2Risk and Return Various Ways to Discount Cash Flows - WACC - APV - FTE We shall see these in action shortlyBut FirstWhat is the WACC
3Risk and Return WACC, A Simple Example A Company wishes to finance a project with 70 % Equity and 30 %DebtTotal needed GBP 50,000,000Tax rate 30 %Cost of Equity 12 %Cost of Debt 7 %
4Risk and Return WACC, A Simple Example SoWACC =Equity bit = 35,000,000 x 12 =50,000,000Debt bit = 15,000,000 x (1 - .3) =WACC =
5Risk 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
6Risk and Return Cost of Equity Rational ‘Economic’ PersonRisk is not bad but greater risk, greater expected returnRisk MeasurementsExpected returnVarianceStandard deviation
7Risk and Return Cost of Equity Returns Deviation from Mean Deviation Squared (9)(8)(6) (18)(2)(8)Mean Var = 1068/n-1SD
8Risk and Return Cost of Equity Assuming a normal distributionRange Probability Downside riskWithin+ / - 1 SD+ / - 2 SD+ / - 3 SDShare 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%
9Risk 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 portfolioE.g. Asset A, ER = 8%, = 30% of portfolioAsset B, ER = 12% = 70% of portfolioPortfolio ER = 8 x x .7 = 10.8%
10Risk 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?
11Variance of a Portfolio But what is the variance?ERUmbrellasERERCider
12Risk and Return Cost of Equity We may have a range of portfolios of differing expected returns and risksThere is a risk free asset, Government stocks (Gilts - Bills and Bonds)Capital Market lineMarket Portfolio
14Risk 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 intoMarket risk = systematic = non-diversifiableriskSpecific risk = unsystematic = diversifiable risk
15Risk and Return Cost of Equity Since diversifiable risk may be diversified away just left to focus onMarket RiskSome shares riskier than othersMeasure of relative risk isBetaBeta = Covariance of the Market and AssetVariance of the Market
16Variance of a Portfolio The riskiness of an asset held in a portfolio is different from that of an asset held on its ownVariance can be found using the following formulaVar Rp = w2Var(RA) + 2w(1-w)Cov(RARB)+(1-w)2VarRBCov stands for CovarianceCovariance is a measure of how random variables, A & B move away from their means at the same time
17Risk and Return Cost of Equity Required return (or expected return)ERA = RF + (ERM – RF)BExampleCompany A Beta of 1.4, Risk Free = 5 %Expected return on market = 10 %ERA = 5 + (10 -5) 1.4 = 12
19Risk and Return Cost of Equity Other modelsGordon Dividend GrowthER = D1 + gP0E.g. Share price = 275 penceCurrent Div = 8.25 penceHistoric growth = 9 %= 12.27275Arbitrage Pricing Theory. Not going to bother but …
20Fama-French 3 Factor Model To estimate the expected returns under APTExpected risk premium, r - rf = b1 (rfactor1-rf) + b2(r factor2 -rf) +b3 (r factor3 -rf) etc etcSo all we have to do isStep 1. Identify a reasonably short list of macroeconomic factors that could affect stock returnsStep 2. Estimate the expected risk premium on each of these factorsStep 3. Measure the sensitivity of each stock to the factors
21Fama-French 3 Factor Model Above average returns onSmall sized companies andHigh book to market valueR – rf = bmarket(rmarket factor)+bsize(rsize factor) +bbook too market(rbook to market factor)
22Fama-French 3 Factor Model Having worked out from market data thatMarket premium = 7%Size premium = 3.7%Book to market premium = 5.2%Then forE.g. computers bmkt =1.67, bsz = .39 and bmkt to bk = -1.07ER = (1.67x7)+(.39 x 3.7) + (-1.07x5.2)== Rf
23Risk and Return Cost of Equity Any problems?Market returns/Market risk premiumIt varies from- market to market- period to period- arithmetic or geometricSo anywhere between 0 and 10!!
24Risk and Return Cost of Equity Real WACCShould 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?
25Risk and Return Cost of Equity Say WACC = 9.87 and inflation is 3%Then the real WACC is1 + nominal wacc - 11 + inflation rate= – 1 = .061 or 6.1 %1.03
26Risk 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 , ,000Int* _____EBT , ,00040% 1, ,000Net , ,000Tot returns 3, ,000Dif = 120 x .4 = 48