Module 3.2

Question 1

Stock Valuation Methods

Answer 1

The Price-Earnings (PE) Method applies the mean price-earnings (PE) ratio based on expected earnings of all traded competitors to the firm’s expected earnings for the next year
Valuation = Expected earnings per share x Mean industry PE ratio
Assumes future earnings are an important determinant of a firm’s value.
Assumes that the growth in earnings in future years will be similar to that of the industry

Question 2

There are many different methods of valuing stocks

Answer 2

Fundamental analysis relies on fundamental financial characteristics (such as earnings)
of the firm and its corresponding industry that are expected to influence stock values.
Technical analysis relies on stock price trends to determine stock values. Our focus is
on fundamental analysis. Investors who rely on fundamental analysis commonly use the
price–earnings method, the dividend discount model, or the free cash flow model to
value stocks. Each of these methods is described in turn.

Question 3

Consider a firm that is expected to generate earnings of $3 per share next year. If the mean ratio of share price to expected earnings of competitors in the same industry is 15, then the valuation of the firm’s shares is

Answer 3

Valuation per Share =Expected Earnings of Firm Price per share x Mean industry P/E ratio
$3X$15=$45

Question 4

Price-Earnings Method

Answer 4

Reasons for Different Valuations
Investors may use different forecasts for the firm’s earnings or the mean industry earnings over the next year.
Investors disagree on the proper measure of earnings.
Limitations of the PE Method
May result in an inaccurate valuation of a firm if errors are made in forecasting the firm’s future earnings or in choosing the industry composite used to derive the PE ratio.

Question 5

Dividend Discount Model

Answer 5

where t = period
D t = dividend in period t
k = discount rate
(See Formula)

Question 6

Relationship with PE Ratio for Valuing & Limitations of the Dividend Discount Model

Answer 6

Relationship with PE Ratio for Valuing
The PE multiple is influenced by the required rate of return and the expected growth rate of competitors.
The inverse relationship between rate of return and value exists in both models.
The positive relationship between required rate of return and value exists in both models.
Limitations of the Dividend Discount Model
Errors can be made in determining the dividend to be paid, the growth rate, and the required rate of return.
Errors are more pronounced for firms that retain most of their earnings.

Question 7

Adjusted Dividend Discount Model

Answer 7

Adjusted Dividend Discount Model
The dividend discount model can be adapted to assess the value of any firm, even those that retain most or all of their earnings.
The value of the stock is equal to the present value of the future dividends plus the present value of the forecasted.
Limitations of the Adjusted Dividend Discount Model
May be inaccurate if errors are made in:
deriving the present value of dividends over the investment horizon or
the present value of the forecasted price at which the stock can be sold at the end of the investment horizon.

Question 8

Adjusted Dividend Discount Model, Breakdown

Answer 8

Adjusted Dividend Discount Model
Constant dividend
The firm will pay a constant dividend forever
This is like preferred stock
The price is computed using the perpetuity formula

Constant dividend growth
The firm will increase the dividend by a constant percent every period
The price is computed using the growing perpetuity model

Supernormal growth
Dividend growth is not consistent initially, but settles down to constant growth eventually
The price is computed using a multistage model

Question 9

Zero Growth

Answer 9

If dividends are expected at regular intervals forever, then this is a perpetuity and the present value of expected future dividends can be found using the perpetuity formula
P0 = D / R
Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price?
P0 = .50 / (.1 / 4) = $20

Question 10

Constant dividend growth

Answer 10

Dividends are expected to grow at a constant percent per period.
P0 = D1 /(1+R) + D2 /(1+R)2 + D3 /(1+R)3 + …
P0 = D0(1+g)/(1+R) + D0(1+g)2/(1+R)2 + D0(1+g)3/(1+R)3 + …

With a little algebra and some series work, this reduces to:
(See slide)

Question 11

Constant dividend growth example 1

Answer 11

Suppose Big D, Inc., just paid a dividend of $0.50 per share.
It is expected to increase its dividend by 2% per year.
If the market requires a return of 15% on assets of this risk, how much should the stock be selling for?

P0 = .50(1+.02) / (.15 - .02) = $3.92

Question 12

Constant dividend growth example 2

Answer 12

Suppose TB Pirates, Inc., is expected to pay a $2 dividend in one year.
If the dividend is expected to grow at 5% per year and the required return is 20%, what is the price?

P0 = 2 / (.2 - .05) = $13.33

Why isn’t the $2 in the numerator multiplied by (1.05) in this example?

