1. Introduction to Risk, Return, and The Opportunity Cost of Capital
Pawel Mielcarz, PhD
Kozminski University
Warsaw, Poland

2. 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

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

4. 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

5. Example I

6. 1$ invested in 1900 in USA 13

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

8. Average Market Risk Premia (by country)

9. Stock Market Index Returns
Rates of Return
Stock Market Index Returns
Percentage Return
Year
Source: Ibbotson Associates 14

10. Measuring Risk Histogram of Annual Stock Market Returns # of Years

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

12. Example II

13. 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

14. Portfolio Risk 19

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

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

17. Measuring Risk 19

18. Example III
Example IV

19. 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

20. 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.

21. Measuring Risk 20

22. Measuring Risk 21

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

24. 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

25. 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

26. 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

27. 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

28. 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

29. 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

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

31. 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 %
The alternative is to estimate forward looking MRP (Reaserch of P. Fernadez)
MRP used by practitioners is in the range % 20

32. 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

33. 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

34. Example V

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

36. 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

37. 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.

38. 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

39. 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

40. 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.

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

42. 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

43. Example VI