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Chapter 10: Problem 16

Sidman Products' stock is currently selling for \(\$ 60\) a share. The firm is expected to earn \(\$ 5.40\) per share this year and to pay a year-end dividend of \(\$ 3.60\). a. If investors require a 9 percent return, what rate of growth must be expected for Sidman? b. If Sidman reinvests retained earnings in projects whose average return is equal to the stock's expected rate of return, what will be next year's EPS? [Hint: \(\mathrm{g}=(1-\) Payout rate)(ROE).]

Short Answer

Expert verified
The expected growth rate is 3%. Next year's EPS is approximately $5.56.

Step by step solution

01

Identify Known Quantities and Variables

We have the following known values:\[ P_0 = \\(60, \ D_1 = \\)3.60, \ \text{EPS} = \$5.40, \ r = 0.09 \]Where:- \( P_0 \): Current stock price- \( D_1 \): Expected dividend at the end of year- EPS: Earnings per share for this year- \( r \): Required rate of returnWe need to determine the expected growth rate \( g \) and next year's EPS.
02

Use Dividend Discount Model to Find g

According to the Dividend Discount Model (DDM) for a constant growth stock: \[ P_0 = \frac{D_1}{r - g} \]Plugging in the known values:\[ 60 = \frac{3.60}{0.09 - g} \]Solving for \( g \):\[ 60 \times (0.09 - g) = 3.60 \]\[ 5.4 - 60g = 3.60 \]\[ 60g = 5.4 - 3.6 \]\[ 60g = 1.8 \]\[ g = \frac{1.8}{60} \]\[ g = 0.03 \text{ or } 3\% \]
03

Calculate Payout and Retention Rates

Calculate the payout ratio:\[ \text{Payout Ratio} = \frac{D_1}{\text{EPS}} = \frac{3.60}{5.40} = \frac{2}{3} \]Hence, the retention ratio (reinvestment rate) is:\[ \text{Retention Ratio} = 1 - \text{Payout Ratio} = 1 - \frac{2}{3} = \frac{1}{3} \]
04

Verify Growth Rate Using ROE Formula

If Sidman invests all retained earnings to projects yielding the expected rate of return (\( r \)), according to:\[ g = (1 - \text{Payout Ratio}) \times ROE \]Let \( ROE = r = 0.09 \) since projects return equals to stock's expected return:\[ g = \frac{1}{3} \times 0.09 = 0.03 \text{ or } 3\% \]
05

Calculate Next Year's EPS

With all earnings reinvested at a return of 9%, the increase in EPS would be:\[ \text{Next Year's EPS} = \text{This Year EPS} \times (1 + g) \]\[ \text{Next Year's EPS} = 5.40 \times 1.03 = 5.562 \]Thus, next year's EPS is approximately \( 5.56 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Stock Valuation
Stock valuation is an essential concept for anyone interested in understanding the financial market and making informed investment decisions. It refers to the process of determining the intrinsic value of a company's stock. The idea is to identify whether a stock is overvalued or undervalued compared to its market price. Understanding this can help investors decide if they should buy, hold, or sell a particular stock.

One popular method of stock valuation is the Dividend Discount Model (DDM). The DDM is used to value a stock by considering the present value of its expected future dividends. For stocks that have a stable dividend payout, DDM can provide a reasonable estimation of a stock's value. The formula is expressed as:
  • \[ P_0 = \frac{D_1}{r - g} \]
Where:- \( P_0 \) is the current stock price,- \( D_1 \) is the dividend expected at the end of the year,- \( r \) is the required rate of return,- \( g \) is the expected growth rate of dividends.

By using this model, investors can determine how much a share is worth based on its future dividend potential and growth.
Earnings Per Share
Earnings Per Share (EPS) is a key indicator of a company's profitability. It represents a company's profit divided by the outstanding shares of its common stock. The formula to calculate EPS is:
  • EPS = \( \frac{\text{Net Income} - \text{Preferred Dividends}}{\text{Average Outstanding Shares}} \)
EPS is important because it gives investors a snapshot of a company's profitability on a per-share basis. This helps in comparing the profit across different companies in the same industry. A higher EPS indicates more profit is available to shareholders, which usually makes the stock more attractive to investors.

In the Sidman Products exercise, this year's EPS is given as \$5.40. By understanding what this figure signifies, we can determine how efficiently the company is operating and how much profit each share of stock is generating. It lays the groundwork for understanding future potential earnings and growth.
Payout Ratio
The Payout Ratio is an important metric in analyzing a company's financial health. It shows the proportion of earnings a company pays to its shareholders in the form of dividends. The Payout Ratio is calculated as:
  • Payout Ratio = \( \frac{D_1}{\text{EPS}} \)
A lower payout ratio often suggests that the company is reinvesting more earnings back into the business, which could potentially lead to growth. Meanwhile, a higher payout ratio indicates that more earnings are being distributed as dividends to shareholders. Each investor might have different preferences on what constitutes a desirable payout ratio.

In Sidman Products' situation, the Payout Ratio is calculated to be \( \frac{2}{3} \) or approximately 66.67%, which means the company distributes about two-thirds of its earnings to shareholders. Recognizing this ratio helps investors determine sustainability and potential for dividend increases.
Retention Ratio
The Retention Ratio complements the Payout Ratio by indicating the portion of earnings not paid out as dividends but retained in the company. It reflects the company's practice of reinvesting its earnings into its operations or other projects. This ratio is calculated by:
  • Retention Ratio = \( 1 - \text{Payout Ratio} \)
A higher retention ratio suggests that a company is focusing on growth and expansion by reinvesting its earnings. Conversely, a lower retention ratio might mean the company is distributing more profits to shareholders as dividends.

