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Risk and Return

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**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

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**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 %

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**Risk and Return WACC, A Simple Example**

So WACC = Equity bit = 35,000,000 x 12 = 50,000,000 Debt bit = 15,000,000 x (1 - .3) = WACC =

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**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

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**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

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**Risk and Return Cost of Equity**

Returns Deviation from Mean Deviation Squared (9) (8) (6) (18) (2) (8) Mean Var = 1068/n-1 SD

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**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%

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**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%

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**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?

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**Variance of a Portfolio**

But what is the variance? ER Umbrellas ER ER Cider

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**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

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**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

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**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

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**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

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**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

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CAPM Security Market Line Rm Market Portfolio Rf Beta

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**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 …

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**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

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**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)

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**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

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**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!!

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**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?

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**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

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**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

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