Question 13

Nonconstant Growth

Answer 13

Suppose a firm is expected to increase dividends by 20% in one year and by 15% in two years.

After that, dividends will increase at a rate of 5% per year indefinitely.

If the last dividend was $1 and the required return is 20%, what is the price of the stock?

Remember that we have to find the PV of all expected future dividends.

Question 14

Nonconstant Growth (cont)

Answer 14

Compute the dividends until growth levels off
D1 = 1(1.2) = $1.20
D2 = 1.20(1.15) = $1.38
D3 = 1.38(1.05) = $1.449

Find the expected future price
P2 = D3 / (R – g) = 1.449 / (.2 - .05) = 9.66

Find the present value of the expected future cash flows
P0 = 1.20 / (1.2) + (1.38 + 9.66) / (1.2)2 = 8.67
Point out that P2 is the value, at year 2, of all expected dividends year 3 on.

The final step is exactly the same as the 2-period example at the beginning of the chapter. We can look at it as if we buy the stock today and receive the $1.20 dividend in 1 year, receive the $1.38 dividend in 2 years and then immediately sell it for $9.66.

Calculator: CF0 = 0; C01 = 1.20; F01 = 1; C02 = 11.04; F02 = 1; NPV; I = 20; CPT NPV = 8.67

Question 15

Free Cash Flow Model

Answer 15

For firms that do not pay dividends:
Estimate the free cash flows that will result from operations.
Subtract existing liabilities to determine the value of the firm.
Divide the value of the firm by the number of shares to derive a value per share.
Limitations — Difficulty of obtaining an accurate estimate of free cash flow per period.

Question 16

Capital Asset Pricing Model

Answer 16

Sometimes used to estimate the required rate of return for any firm with publicly traded stock.
The only important risk of a firm is systematic risk.
Suggests that the return of a stock (Rj) is influenced by the prevailing risk-free rate (Rf), the market return (Rm), and the beta (Bj): Rj = Rf + Bj(Rm – Rf)where Bj is measured as the covariance between Rj and Rm, which reflects the asset’s sensitivity to general stock market movements.

Question 17

Capital Asset Pricing Model (Cont.)

Answer 17

Estimating the Market Risk Premium
The yield on newly issued Treasury bonds is commonly used as a proxy for the risk-free rate.
The term, (Rm – Rf), is the market risk premium: the return of the market in excess of the risk-free rate.
Historical data for 30 or more years can be used to determine the average market risk premium over time.
Estimating the Firm’s Beta — Typically measured by applying regression analysis to determine the sensitivity of the asset’s return to the market return based on monthly or quarterly data.

Question 18

Calculate Required Rate

Answer 18

The beta of the stock for Vaxon, Inc., is estimated as 1.2 according to the regression analysis just explained. The prevailing risk-free rate is 6 percent, and the market risk premium is estimated to be 7 percent based on historical data. A stock’s risk premium is computed as the market risk premium multiplied by the stock’s beta, so Vaxon stock’s risk premium (above the risk-free rate) is 0.07 × 1.2 ¼ 8.4 percent. Therefore, the required rate of return on Vaxon stock is
R=6%+1.2(7%)=14.4/5

Question 19

Capital Asset Pricing Model (Cont.)

Answer 19

Application of the CAPM
Given the risk-free rate as well as estimates of the firm’s beta and the market risk premium, it is possible to estimate the required rate of return from investing in the firm’s stock.
At any given time, the required rates of return estimated by the CAPM will vary across stocks because of differences in their risk premiums, which are due to differences in their systematic risk (as measured by beta). Historical data for 30 or more years can be used to determine the average market risk premium over time.

Question 20

Factors that Affect Stock Prices

Answer 20

Economic Factors
Impact of Economic Growth (Exhibit 11.1)
An increase in economic growth is expected to increase the demand for products and services produced by firms and thereby increase a firm’s cash flows and valuation.
Impact of Interest Rates
Given a choice of risk-free Treasury securities or stocks, investors should purchase stocks only if they are appropriately priced to reflect a sufficiently high expected return above the risk-free rate.
Interest rates commonly rise in response to an increase in economic growth.

Question 21

Economic Factors (Cont.)

Answer 21

Impact of the Dollar’s Exchange Rate Value
Foreign investors prefer to purchase U.S. stocks when the dollar is weak and to sell them when the dollar is near its peak.
Stock prices are also affected by the impact of the dollar’s changing value on cash flows.
Stock prices of U.S. companies may also be affected by exchange rates if stock market participants measure performance by reported earnings.
The changing value of the dollar can also affect stock prices by affecting expectations of economic factors that influence the firm’s performance.

