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.