3. FM - Risk and Decision Making Flashcards
What are the problems that investment appraisals face?
- All decisions are based on forecasts
- All forecasts are subject to uncertainty
- This uncertainty needs to be reflected in the financial evaluation
What is the difference between risk and uncertainty?
Risk = quantifiable, where probabilities are known (i.e. roulette wheel) Uncertainty = Unquantifiable -- outcomes can't be mathematically predicted (i.e. most businessd decisions)
What do we assume about the risk levels of investors in FM?
Assume that investors are rational and risk averse
Even risk averse investors will have diff attitudes towards risk. Some will need greater levels of compensation than others for the same level of risk
What does it mean to be risk averse?
- Investors demand an increase in return for the increase in risk
- If 2 projects offers the same expected return, the one with the lower risk is preferred
Even risk averse investors will have diff attitudes towards risk. Some will need greater levels of compensation than others for the same level of risk
What are the practical ways to incorporate uncertainty?
Many practical ways to address uncertainty
- Minimum payback periods
- Prudent estimates of cash flows
- Assessment of best and worst outcomes
- Higher discount rates
What is EV?
Expected value
Used when there is a number of possible outcomes for a decision and probabilities can be assigned to each, then EV is calculated
This value can then be used for the purposes of investment appraisal
How do you calculate EV?
EV = sum of px
where X = value of the outcome
p = probability of the outcome
What does EV show (and not show)?
DOESN’T show the most likely result - may not even be a possible result
Shows the long run average outcome
TYU1: Cash flows from a new restaurant venture may depend on whether a competitor decides to open up in the same area. The following estimates have been made:
- Chance that the competitor opens up 30%
- Revenue if competitor opens up £4k
- Revenue if competitor does not open up £10k
What is the expected value of the revenue?
Competitor opens up - yes probability 0.3
Revenue £4k
EV = 0.3 x £4k = £1,200
Competitor opens up - No
Probability 0.7
Revenue £10k
EV = £7k
Therefore total EV = £1,200 + £7k
= £8,200
What are the limitations of expected values?
- Discrete outcomes
- Subjective probabilities
- Ignores risk
- Not a possible outcome, so less applicable to one off projects
What question does sensitivity analysis answer?
‘What % change in a particular estimate would lead to us to change the decision about the project?’
What is sensitivity?
It is the %age change in an estimate that gives NPV of nil
How do you calculate sensitivity?
2 methods depending on the time of estimate
- Sensitiviity to factors affecting cash flows e.g. price, volume, tax rate
= NPV of whole project / NPV of cash flows affected by the change
- Sensitivity to other factors
Sensitivity to discount rate = difference between the cost of capital and the IRR
Sensitivity to product life= discounted payback
How do you calculate sensitivity when it is factors affecting cash flows? and give some examples of what these factors could be
e.g. price, volume, tax rate
= NPV of whole project / NPV of cash flows affected by the change
How do you calculate sensitivity when it is sensitivity to the discount rate?
- Difference between the cost of capital and the IRR
How do you calculate sensitivity when it is sensitivity to project life?
Calculate discounted payback
What must be done when tax is included in sensitivity analysis?
The principle is the same, but you must include the tax effect, therefore the sensitivity calc becomes
= NPV of whole project / NPV of the cash flows affected net of tax
What are the limitations of sensitivity analysis?
- Assumes variables change independently of each other
- Does not assess the likelihood of a variable changing
- Does not identify a correct decision
What is the difference between sensitivity and simulation?
Sensitivity considers the effect of changing one variable at a time
Simulation improves on this by looking at the impact of many variables changing at the same time
How does simulation work and what are the steps for calculating it?
It uses a mathematical model to product a distribution of the possible outcomes from the project. The probability of diff outcomes can then be calculated.
3 stages
- Specify major variables and their probabilities
- Specify the relationships between the variables
- Simulate the environment
Results will usually be a probability distribution
What is the benefit of diversification?
It can reduce (BUT NOT ELIMINATE) risk
What is the effect of diversification?
If an inv holds a single share, then the return will fluctuate over time
If adds a second, it will also fluctuate but not in the same way as the first
So the average return achieved will be more stable as the are moving independently
How much risk can generally be removed?
As long as inv return profiles differ by at lease some degree, then risk will be reduced
- Initial inv diversification will bring a substantial risk reduction, but as additional inv are added this difference will reduce
i. e. will remove all the unsystematic risk, but can’t remove the systematic risk (market risk)
What type of risk can and can’t diversification reduce and WHY?
Can reduce Unsystematic risk (unique risk) - as these impact each firm differently depending on their circs
Can’t reduce systematic risk (market risk) - as these affect all companies in the same way (but to varying degrees)
Give an example of specific (non-systematic risk)
Company/ industry specific factors
Give an example of systematic risk?
Market wide factors such as the state of the economy
What are the implications of diversification and the portfolio effect?
