Cost of Capital Dr Bryan Mills

Risk and Return % return % risk

Order of risk Treasury bills and gilts (risk free) Loan Notes –But ranked from AAA to BBB – with specialist ‘junk bonds’ being BB and less Equity

Dividend Valuation Model Share price must be equal to or less than future cash flows: We can assume that D’s growth will be constant. (geometric progression).

Assumptions Uses next year’s dividend so must be ex div Fixed rate of growth Dividends paid in perpetuity Share price is discounted future cashflow P Time P0P0 Cum Div Dividend Stream

Dividend growth: Either old dividend divided by new dividend and answer looked up on discount factor table for that number of years or;

Example: If a company now pays 32p and used to pay 20p 5 years ago what is the rate of growth? 20(1+g) n = 32 (1+g) n = g = (1.60)1/5 1 + g = 1.1 growth is 10%

Gordon’s Growth Model Balance sheet asset value of £200, a profit of £20 in the year and a dividend pay out of 40% (in this case £8) we would expect the new balance to be £212 (old + retained profit). If the ARR and retention policy remain the same for the next year what will the dividend growth be? Profit as a % of capital employed is £20/£200 = 10% Next year has the same ARR then: 10% X £212 = £21.20 is our new profit as the dividend is 40% this equates to: 40% X £21.20 = £8.48 Which represents a growth of (8.48-8)/8 = 6% Which could have been found much quicker (!) by: g = rb, g = 10% X 60%, g = 6%

Test Share price is £2, dividend to be paid soon is 16p, current return is 12.5% and 20% is paid out – what is cost of equity? g is rb – refer back to DVM for cost of equity

Portfolio theory Investment A Investment B Time Rat e of Ret urn Time Combined effect (Portfolio Return)

Systematic risk Portfolio Risk Number of securities Systematic (Market) Risk Unsystematic (unique) Risk

CAPM RfRf RmRm Retur n 1 Systematic Risk  Security Market Line (SML)

Rf = Risk Free therefore  = 0 Rm = Market Portfolio (max diversification - all systematic) therefore  = 1  SML can be written as an equation: R j = R f +  j (R m - R f ) Called CAPM

RyRy Market Return R m Slope =  >1 RyRy Market Return R m Slope =  <1

Test Paying a return of 9%, gilts are at 5.5% and the FTSE averages 10.5% - what is the beta – and what does this value mean?

Aggressive and Defensive Shares If the risk free rate is 10% and the market index has been adjusted upward from 16% to 17% what will be the effect on shares with Betas of 1.4 and 0.7 accordingly? Shares with Betas greater than 1 are aggressive - they are over-sensitive to the market Shares with Betas less than 1 are defensive - they are under-sensitive to the market

Assumptions of CAPM perfect capital market unrestricted borrowing at the risk free rate uniformity of investor expectations forecasts based on a single time period Advantages of CAPM: provides a market based relationship between risk and return demonstrates the importance of systematic risk is one of the best methods of calculating a company's cost of equity capital can provide risk adjusted discount rates for project appraisal

Limitations of CAPM: avoids unsystematic risk by assuming a diversified portfolio - how reliable is this? Only looks at return in the most simple of ways (rate of return not split into growth, dividends, etc.) Only based on one-period Can be difficult to estimate Rf Rm  Does not work well for investments that have low betas, seasonality, low PE ratios - partly because it overstates the rate of return needed for high betas and understates the rate needed for low betas

Irredeemable Securities: In this case the company never returns the principal but pays interest in perpetuity. An equation we have seen before with I (interest) replacing the dividend (D) Note that tax relief relates to the company and not the market value

Redeemable Securities: Debenture priced at £74 with a coupon of 10% (remember this is 10% of £100). The interest has just been paid and there are four years until the redemption (at par) and final interest are paid. IRR of cashflows

YearCashflowDiscount FactorPV (74.00)1.00(74.00) YearCashflowDiscount FactorPV (74.00)1.00(74.00)

IRR = original % + Lowest %0.15 Difference in %0.07 Higher return11.73 Range between high and low Higher Divided by Range Times by Difference Return pa20%

Interesting point: Debt redeemable at current market price has the same cost (and formula) as irredeemable debt

Others Convertible –Redemption value is higher of cash redemption or future value of shares Non-tradable debt –‘normal’ loans – just use (1-t) Preference sahres –Not really debt but use D/P

WACC Step by Step Approach: Calculate weights for each source of capital (source/total) Estimate cost of each source Multiply 1 and 2 for each source Add up the result of 3 to get combined cost of capital

WACC 0 Cost of Cap % X Gearing Cost of equity WACC Cost of debt

Market Value of firm 0 £ X Gearing Market value of equity

Market value MV of company = Future Cash Flows WACC