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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 ReturnWACC, 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 ReturnWACC, A Simple Example

• So

WACC =

Equity bit = 35,000,000 x 12 = 8.4

50,000,000

Debt bit = 15,000,000 x (1 - .3) = 1.47

50,000,000

WACC = 9.87

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Risk and Return

• But, A Few Quick Questions

1) How do we get the cost of debt?

Easy, ask a bank

(We will return to the 1-t issue)

2) How do we get the cost of equity?

A bit trickier

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Risk and ReturnCost 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 ReturnCost of Equity

• Returns Deviation from Mean Deviation Squared 3 (9) 81

• 4 (8) 64• 33 21 441• (6) (18) 324• 10 (2) 4• 21 9 81• 4 (8) 64• 12 0 0• 15 3 9• 12 0 0 120 1068 Mean 12 Var 118.7 = 1068/n-1 SD 10.89

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Risk and ReturnCost of Equity

• Assuming a normal distribution

• Range Probability Downside risk Within+ / - 1 SD 66.67 16.67+ / - 2 SD 95.00 2.5+ / - 3 SD 99.75 .125Share has Av return of 14%SD of 4 %Need min return of 8%, with only 2.5% chance of lessDo we invest?No as 2.5 = 2 SD = 8 % and 14% -8% = 6%

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Risk and ReturnCost 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 .3 + 12 x .7 = 10.8%

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Risk and ReturnCost 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?Umbrellas

Cider

ER

ER

ER

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Risk and ReturnCost 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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E Rp

Portfolio Opportunity Set sd Rp

A

C

Generalise from 2 Asset Model

A C = Efficient Set

Market Portfolio

Rf

CML

E Rp

Portfolio Opportunity Set sd Rp

A

C

Generalise from 2 Asset Model

A C = Efficient Set

Market Portfolio

Rf

CML

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Risk and ReturnCost 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 ReturnCost 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 BetaBeta = 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 ReturnCost 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

0 1.0 2.0 Beta

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Risk and ReturnCost 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 % 8.99 + .09 = 12.27 275Arbitrage Pricing Theory. Not going to bother but …

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Fama-French3 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-French3 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-French3 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)=

= 7.6 + Rf

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Risk and ReturnCost 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 ReturnCost 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 ReturnCost of Equity

• Say WACC = 9.87 and inflation is 3%

• Then the real WACC is

1 + nominal wacc - 1

1 + inflation rate

1.0987 = 1.061 – 1 = .061 or 6.1 %

1.03

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Risk and ReturnCost 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 5,000 5,000• Int* 120 _____ • EBT 4,880 5,000• Tax @ 40% 1,952 2,000 • Net 2,928 3,000• Tot returns 3,048 3,000• Dif = 120 x .4 = 48