Question 22

Market-Related Factors

Answer 22

Investor Sentiment
Represents the general mood of investors in the stock market.
January Effect
Portfolio managers prefer investing in riskier, small stocks at the beginning of the year and then shifting to larger, more stable companies near the end of the year in order to lock in their gains.
This tendency places upward pressure on small stocks in January each year.

Question 23

Firm-Specific Factors

Answer 23

Change in Dividend Policy
An increase in dividends may reflect the firm’s expectation that it can more easily afford to pay dividends.
Earnings Surprises
When a firm’s announced earnings are higher than expected, some investors raise their estimates of the firm’s future cash flows and hence revalue its stock upward.
Acquisitions and Divestitures
The expected acquisition of a firm typically results in an increased demand for the target’s stock, which raises its price.
Expectations
Attempting to anticipate new policies so that they can make their move in the market before other investors

Question 24

Tax Effects & Integration of Factors Affecting Stock Prices

Answer 24

Tax Effects
Differences in tax laws for short-term vs. long-term capital gains affect the after tax cash flows investors receive from selling stocks.
Tax laws cause some stocks to be more desirable than others (i.e. dividend vs. non-dividend paying).
Integration of Factors Affecting Stock Prices
Whenever indicators signal the expectation of higher interest rates, there is upward pressure on the required return by investors and downward pressure on a firm’s value. (Exhibit 11.2)

Question 25

Having an Edge in the Valuation Process

Answer 25

Information Leakages
Under Regulation FD, when firms disclose material information, they must do it publicly.
Analysts no longer have an information advantage.
Reliance on Expert Networks
Private information can also be obtained by hiring experts in the field as consultants.
Experts are not supposed to provide inside information.

Question 26

Stock Risk

Answer 26

The return from investing in stock over a particular period is measured as
(see slide for formula)

The risk of a stock can be measured by using its price volatility, its beta, and the value-at-risk method

Question 27

Volatility of a Stock

Answer 27

Volatility of a Stock or total risk serves as a measure of risk because it may indicate the degree of uncertainty surrounding the stock’s future returns.
Using Standard Deviation to forecast Stock Price Volatility
Using the historical method — A historical period is used to derive a stock’s standard deviation of returns, and that estimate is then used as the forecast over the future.

Question 28

Volatility of a Stock (con’d)

Answer 28

Using Volatility Patterns to Forecast Stock Price Volatility
A time series trend is applied to the standard deviations to account for changes in economic trends during the previous periods.
Using Implied Volatility to Forecast Stock Price Volatility
Derive a stock’s implied standard deviation from a stock option pricing model.

Question 29

Forecasting Stock Price Volatility of the Stock Market

Answer 29

Monitor the volatility index (VIX) derived from stock options on the S&P 500 stock at a given point in time.
The VIX measures investors’ expectation of the stock market volatility over the next 30 days. (Exhibit 11.3)

Question 30

Volatility of a Stock Portfolio

Answer 30

The portfolio’s volatility can be measured by the standard deviation:
See slide

Question 31

Beta of a Stock

Answer 31

Beta of a Stock Portfolio can be measured as the weighted average of the betas of stocks that make up the portfolio
See formula in slide

High-beta stocks are expected to be relatively volatile because they are more sensitive to market returns over time. Likewise, low-beta stocks are expected to be less volatile because they are less responsive to market returns

Question 32

Value at Risk

Answer 32

Estimates the largest expected loss to a particular investment position for a specified confidence level.
Is intended to warn investors about the potential maximum loss that could occur.
Is commonly used to estimate the risk of a portfolio

Question 33

Application Using Historical Returns

Answer 33

E.g. an investor may determine that out of the last trading 100 trading days, a stock experienced a decline of greater than 7% on five different days.
The investor could infer a maximum daily loss of no more than 7% for that stock based on a 95% confidence level.

Question 34

Application Using the Standard Deviation

Answer 34

Measure the standard deviation of daily returns over the previous period,
then apply it to derive boundaries for a specific confidence level.

Question 35

Application Using Beta and Deriving the Maximum Dollar Loss

Answer 35

Application Using Beta — A third method of estimating the maximum expected loss for a given confidence level is to apply the stock’s beta.
Deriving the Maximum Dollar Loss — Once the maximum percentage loss for a given confidence level is determined, it can be applied to derive the maximum dollar loss of a particular investment.

