2.  Cost of capital must include the opportunity costs from all sources of capital – since free cash flow is available to all investors, who expect compensation for the risks they take.  It must weight each security’s required return by its target market-based weight. 2

3.  It must be computed after corporate taxes (since free cash flow is calculated in after-tax terms). ◦ Any financing-related tax shields not included in free cash flow must be incorporated into the cost of capital or valued separately (as done in adjusted present value).  It must be denominated in nominal terms when cash flows are stated in nominal terms.  It must be denominated in the same currency as free cash flow. 3

4.  If the target capital structure is expected to change significantly (e.g., LBO), a constant WACC may overstate or understate the impact of interest tax shield.  In this situation, ◦ discount free cash flow by unlevered cost of equity and value tax shields and other financing effects separately. 4

5. Best practices in implementation of CAPM 5

6.  E(R f ) = r f +ß i × [E(R m ) – r f ] ◦ E(R f ) = Security’s expected return ◦ r f = Risk-free rate ◦ ß i = Stock’s sensitivity to the market ◦ E(R m ) = Expected return of the market ◦ In the CAPM, the risk-free rate and the market premium are common to all companies; only beta varies across companies. 6

7.  ß measures a stock’s incremental risk to a diversified investor, where the risk is defined by how much the stock covaries with the aggregate stock market. ◦ Consider a cereal manufacturer and a maker of network router. ◦ Consumers cereal purchases are relatively independent of stock market’s value, so the ß is low. ◦ Technology companies tend to have high ß.

8. ◦ The cereal manufacturer offers greater protection against market downturns than the technology company. ◦ Therefore, investors are willing to pay a premium for the stock, driving down expected return. ◦ Since the technology company offers little diversification to the market portfolio, the company must earn higher returns to entice investors.

9.  Ideally, each cash flow should be discounted using government bond with a similar maturity.  In practice, most choose a single yield-to- maturity from one government bond that best matches the entire cash flow stream. ◦ The best proxy is 10-year government bond, because of its liquidity. ◦ Using the yield from a short-term bond as risk-free rate fails to recognise that a bond holder must reinvest at higher rates when the short-term bond matures. ◦ Thus, short-term bond rate misestimates the opportunity cost for investment for long-term projects 9

10.  Estimating the future risk premium by measuring and extrapolating historical excess returns.  Using regression analysis to link current market variables, such as the aggregate dividend-to-price ratios, to project the expected the expected market risk premium.  Using DCF valuation, along with estimates of return on investment and growth, to reverse engineer the market’s cost of capital 10

11.  Calculate the premium relative to long-term government bonds.  Use the largest period possible.  Use an arithmetic average of longer-dated intervals (such as five years).  Adjust the result for econometric issues, such as survivorship bias. 11

12.  An arithmetic average sums each year’s observed premium and divides it by the number of observations.  A geometric average compounds each year’s excess return and takes the root of the resulting product. ◦ Arithmetic averages always exceed geometric averages when returns are volatile

13.  To estimate the mean (expectation) for any random variable, well accepted statistical principles dictate that the arithmetic average is the best unbiased estimator. ◦ Therefore, to determine a security’s expected return for one period, the best unbiased predictor is the arithmetic average of many one-period returns. ◦ A one-period risk premium, however, cannot value a company with many years of cash flow. Instead, long- dated cash flows must be discounted using a compounded rate of return. ◦ But when compounded, the arithmetic average will be biased upward (too high)

14.  To estimate the mean of a distribution, statistical theory requires to average the observations. In a finite sample, the sample average (R A ) will equal the true mean (μ) plus an error term (ε).  Some time the error term is positive, and at other times the error term is negative. But the average error term equals zero, so the sample average is an unbiased estimator of the true mean.

15.  To value a cash flow beyond one period, we must determine the discount factor by raising R A to a given power.  For example, to estimate a two-period discount rate, we calculate R A squared.  Since μ is constant and ε is zero, 2με equals zero. The expectation of ε^2 will be positive. Therefore, R A squared will be greater than μ squared.

16.  The general consensus is that the aggregate stock market exhibits negative autocorrelation.  Negative autocorrelation implies low returns follow high returns and high returns follow low returns.  In this case the arithmetic average is biased upwards.

17.  Calculate multi-period holding return directly from the data, rather than compound single- period averages.

18.  To predict the market risk premium using financial ratios, excess market returns are regressed against a financial ratio, such as the market’s aggregate dividend-price ratio.  The major drawback is that the risk-premium prediction may be negative. 18

19.  P = Dividend/(k e –g)  K e =(Dividend/P) +g  K e =[Earnings×(1-g/ROE)]/P+ g ◦ such that CF e = [Earnings×(1-g/ROE)] 19

20.  For USA 4.5 to 5.5 percent is the appropriate range. 20

21.  Emerging-market risks refers to risks caused by greater volatility in capital markets and in the macroeconomic and political environment.  Two approaches: ◦ Scenario DCF approach ◦ Country risk premium DCF approach

22.  Simulate alternative trajectories for future cash flows – at the minimum two: ◦ Cash flows reflecting business as usual (Base case) ◦ Cash flows assuming that any emerging market risks materialises  Assign weights (i.e., probabilities) to all the scenarios and calculated expected cash flows.  Discount expected cash flows by WACC of the company.

23.  There is no agreed upon approach to estimate country risk premium.  The country’s sovereign risk premium is the difference between a long term (e.g., 10- year) U.S Government bond yield and a dollar-denominated local bond with the same maturity.  This is often taken as the country risk premium.  India does not issue dollar denominated sovereign bond.

24.  Country risk premium should not be set two high.  India’s political environment is significantly stable and the variability in the capital market is not significantly different from the US market.  Usually the country risk premium for India is taken at 2.  India’s market risk premium may be taken in the range of (4.5 +2) that is 6.5 percent and (5.5 +2), that is 7.5 per cent.

25.  Calculate levered equity beta (raw beta) of comparable companies.  Based on levered equity beta, calculate un- levered beta of comparable companies.  Take the median as the industry beta.  Based on the un-levered industry beta calculate the levered equity beta of the company taking into account the target capital structure.

26.  The most common regression used to estimated company’s raw beta os the market model: ◦ R i = α +βR m + ε  Stock’s return is regressed against the market return  Take BSE-500 as a proxy for market.

27.  Take monthly return for five years (60 data points).  View rolling-beta to examine any significant change over years.  Do not use weekly or daily return because: ◦ Handling high-frequency data is statistically difficulty ◦ Thinly trading securities will show many zero returns because of lack of trading ◦ Bid/ask bounce causing distortion in beta estimation