In the case of Sidman Products, the retention ratio is \( \frac{1}{3} \) or 33.33%, implying one-third of the company's earnings are retained. This retained portion can be a key indicator of a company's growth potential, as the reinvested earnings are expected to contribute to the company's future earnings and, in turn, possibly increase the stock鈥檚 EPS and market value.

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Most popular questions from this chapter

The Evanec Company's next expected dividend, \(D_{1}\), is \(\$ 3.18\); its growth rate is 6 percent; and the stock now sells for \(\$ 36 .\) New stock (external equity) can be sold to net the firm \(\$ 32.40\) per share. a. What is Evanec's cost of retained earnings, \(k\) ? b. What is Evanec's percentage flotation cost, \(\mathrm{F}\) ? c. What is Evanec's cost of new common stock, \(\mathrm{k}_{\mathrm{e}}\) ?

Here is the condensed balance sheet for Skye Computer Company (in thousands of dollars): Skye Computer's earnings per share last year were \(\$ 3.20 ;\) the stock sells for \(\$ 55,\) and last year's dividend was \(\$ 2.10 .\) A flotation cost of 10 percent would be required to issue new common stock. Skye's preferred stock pays a dividend of \(\$ 3.30\) per share, and new preferred could be sold at a price to net the company \(\$ 30\) per share. Security analysts are projecting that the common dividend will grow at a rate of 9 percent per year. The firm can issue additional long-term debt at an interest rate (or before-tax cost) of 10 percent, and its marginal tax rate is 35 percent. The market risk premium is 5 percent, the risk-free rate is 6 percent, and Skye's beta is \(1.516 .\) In its cost of capital calculations, the company considers only long-term capital, hence it disregards current liabilities for this purpose. a. Calculate the cost of each capital component, that is, the after-tax cost of debt, the cost of preferred stock, the cost of equity from retained earnings, and the cost of newly issued common stock. Use the DCF method to find the cost of common equity. b. Now calculate the cost of common equity from retained earnings using the CAPM method. c. What is the cost of new common stock, based on the CAPM? (Hint: Find the difference between \(k_{c}\) and \(k_{s}\) as determined by the \(D C F\) method, and add that differential to the CAPM value for \(\left.k_{s} .\right)\) d. If Skye Computer continues to use the same capital structure, what is the firm's WACC assuming (1) that it uses only retained earnings for equity and (2) that it expands so rapidly that it must issue new common stock? e. Suppose Skye is evaluating three projects with the following characteristics: Each project has a cost of \(\$ 1\) million. They will all be financed using the target mix of long-term debt, preferred stock, and common equity. The cost of the common equity for each project should be based on the beta estimated for the project. All equity will come from retained earnings. Equity invested in Project A would have a beta of 0.5 and an expected return of 9.0 percent. Equity invested in Project \(\mathrm{B}\) would have a beta of 1.0 and an expected return of 10.0 percent. Equity invested in Project \(C\) would have a beta of 2.0 and an expected return of 11.0 percent. Analyze the company's situation and explain why each project should be accepted or rejected.

The earnings, dividends, and stock price of Carpetto Technologies Inc. are expected to grow at 7 percent per year in the future. Carpetto's common stock sells for \(\$ 23\) per share, its last dividend was \(\$ 2.00\), and the company will pay a dividend of \(\$ 2.14\) at the end of the current year. a. Using the discounted cash flow approach, what is its cost of common equity? b. If the firm's beta is \(1.6,\) the risk-free rate is 9 percent, and the average return on the market is 13 percent, what will be the firm's cost of common equity using the CAPM approach? c. If the firm's bonds earn a return of 12 percent, what will \(\mathrm{k}_{\mathrm{s}}\) be using the bond-yieldplus-risk-premium approach? (Hint: Use the midpoint of the risk premium range.) d. On the basis of the results obtained in parts a through \(c,\) what would you estimate Carpetto's cost of common equity to be?

The following tabulation gives earnings per share figures for the Foust Company during the preceding 10 years. The firm's common stock, 7.8 million shares outstanding, is now \((1 / 1 / 02)\) selling for \(\$ 65\) per share, and the expected dividend at the end of the current year (2002) is 55 percent of the 2001 EPS. Because investors expect past trends to continue, g may be based on the earnings growth rate. (Note that 9 years of growth are reflected in the data.) $$\begin{array}{lccc}\text { YEAR } & \text { EPS } & \text { YEAR } & \text { EPS } \\ \hline 1992 & \$ 3.90 & 1997 & \$ 5.73 \\ 1993 & 4.21 & 1998 & 6.19 \\\1994 & 4.55 & 1999 & 6.68 \\ 1995 & 4.91 & 2000 & 7.22 \\\1996 & 5.31 & 2001 & 7.80\end{array}$$ The current interest rate on new debt is 9 percent. The firm's marginal tax rate is 40 percent. Its capital structure, considered to be optimal, is as follows: a. Calculate Foust's after-tax cost of new debt and common equity. Calculate the cost of cquity as \(k_{s}=D_{1} / P_{0}+g\) b. Find Foust's weighted average cost of capital.

The Bouchard Company's EPS was \(\$ 6.50\) in 2001 and \(\$ 4.42\) in \(1996 .\) The company pays out 40 percent of its earnings as dividends, and the stock sells for \(\$ 36\) a. Calculate the past growth rate in earnings. (Hint: This is a 5 -year growth period.) b. Calculate the next expected dividend per share, \(\mathrm{D}_{1} .\left(\mathrm{D}_{0}=0.4(\$ 6.50)=\$ 2.60 .\right) \mathrm{As}\) sume that the past growth rate will continue. c. What is the cost of retained earnings, \(k\), for the Bouchard Company?
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