Question 36

Value at Risk (cont.)

Answer 36

Application to a Stock Portfolio — The three methods can be used to derive the maximum expected loss of a stock portfolio for a given confidence level.
Adjusting the Investment Horizon Desired — The same methods can be applied over a week or a month.
Adjusting the Length of the Historical Period — If conditions have changed such that only the most recent days reflect the general state of market conditions, then those days should be used.
Limitations of the Value-at-Risk Method — Portfolio managers may be using a relatively calm historical period when assessing possible future risk.

Question 37

Sharpe Index

Answer 37

The reward-to-variability ratio, or Sharpe Index, measures risk-adjusted returns when total variability is the most appropriate measure of risk.

(See Formula)

This index measures the excess return above the risk-free rate per unit of risk.

Question 38

Treynor Index

Answer 38

The Treynor Index measures risk-adjusted returns when beta is the most appropriate measure of risk.
(See formula on slide)

Question 39

Stock Market Efficiency v

Answer 39

Forms of Efficiency
Weak-Form Efficiency — Suggests that security prices reflect all market-related information, such as historical security price movements and volume of securities trades.
Semistrong-Form Efficiency — Suggests that security prices fully reflect all public information, such as firm announcements, economic news, or political news.
Strong-Form Efficiency — Suggests that security prices fully reflect all information, including private or insider information.

Question 40

Tests of the Efficient Market Hypothesis

Answer 40

Test of Weak-Form Efficiency — Weak-form efficiency has been tested by searching for a nonrandom pattern in security prices.
Test of Semistrong-Form Efficiency — Semistrong-form efficiency has been tested by assessing how security returns adjust to particular announcements.
Test of Strong-Form Efficiency — Tests of strong-form efficiency are difficult because the inside information used is not publicly available and cannot be properly tested.

Question 41

Valuation of Foreign Stocks

Answer 41

Price–Earnings Method
The expected earnings per share are multiplied by the PE ratio (based on the firm’s risk and local industry) to determine the price of the stock.
The PE ratio for an industry may change, especially when the industry consists of few firms.
The value derived by this method is denominated in the local foreign currency.
Dividend Discount Model — Can be applied by discounting the stream of expected dividends while adjusting to account for expected exchange rate movements.

Question 42

International Market Efficiency and Measuring Performance from Investing in Foreign Stocks

Answer 42

International Market Efficiency
Some foreign markets are likely to be inefficient because a small number of analysts and portfolio managers may monitor the stocks.

Measuring Performance from Investing in Foreign Stocks
The returns from investing in foreign stocks is most properly measured in terms of the investor’s objectives

Question 43

Performance from Global Diversification

Answer 43

Research has demonstrated that investors in stocks can benefit by diversifying internationally.
Diversification among Emerging Stock Markets:
The correlation between stocks of different countries is low, so investors can reduce risk by including some stocks from these markets in their portfolios.

Question 44

Stocks are commonly valued using

Answer 44

using the price–earnings (PE) method, the dividend discount model, or the free cash flow model. The PE method applies the industry PE ratio to the firm’s earnings to derive its value. The dividend discount model estimates the value as the present value of expected future dividends. The free cash flow model is based on the present value of future cash flows.

Question 45

When applying the free cash flow model to value a stock,

Answer 45

a required rate of return must be estimated. One method of estimating the required rate of return is to apply the capital asset pricing model, in which the required return depends on the risk-free interest rate and the firm’s beta.

Question 46

Stock prices are affected by

Answer 46

those factors that affect future cash flows or the required rate of return by investors. Economic conditions, market conditions, and firm-specific conditions can affect a firm’s cash flows or the required rate of return.

Question 47

The risk of a stock is measured by

Answer 47

its volatility, its beta, or its value-at-risk estimate. Investors are giving more attention to risk measurement in light of abrupt downturns in the prices of some stocks in recent years.

Question 48

The Sharpe index and the Treynor index are

Answer 48

common methods of measuring risk-adjusted stock performance

Question 49

Stock market efficiency implies that

Answer 49

that stock prices reflect all available information. Weak-form efficiency suggests that security prices reflect all trade-related information, such as historical security price movements and the volume of securities trades. Semistrong-form efficiency suggests that security prices fully reflect all public information. Strong-form efficiency suggests that security prices fully reflect all information, including private or insider information. Evidence supports weak-form efficiency to a degree, but there is less support for semistrong or strong-form efficiency.