12. The Cost Of Capital (5%) (P6)

Front 1

Importance of cost of capital

Back 1

It is the return that co gives to the providers of capital. Co’s face business risks (areas of bus & prospects) & financial risks (financial structure). As level of risk increase, return expected increases as compensation for bearing add risk = ‘risk premium’. This acts to raise the req/d return above the risk-free rate (RFR).

S/hs expect mix of dividend income & capital growth. Loan stock holders expect regular, usually fixed, interest payments & redemption proceeds. There is some scope for capital gain.

Need to know re cost of capital to make informed choices re capital structure & in order to use discount rate in project appraisal.

Front 2

The dividend valuation model

(Cost of equity)

Back 2

Relates divs paid and expected to be paid to share price. Takes account of risk implicitly b/c higher risk co’s pay higher divs or are expected to grow faster than lower-risk cos.

Based on principle that market value of a share is the PV of the divs paid on the share (obtained by discounting all expected future divs). DR used is the cost of capital for equity. Used if divs expected to be constant each yr.

Po = Do / Ke

Po is current value of share, Do is dividend at yr 0, Ke is cost of equity.

Ke = Do / Po

Front 3

The dividend growth model

(Cost of equity)

Back 3

Relates divs paid and expected to be paid to share price. Takes account of risk implicitly b/c higher risk co’s pay higher divs or are expected to grow faster than lower-risk cos.

When divs are expected to grow at a constant annual % rate, rel between share price & future divs is given by Gordon’s model of dividend growth (div growth model).

Po = Do (1 + g) / (Ke – g)

Po is current share price (ex div), Ke is cost of equity, Do dividend at yr 0, g is annual rate of growth in divs. Implies that if value of share is based on expected future divs, then value will increase at rate of growth of divs.

Formula implies that value of co is increased by higher divs, higher growth in divs & lower cost of equity.

Ke = [Do (1 + g) / Po] + g (=%)

Growth rate (g) = (n√latest div/earliest div) – 1

(N is no of yrs of growth)

Front 4

Assumption of dividend valuation & growth methods

(Cost of equity)

Back 4

INCEPT

Info same & perfect level for all investors
No costs of issuing shares
Cost of capital unaltered by new issue of shares
Equal risk level of new projects to existing activities
Paid dividends must be from after-tax profits
Tax rates same for all investors

Front 5

Capital asset pricing model (CAPM)

(Cost of equity)

Back 5

Takes account of risk explicitly. Establishes ‘correct’ equilibrium market value of co’s shares & calculate cost of firm’s equity.

Implies equilibrium between risk & expected return. Used to assess risk. Consider diff types & how they can be used to calculate return investors require. Cost of equity capital obtained under CAPM = ‘risk adjusted discount rate’ (RADR). Used for investment appraisal as long as we know its beta value.

Unsystematic risk – unique to co, ind from economic factors, can be diversified away, uncorrelated.
Systematic risk – (‘market risk’) – unavoidable, non-diversifiable, adverse trends in economy, no control. Diff for diff industries. Risk premium will be the systematic risk of a share. CAPM relies on premise that rational investors reduces overall risk by investing in optimum portfolio thereby eliminating unsystematic risk.

Front 6

CAPM – measuring systematic risk

(Cost of equity)

Back 6

Measure systematic risk & linking to required returns. Rel between excess returns of ind share to on the market using regression analysis. Findings:

- Excess returns of a shares positively correlated to excess returns on the market, & both correlated w/ boom/recession.
- Gradient of regression line is termed beta. If gradient is 45 degrees, systematic risk of a share is equal to that of market (share’s beta = 1); if greater, systematic risk of share exceeds that of market (beta greater than 1); if less, systematic risk of market exceeds that of specific shares (share’s beta is less than 1). So the greater the beta, the greater the systematic risk & the greater the return required. (p204)

Front 7

CAPM – linking beta (measurement of systematic risk) with required returns – security market line (SML) (Calculating RADR)

(Cost of equity)

Back 7

SML gives cost of equity given share/investment & indicates the risk-adjusted return req’d for any level of systematic risk.

