**CFA Level 1 - Equity Investments**

**Earnings Per Share of a Stock Market Series**

The earnings per share of a stock market series can be calculated as follows:

= the operating margin is typically calculated as a percentage of sales

Assuming the following estimates for a stock market series, sales per share = $100.00, OM = 50%, depreciation of $20.00, interest of $2.00 and a corporate tax rate of 40%, calculate the forecasted EPS of the stock market series?

EPS = [($100.00)(50%) - $20.00 - $2.00](1-0.40) = $16.80 per share

Similar to determining the earnings multiplier of a stock, the earnings multiplier of a stock market series can be derived by the DDM.

**Formula 13.8**EPS_{stock market series} = [(sales)( |

__Where:__**Sales**= sales per share of the estimated series is determined through regression**OM**

**Depreciation**= this is determined by either continuing the trend of the current depreciation or focusing on the expected capital expenditures and how that number relates to future dividends.**Interest**= interest is determined by outstanding debt and the interest rate on that debt.**Example: Calculate the EPS of a stock market series**Assuming the following estimates for a stock market series, sales per share = $100.00, OM = 50%, depreciation of $20.00, interest of $2.00 and a corporate tax rate of 40%, calculate the forecasted EPS of the stock market series?

**Answer:**EPS = [($100.00)(50%) - $20.00 - $2.00](1-0.40) = $16.80 per share

**The Expected Return of a Stock Market Series**Similar to determining the earnings multiplier of a stock, the earnings multiplier of a stock market series can be derived by the DDM.

**Formula 13.9**

Earnings multiplier |

In addition to the EPS, the series' required rate of return, growth and dividend are needed.

Next year's EPS for the series was determined to be $16.80. With a dividend of $4.00 for next year's dividend payout, calculate the stock series' earnings multiplier assuming 10% required return and 5% growth.

Earnings Multiplier

(0.10-0.05)

To determine value of the earnings multiplier for a stock market series the following inputs must be determined:

1.EPS

2. Dividend

3. Future price

4. Required rate of return

5. Expected growth rate

Next year's EPS must be forecasted to determine the earnings multiplier.

This return is derived from the CAPM model (R

The expected growth rate can be derived from both the retention rate (1-payout rate) and corporate ROE. (g = (retention rate)(ROE)). If the expected growth rate increases, the multiplier increases.

To determine the dividend to be used in the DDM, last year's dividend must first be calculated as the dividend in the DDM is next year's dividend. Given last year's corporate earnings as well as the corporate payout ratio, last year's dividend can be calculated. Using the growth rate derived above, next year's dividend can be determined.

The future price for the company can be derived with next year's dividend divided by the difference in the company's required rate of return and its growth rate.

The expected return rate of return of a stock market series, including the dividend, is the relative change that is anticipated in the stock market series over a specified time period.

For a stock market series, it is estimated to have a dividend of $5.00 and an ending value of $25. If the current value of the stock market series is $15, calculate the expected return for the stock market series.

E(R) =

$15

**Example: Calculate the expected P/E ratio of a stock market series**Next year's EPS for the series was determined to be $16.80. With a dividend of $4.00 for next year's dividend payout, calculate the stock series' earnings multiplier assuming 10% required return and 5% growth.

**Answer:**Earnings Multiplier

_{stock mkt series}=__4.00/16.80__= 4.7x(0.10-0.05)

**Estimate and Interpret the Earnings Multiplier of a Stock Market Series**To determine value of the earnings multiplier for a stock market series the following inputs must be determined:

1.EPS

2. Dividend

3. Future price

4. Required rate of return

5. Expected growth rate

**1. EPS**Next year's EPS must be forecasted to determine the earnings multiplier.

**2. Required Rate of Return**This return is derived from the CAPM model (R

_{series}= R_{f}+ B_{series}(R_{market }- R_{f}). If the required rate of return increases, the multiplier decreases.**3. Expected Growth Rate**The expected growth rate can be derived from both the retention rate (1-payout rate) and corporate ROE. (g = (retention rate)(ROE)). If the expected growth rate increases, the multiplier increases.

**4. Dividend**To determine the dividend to be used in the DDM, last year's dividend must first be calculated as the dividend in the DDM is next year's dividend. Given last year's corporate earnings as well as the corporate payout ratio, last year's dividend can be calculated. Using the growth rate derived above, next year's dividend can be determined.

**5.Future price**The future price for the company can be derived with next year's dividend divided by the difference in the company's required rate of return and its growth rate.

**The Expected Rate of Return for a Stock Market Series**The expected return rate of return of a stock market series, including the dividend, is the relative change that is anticipated in the stock market series over a specified time period.

**Formula 13.11**E(R) = End value of series + Dividend - Beg. value of serieBeg. value of series |

**Example: Calculate the expected rate of return for a stock market series**For a stock market series, it is estimated to have a dividend of $5.00 and an ending value of $25. If the current value of the stock market series is $15, calculate the expected return for the stock market series.

**Answer:**__($25 + $5 - $15)__= 1.0 or 100% return$15

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