Introduction to Risk, Return, and The Opportunity Cost of Capital Pawel Mielcarz, PhD Kozminski University Warsaw, Poland pmielcarz@kozminski.edu.pl

Topics Covered Short Supplement to Capital Budgeting Over a Century of Capital Market History Measuring Portfolio Risk Calculating Portfolio Risk Beta and Unique Risk Diversification & Value Additivity CAPM and cost of equity capital

Break Even Revenue Creating NPV = 0 (supplement to capital budgeting course)

BEPET – Break even revenue (NPV = 0) RV - residual value   BEPET – Break even revenue (NPV = 0) FC – fixed costs M% - operational margin CI - capital invested in a project WACC – weighted average cost of capital RV - residual value n – number of years of analyzed project A – costs of amortization T – Tax rate

Example I

1$ invested in 1900 in USA 13

The Value of an Investment of $1 in 1900 Real Returns 13

Average Market Risk Premia (by country)

Stock Market Index Returns Rates of Return 1900-2003 Stock Market Index Returns Percentage Return Year Source: Ibbotson Associates 14

Measuring Risk Histogram of Annual Stock Market Returns # of Years

Measuring Risk Standard Deviation - Average value of squared deviations from mean. A measure of volatility.

Example II

Measuring Risk Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments. Unique Risk - Risk factors affecting only that firm. Also called “diversifiable risk.” Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called “systematic risk.” 18

Portfolio Risk 19

riA – historical rate of return of the first share raA – average historical rate of return of the first share

Portfolio Risk The variance of a two stock portfolio is the sum of these four boxes 19

Measuring Risk 19

Example III Example IV

Portfolio Risk To calculate portfolio variance add up the boxes The shaded boxes contain variance terms; the remainder contain covariance terms. 1 2 3 4 5 6 N To calculate portfolio variance add up the boxes STOCK STOCK

Beta and Unique Risk Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market index, such as the S&P Composite, is used to represent the market. Beta - Sensitivity of a stock’s return to the return on the market portfolio.

Measuring Risk 20

Measuring Risk 21

Beta and Unique Risk Covariance with the market Variance of the market

Cost of capital The cost of capital is the minimum rate of return the firm should expect to earn on its invested funds so that all providers of funds just earn their required rate of return Cost of capital is also called discount rate, hurdle rate, or required rate of return 3 10

Risk and return Required rate of return = rf + risk premium Shareholders’ required rate of return, rE, compensates for Time value of money – risk free rate of return, rf ; and Risk - they require a risk premium depending on the risk level. Quantifying risk - what is the risk premium? Required rate of return = rf + risk premium 10

Market vs. specific risk (Total) Risk Systematic Risk (Market Risk) Specific Risk (Unique, residual,diversifiable) Affects a particular company and can be reduced by diversification A competitor patents new technology The union at a production plant walks out on strike A major new competitor enters the industry Affects all companies and cannot be reduced by diversification Inflation rises unexpectedly Political instability, war… Federal Reserve raises interest rates Industrial or economic cycle changes Specific risk should be reflected in the forecasted cash flows, not in the discount rate Market risk should be reflected in cash flows and the cost of capital. It cannot be diversified away and investors want to be compensated for bearing it 14

Risk and return Investors hold well diversified portfolios The risk of an individual security is measured by its contribution to the portfolio's risk denoted by Beta -  It measures how much risk a single security adds to the market portfolio. It reflects the sensitivity of the returns to movements in the economy 15

Risk and return (continue) Non-Cyclical or Defensive Stocks They don't move much with the market (beta is low), e.g., basic food, hospitals. Therefore they reduce portfolio volatility Pro-Cyclical or Offensive Stocks They move a lot with the market (beta is high), e.g., automotive industry, construction industry. Therefore they increase portfolio volatility 16 27

Capital Asset Pricing Model - CAPM Required rate of return = risk free rate + risk premium the market risk premium is the compensation investor require for the “average” risk. It is the expected rate of return on the market portfolio minus the risk free rate of return Required rate of return = risk free rate+ * market risk premium 17 30

CAPM estimation rf = riskless rate of return Use YTM on medium-long maturity government bonds Beta  is estimated using a standard statistical procedure called linear regression: historical data on the asset rates of return and the market returns are used to estimate  Commercial companies estimate  for virtually any public firm 19 34

CAPM estimation (continue) = expected market risk premium (MRP) Historical estimate: look on historical premium return on market index (like Standard and & Poor’s 500) over the 10-year government bond return. A good estimate for the U.S. over the last 50 years is 7 -7.5% The alternative is to estimate forward looking MRP (Reaserch of P. Fernadez) MRP used by practitioners is in the range 5 - 8 % 20

Incorporating risk in DCF valuations In calculating NPV we discount expected cash flows by the cost of capital All Risks (Specific and Systematic) are incorporated into expected cash flows Expected Cash Flow Cost of Capital NPV = Systematic Risk is incorporated into the cost of equity using CAPM 18

The importance of the cost of capital The cost of capital is used to evaluate projects and to estimate value of companies. It accounts for both time value of money and risk The effect of an error in estimating the cost of capital Underestimation of hurdle rates leads to acceptance of negative NPV projects Overestimation of hurdle rates results in rejection of positive NPV projects 4 7

Example V

WACC (Weighted Average Cost of Capital) Cost of Capital: WACC WACC (Weighted Average Cost of Capital) Formula Example 7

Debt financing and WACC When proportion of debt increases we have: More of the “cheaper” source of financing Interest tax shield increases Less equity, i.e., less of the more costly financing Cost of equity increases Ignoring tax shields, WACC does not change when leverage increases. The only reason why WACC may go down is the tax shield due to debt financing. 22 32

Integration of Tax Effects and Financial Distress Costs There is a trade-off between the tax advantage of debt and the costs of financial distress. It is difficult to express this with a precise and rigorous formula.

Integration of Tax Effects and Financial Distress Costs Value of firm (V) Value of firm under MM with corporate taxes and debt Present value of tax shield on debt VL = VU + TCB Maximum firm value Present value of financial distress costs V = Actual value of firm VU = Value of firm with no debt Debt (B) B* Optimal amount of debt

Cost of financial destress Costs of financial distress cause firms to restrain their issuance of debt. Direct costs Lawyers’ and accountants’ fees Indirect Costs Impaired ability to conduct business Incentives to take on risky projects Incentives to underinvest Incentive to milk the property Three techniques to reduce these costs are: Protective covenants Repurchase of debt prior to bankruptcy Consolidation of debt

How Firms Establish Capital Structure Most Corporations Have Low Debt-Asset Ratios. Changes in Financial Leverage Affect Firm Value. Stock price increases with increases in leverage and vice- versa; this is consistent with M&M with taxes. Another interpretation is that firms signal good news when they lever up. There are Differences in Capital Structure Across Industries. There is evidence that firms behave as if they had a target Debt to Equity ratio.

Debt financing and cost of equity capital The lever/unlever formula Shortcut if debt is risk free 25

Finding WACC for target leverage: lever/unlever procedure Find (from historical data or comparables) Unlever: Solve for using the lever/unlever equation. Find average for comparables Relever: Find for “target” leverage Use CAPM to calculate Calculate WACC for target leverage 26

Example VI