/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 19 You buy a share of The Ludwig Co... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

You buy a share of The Ludwig Corporation stock for \(\$ 21.40 .\) You expect it to pay dividends of \(\$ 1.07, \$ 1.1449,\) and \(\$ 1.2250\) in Years \(1,2,\) and \(3,\) respectively, and you expect to sell it at a price of \(\$ 26.22\) at the end of 3 years. a. Calculate the growth rate in dividends. b. Calculate the expected dividend yield. c. Assuming that the calculated growth rate is expected to continue, you can add the dividend yield to the expected growth rate to obtain the expected total rate of return. What is this stock's expected total rate of return?

Short Answer

Expert verified
Dividend growth rate: 7%, Dividend yield: 5%, Total return: 12%.

Step by step solution

01

Calculate the Growth Rate in Dividends (Step 1)

The dividend growth rate can be calculated using the formula for the growth rate: \[ g = \frac{D_2}{D_1} - 1 \]Where \(D_1\) is the dividend in the first year and \(D_2\) is the dividend in the second year. So, \[ g = \frac{1.1449}{1.07} - 1 \approx 0.07 \text{ or } 7\% \] This indicates the dividends grow at a rate of 7\% per year.
02

Calculate the Expected Dividend Yield (Step 2)

The dividend yield is calculated as the dividend of the next year divided by the current stock price. Using Year 1 dividend:\[ \text{Dividend Yield} = \frac{1.07}{21.40} \approx 0.05 \text{ or } 5\% \] So, the expected dividend yield is 5\%.
03

Calculate the Expected Total Rate of Return (Step 3)

The expected total rate of return is the sum of the dividend yield and the growth rate. If the growth rate continues as calculated:\[ \text{Total Rate of Return} = \text{Dividend Yield} + g = 0.05 + 0.07 = 0.12 \text{ or } 12\% \] Therefore, the expected total rate of return on the stock is 12\%.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

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

Expected Dividend Yield
The expected dividend yield is a fundamental concept in stock investing. Simply put, it represents the amount of cash you can expect to earn from dividends as a percentage of the initial stock investment. Think of it as the income you might receive on your investment, expressed as a percentage.

In the context of The Ludwig Corporation stock, the expected dividend yield is calculated using the always important formula:
  • Formula: \( \text{Dividend Yield} = \frac{\text{Next Year's Dividend}}{\text{Current Stock Price}} \)
By substituting the expected dividend for Year 1, which is \( \\(1.07 \), and the buying price of the stock, \( \\)21.40 \), we get:
  • \( \frac{1.07}{21.40} \approx 0.05 \text{ or } 5\% \)
This indicates that holding the stock offers a 5% return in terms of dividends based on your initial purchase price. It's important to evaluate the dividend yield as it helps investors understand the potential cash income from the stock relative to their investment cost.
Total Rate of Return
When investing in stocks, understanding the total rate of return is key to assessing the stock's overall profitability. It places investor returns into a comprehensive framework by considering both the dividend income and any potential capital gains or growth.

The total rate of return for a stock, like the one from The Ludwig Corporation, can be found by summing its expected dividend yield and growth rate. The calculations are straightforward:
  • Formula:
    \( \text{Total Rate of Return} = \text{Dividend Yield} + g \)
Where "g" is the growth rate of the stock's dividends, calculated as 7% in this case. Given that the dividend yield was found to be 5%, we calculate:
  • \( \text{Total Rate of Return} = 0.05 + 0.07 = 0.12 \text{ or } 12\% \)
This 12% return comprises both the dividend income and the expected increase in stock price, providing a holistic view of the potential investment benefit. Understanding this rate helps investors decide if the stock meets their return requirements.
Stock Valuation
Stock valuation is a critical practice for investors seeking to determine the worth of a stock and make informed investment decisions. It involves understanding not only the current and expected dividends but also anticipated future growth.

For The Ludwig Corporation, valuation starts by analyzing the dividends expected over the coming years: \( \\(1.07 \), \( \\)1.1449 \), and \( \\(1.2250 \) for Years 1, 2, and 3 respectively. This forecast provides a basis for calculating potential earnings from holding the stock.

Additional to the dividend estimates, investors look at price appreciation possibilities—like the expected selling price of \( \\)26.22 \) at the end of Year 3—which combined with dividends, influences a stock's attractiveness. By computing dividend yield, growth rates, and future resale prices, investors gauge if the stock's current market price aligns with its intrinsic value.

Effective stock valuation, therefore, melds dividend analysis with growth assessment, equipping investors to predict future returns and make strategic buy, hold, or sell decisions.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

What will be the nominal rate of return on a preferred stock with a \(\$ 100\) par value, a stated dividend of 8 percent of par, and a current market price of \((\mathrm{a}) \$ 60,(\mathrm{b}) \$ 80,(\mathrm{c})\) \(\$ 100,\) and \((d) \$ 140 ?\)

Thomas Brothers is expected to pay a \(\$ 0.50\) per share dividend at the end of the year (i.e., \(D_{1}=\$ 0.50\) ). The dividend is expected to grow at a constant rate of 7 percent a year. The required rate of return on the stock, \(\mathrm{k}_{\mathrm{s}}\), is 15 percent. What is the value per share of the company's stock?

Warr Corporation just paid a dividend of \(\$ 1.50\) a share (i.e., \(D_{0}=\$ 1.50\) ). The dividend is expected to grow 5 percent a year for the next 3 years, and then 10 percent a year thereafter. What is the expected dividend per share for each of the next 5 years?

Today is December \(31,2001 .\) The following information applies to Vermeil Airlines: \(\bullet\) After-tax, operating income \([\mathrm{EBIT}(1-\mathrm{T})]\) for 2002 is expected to be \(\$ 500\) million. \(\bullet\) The company's depreciation expense for 2002 is expected to be \(\$ 100\) million. \(\bullet\) The company's capital expenditures for 2002 are expected to be \(\$ 200\) million. \(\bullet\) No change is expected in the company's net operating working capital. \(\bullet\) The company's free cash flow is expected to grow at a constant rate of 6 percent per year. \(\bullet\) The company's cost of equity is 14 percent. \(\bullet\) The company's WACC is 10 percent. \(\bullet\) The market value of the company's debt is \(\$ 3\) billion. \(\bullet\) The company has 200 million shares of stock outstanding. Using the free cash flow approach, what should the company's stock price be today?

Fee Founders has preferred stock outstanding that pays a dividend of \(\$ 5\) at the end of each year. The preferred stock sells for \(\$ 60\) a share. What is the preferred stock's required rate of return?

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.