Cost of capital known as risk-adjusted discount rate (RADR). Risk free capital has a beta of 0. Beta for the market as a whole is 1. SML calculates req’d market return for any degree of systematic risk.

SML equation used to determine cost of equity:

RADR = RFR + beta(RM – RFR)

RFR is risk-free rate of interest; RM is return on the stock market portfolio; beta is the statistically derived beta of the share.

Front 8

Assumptions underpinning CAPM

Back 8

Supported assumption:

Investors are rational – req greater return for taking greater risks – supported by empirical evidence

Assumptions for which CAPM can be modified & maintains predictive abilities: BITE

Borrowing & lending rates equal – in practice borrowing rates higher
Inflation ignored – when incorporated, model still predict the req’d return accurately.
Taxation ignored – if relaxed, CAPM still found to maintain predictive abilities
Expectations are homogenous – but clearly not all investors have same view re prospects

Incorrect assumptions: MERIT

Market imperfections ignored – beyond ST, lack divisibility of investments, fixed charges & imperfect info means model has poor predictive ability.
Efficient diversification away from unsystematic risk by ind investors easy – in practice reqs cost/effort to manage portfolio
RFR is equal to return on govt bonds – in practice many diff govt securities w/ diff rates of return.
Insolvency risks ignored – investors must consider these.
Transaction costs ignored – but they may mean investors don’t undertake all req’d transactions to make portfolios efficient – SML may be a band rather than a line.

Front 9

Criticisms of CAPM

Back 9

ORLON

Obtaining beta of project operationally diff. Usually use beta of co but project’s systematic risk may be diff.
Rel found between excess returns & other measures (not beta, e.g. firm size, book/market value)
Linearity of SML lost during some periods – changes of gradient at diff levels of beta
One-year model only & req’s re-computing each yr, so LT projects appraised using a DR based on 1 yr model.
No. of divisions in a large co & systematic risk of projects in these divisions diff, but single beta is based on stock market perf of whole co.

Front 10

Cost of preference shares

Back 10

Kp = Dp/Sp
Kp is cost of pref shares; Dp is fixed dividend based on nominal value of shares; Sp is market price of pref shares.

Front 11

Irredeemable debt

(Cost of debt capital)

Back 11

Kd = I(1-t) / Sd

Kd is cost of debt capital; I is annual interest; t is corp tax rate; Sd is market price of debt.

Rate of tax imp (so after-tax cost worked out) b/c higher the rate, lower after tax cost of debt capital. So cost of debt capital is lower than cost of pref shares w/ same coupon rate & market value b/c no tax relief on pref divs.

Front 12

Redeemable debt

(Cost of debt capital)

Back 12

Redeemable debt payable at future date. Cost of debt capital can be found using internal rate of return (IRR).

IRR = DRa + [NPVa / (NPVa - NPVb) X (DRb - DRa) ]

DRa / DRb = the low/high discount rate used
NPVa / NPVb = the NPV obtained w the low/high discount rate

Work out in a table (see p209).

Kd = (1-t) (don’t divide by market price of debt for redeemable) – gives you the yearly CF(final yr is redeemable amount).

Front 13

Weighted average cost of capital (WACC)

(combine cost of equity & debt)

Back 13

Each cost weighted by its proportional value in total market value of co.

WACC = Ke x [E/E+D] + Kd(1-t) x [D/E+D]

Ke is cost of equity capital; Kd is cost of loan capital (debt); E is total market value of equity (ex div); D is total market value of debt (ex interest); t is rate of corp tax.

Work out Ke, then Kd.
E = total no. of shares x market value per share & D = total debt x (market value of debt/nominal value). Put % of total capital for each & multiply by cost of equity/debt to give WACC (%).

Front 14

Problems with using WACC as a discount rate for a project

Back 14

Way project is financed will change co’s level of gearing which will have an impact on cost of capital

Project may have diff risk characteristics to co’s existing projects & existing WACC reflects average risk of firm’s existing projects.