Rational risk averse investors would wish to reduce the risk they faced to a minimum, so would arrange their portfolio to max risk reduction.
Done by holding at least 15-20 different investments. Tends to be true for most SH of listed companies.
What are the consequences of risk averse investors diversifying as much as possible for risk reduction?
As inv in listed companies are already fully diversified, they don’t suffer specific risk. Therefore, when estimating their required return, they only need to be compensated for systematic risk
When directors of listed companies are making strategic decisions, they shouldn’t try and reduce risk for their SH by diversification. This is because SH are already diversified and therefore cannot reduce their risk any further.
What does CAPM stand for?
Capital asset pricing model
What does CAPM do
It is a way of estimate the rate of return that a full diversified equity SH would require from a particular investment
Done by considering the level of systematic risk and comparing it to the average
What is the formula for CAPM?
Rj = Rf + B(Rm - Rf)
Rj = required return from an inv
Rf = risk free rate (assumed to be treasury bills
Rm = average return on the market
(Rm - Rf) = equity risk premium
B = systematic risk of the investment compared to the market (and therefore the amount of premium needed)
When is CAPM most commonly used?
Used to find the required rate from a project in situations where the project has a different risk profile from the company’s current business operations
How do investors use CAPM?
They will review results of CAPM to determine which shares to invest into.
if returns from a company are currently higher tan the CAPM return, then inv will be attracted to these shares
This is said to have +ve alpha value, where alpha value is calc as difference between current return and CAPM return
Note: likely to be ST issue, as additional attraction causes the share price to increase and hence returns will be more reflective of CAPM return.
TYU5: G plc is an all equity company. Current average market rate of return being paid on risky investments in 12%, compared to 5% on treasury bills.
G plc has a beta of 1.2
What is the return that would be required on projects by G plc
Use CAPM: Rj = Rf + B(Rm - Rf)
Rj = 3% + 1.2 x (12% - 5%)
TYU5: G plc is an all equity company. Current average market rate of return being paid on risky investments in 12%, compared to 5% on treasury bills.
G plc has a beta of 1.2
What is the return that would be required on projects by G plc
Use CAPM: Rj = Rf + B(Rm - Rf)
Rj = 5% + 1.2 x (12% - 5%)
= 13.4%
What are the pros and cons of CAPM?
Pro
- Used widely due to its simplicity
Cons
- Estimating Rm - in practice this is usually done using historic rather than expected future returns
- Estimating Rf : Gilts are not risk free, return on gilts will vary with the term of the bond
- Calculation of beta: beta is cal’ed using statistical analysis of the diff between market retune and return of particular share/industry. lots of research shows this is too simplistic to estimate risk, and that risk premiums are made up of multiple factors rather than 1 single market factor
Beta takes account of systematic risk ONLY, therefore need to assume that SH are FULLY DIVERSIFIED
What is the main problem with beta?
- Calculation of beta: beta is cal’ed using statistical analysis of the diff between market retune and return of particular share/industry. lots of research shows this is too simplistic to estimate risk, and that risk premiums are made up of multiple factors rather than 1 single market factor
What are the alternative to calculating CAPM?
Arbitrage Pricing Theory (APT)
Bond yield plus premium approach
Dividend valuation model
Describe the Abitrage Pricing theory (APT)
Similar concept to CAPM as it adds premium to risk free rate, but rather than being a single premium, it dividends the premium down into lots of bits.
i.e. return = risk free rate + (beta 1 x premium for factor 1) + (beta 2 x premium for factor 2) etc.
Problem is then deciding which bits to use!
What is the main problem with APT?
As it adds lots of premiums together
i.e. return = risk free rate + (beta 1 x premium for factor 1) + (beta 2 x premium for factor 2) etc.
So you have to decide which factors affect the risk premiums
Diff authors have suggested different things, such as inflation, level of industrial output, interest rates and the size of the company
What is the bond yield plus premium approach?
Rather than using the risk free rate as the starting point like CAPM, it uses the rate of interest the company is able to borrow as the starting point
Logic is tat the risk of the company will be affected by the borrowing rate. Then a fixed premium is added to reflect the fact that equity is more risk than debt
i.e. return = companies borrowing rate + fixed premium
What is the bond yield plus premium approach?
Rather than using the risk free rate as the starting point like CAPM, it uses the rate of interest the company is able to borrow as the starting point
Logic is tat the risk of the company will be affected by the borrowing rate. Then a fixed premium is added to reflect the fact that equity is more risk than debt
i.e. return = companies borrowing rate + fixed premium
Describe the dividend valuation model
- Rather than trying to estimate from scratch what return should be achieved on a share due to its risk, this method takes a completely diff approach
By looking at the predicted future dividends on a share compared to its share price, we can measure what is actually being achieved.
If we assume that the market is perfect efficient, then this will also be the return that should be achieved to compensate the risk
