.

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

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.  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. Objective Probabilities

5. Frequency distribution of
supermarket profitability

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

8. Acmarts plc (continued)
•Required rate of return on a project of this risk
class is 15 per cent
•Expected net present value:

13. Sensitivity graph for Marts

14. 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 28
pence before break-even is reached:
800,000 = c × 1,000,000 × 2.855
800,000
c = ––––––––––––––––– = 0.2802
2.855 ×1,000,000

15. 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
£800,000 300,000 ×after discounting.800,000
annuity factor =
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.
18.5 - 15
× 100 = 23.3
15

16. 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

17. Scenario analysis: Acmart
Acmart plc:

19. Acmart plc

21. 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.

23. 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.