1. Risk and Return

2. Risk and Return Various Ways to Discount Cash Flows - WACC - APV - FTE
We shall see these in action shortly
But First
What is the WACC

3. Risk and Return WACC, A Simple Example
A Company wishes to finance a project with 70 % Equity and 30 %Debt
Total needed GBP 50,000,000
Tax rate 30 %
Cost of Equity 12 %
Cost of Debt 7 %

4. Risk and Return WACC, A Simple ExampleSo
WACC =
Equity bit = 35,000,000 x 12 =
50,000,000
Debt bit = 15,000,000 x (1 - .3) =
WACC =

5. Risk and Return But, A Few Quick Questions
How do we get the cost of debt?
Easy, ask a bank
(We will return to the 1-t issue)
How do we get the cost of equity?
A bit trickier

6. Risk and Return Cost of Equity
Rational ‘Economic’ Person
Risk is not bad but greater risk, greater expected return
Risk Measurements
Expected return
Variance
Standard deviation

7. Risk and Return Cost of Equity
Returns Deviation from Mean Deviation Squared (9)
(8)
(6) (18)
(2)
(8)
Mean Var = 1068/n-1 SD

8. Risk and Return Cost of Equity
Assuming a normal distribution
Range Probability Downside risk
Within
+ / - 1 SD
+ / - 2 SD
+ / - 3 SD
Share has Av return of 14%
SD of 4 %
Need min return of 8%, with only 2.5% chance of less
Do we invest?
No as 2.5 = 2 SD = 8 % and 14% -8% = 6%

9. Risk and Return Cost of Equity
Risk ‘changes’ in a portfolio( = 2 or more assets)
Expected Return of a portfolio =
Weighted average of the assets in a portfolio
E.g. Asset A, ER = 8%, = 30% of portfolio
Asset B, ER = 12% = 70% of portfolio
Portfolio ER = 8 x x .7 = 10.8%

10. Risk and Return Cost of Equity
But what about the risk of a portfolio?
What happens when we put assets together that react differently to overall market movements?

11. Variance of a Portfolio
But what is the variance? ER
Umbrellas ER ER
Cider

12. Risk and Return Cost of Equity
We may have a range of portfolios of differing expected returns and risks
There is a risk free asset, Government stocks (Gilts - Bills and Bonds)
Capital Market line
Market Portfolio

14. Risk and Return Cost of Equity
But how to ‘price’ an individual asset?
How does the risk of the individual asset vary from that of the Market Portfolio?
Risk split into
Market risk = systematic = non-diversifiable
risk
Specific risk = unsystematic = diversifiable risk

15. Risk and Return Cost of Equity
Since diversifiable risk may be diversified away just left to focus on
Market Risk
Some shares riskier than others
Measure of relative risk is
Beta
Beta = Covariance of the Market and Asset
Variance of the Market

16. Variance of a Portfolio
The riskiness of an asset held in a portfolio is different from that of an asset held on its own
Variance can be found using the following formula
Var Rp = w2Var(RA) + 2w(1-w)Cov(RARB)+(1-w)2VarRB
Cov stands for Covariance
Covariance is a measure of how random variables, A & B move away from their means at the same time

17. Risk and Return Cost of Equity
Required return (or expected return)
ERA = RF + (ERM – RF)B
Example
Company A Beta of 1.4, Risk Free = 5 %
Expected return on market = 10 %
ERA = 5 + (10 -5) 1.4 = 12

18. CAPM
Security Market Line
Rm Market Portfolio Rf
Beta

19. Risk and Return Cost of Equity
Other models
Gordon Dividend Growth
ER = D1 + g P0
E.g. Share price = 275 pence
Current Div = 8.25 pence
Historic growth = 9 %
= 12.27
275
Arbitrage Pricing Theory. Not going to bother but …

20. Fama-French 3 Factor Model
To estimate the expected returns under APT
Expected risk premium, r - rf = b1 (rfactor1-rf) + b2(r factor2 -rf) +b3 (r factor3 -rf) etc etc
So all we have to do is
Step 1. Identify a reasonably short list of macroeconomic factors that could affect stock returns
Step 2. Estimate the expected risk premium on each of these factors
Step 3. Measure the sensitivity of each stock to the factors

21. Fama-French 3 Factor Model
Above average returns on
Small sized companies and
High book to market value
R – rf = bmarket(rmarket factor)+bsize(rsize factor) +bbook too market(rbook to market factor)

22. Fama-French 3 Factor Model
Having worked out from market data that
Market premium = 7%
Size premium = 3.7%
Book to market premium = 5.2%
Then for
E.g. computers bmkt =1.67, bsz = .39 and bmkt to bk = -1.07
ER = (1.67x7)+(.39 x 3.7) + (-1.07x5.2)=
= Rf

23. Risk and Return Cost of Equity
Any problems?
Market returns/Market risk premium
It varies from
- market to market
- period to period
- arithmetic or geometric
So anywhere between 0 and 10!!

24. Risk and Return Cost of Equity
Real WACC
Should always use market values for Equity and Book values are used for debt (relevant for leverage discussions)
WACC we work out will probably be nominal cost of capital. Suppose we want the real cost of capital?

25. Risk and Return Cost of Equity
Say WACC = 9.87 and inflation is 3%
Then the real WACC is
1 + nominal wacc - 1
1 + inflation rate
= – 1 = .061 or 6.1 %
1.03

26. Risk and Return Cost of Equity
Lastly the 1 – t issue.
Because interest on debt is allowed as an expense before tax the government subsidises the cost of debt.
EBIT , ,000
Int* _____
EBT , ,000
40% 1, ,000
Net , ,000
Tot returns 3, ,000
Dif = 120 x .4 = 48