/*! 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 10 A stock is trading at \(\$ 80\) ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 10

A stock is trading at \(\$ 80\) per share. The stock is expected to have a year- end dividend of S4 per share \(\left(\mathrm{D}_{1}=\$ 4.00\right),\) which is expected to grow at some constant rate \(\mathrm{g}\) throughout time. The stock's required rate of return is 14 percent. If you are an analyst who believes in efficient markets, what would be your forecast of \(\mathrm{g}\) ?

Short Answer

Expert verified
The forecasted growth rate \( g \) is 9\%.

Step by step solution

01

Understand the Dividend Discount Model

The Dividend Discount Model (DDM) for valuing a stock is given by \( P_0 = \frac{D_1}{r - g} \), where \( P_0 \) is the current stock price, \( D_1 \) is the expected dividend, \( r \) is the required rate of return, and \( g \) is the growth rate of the dividend.
02

Plug in Known Values

We know \( P_0 = \\(80 \), \( D_1 = \\)4 \), and \( r = 0.14 \) (14%). Substituting these values into the formula gives:\\[ 80 = \frac{4}{0.14 - g} \]
03

Rearrange the Equation

To find \( g \), first rearrange the equation to solve for \( 0.14 - g \):\\[ 0.14 - g = \frac{4}{80} \]
04

Simplify the Equation

Calculate \( \frac{4}{80} \) which simplifies to \( 0.05 \). This gives us:\\[ 0.14 - g = 0.05 \]
05

Solve for g

Solve the equation \( 0.14 - g = 0.05 \) for \( g \):\\[ g = 0.14 - 0.05 \] \\[ g = 0.09 \]
06

Convert Growth Rate to Percentage

Since the growth rate \( g \) is in decimal form, convert it to a percentage by multiplying by 100:\\[ g = 0.09 \times 100 = 9\% \]

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 91影视!

Key Concepts

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

Stock Valuation
Stock valuation is the process of determining the intrinsic value of a stock. This means finding out how much a stock is truly worth based on various models and assumptions, rather than just its current market price.
The Dividend Discount Model (DDM) is one of the most used methods to value a stock, especially when the company is known for paying consistent dividends. It helps investors understand if a stock is overpriced or undervalued.
The basic formula for DDM is:
  • \( P_0 = \frac{D_1}{r - g} \)
This formula requires a few key inputs:
  • \( P_0 \): Current price of the stock.
  • \( D_1 \): Dividend expected at the end of the year.
  • \( r \): Required rate of return.
  • \( g \): Growth rate of dividends.
Investors use this model to determine if a stock's trading price aligns with its calculated intrinsic value, making it an essential tool in stock analysis.
Required Rate of Return
The required rate of return is a crucial concept in finance as it represents the minimum percentage of return an investor expects to earn from an investment to consider it worthwhile.
This rate accounts for the risk of the investment, inflation, and opportunity cost. In our exercise, it is represented as 14%.
It can vary based on different investor preferences or market conditions. Risk plays a significant role here; the higher the perceived risk associated with an investment, the higher the required rate of return. This rate helps investors decide if they should invest in a particular stock or explore other options.
  • A higher rate indicates a riskier investment compared to others with a lower rate.
  • It is used in the DDM to help calculate stock value and forecast future prices based on expected risk-adjusted returns.
This rate is an integral component of the stock valuation process, aiding in the determination of what investors believe is a fair market value for the stock.
Dividend Growth Rate
The dividend growth rate is the expected annual percentage increase in dividends paid to shareholders. This rate is a crucial factor in stock valuation as it impacts the future income investors can receive.
In the Dividend Discount Model, it is denoted by \( g \).
The growth rate indicates how much an investor can expect the company to increase its dividend over time. It is a valuable measure of a company鈥檚 profitability and growth potential.There are several ways to estimate \( g \):
  • Historical dividend growth: using past data to predict future increases.
  • Analyst forecasts: considering expert estimates and market trends.
  • Company earnings growth: analyzing increases in earnings that may hint at dividend growth potential.
In our example, after calculations, \( g \) came out to be 9%. This means investors can expect a 9% increase in dividends annually.Ultimately, understanding the dividend growth rate aids investors in making well-informed decisions regarding stock purchases, as it significantly affects stock valuation and future income predictions.

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

Ezzell Corporation issued preferred stock with a stated dividend of 10 percent of par. Preferred stock of this type currently yields 8 percent, and the par value is \(\$ 100\). Assume dividends are paid annually. a. What is the value of Ezzell's preferred stock? b. Suppose interest rate levels rise to the point where the preferred stock now yields 12 percent. What would be the value of Ezzell's preferred stock?

Martell Mining Company's ore reserves are being depleted, so its sales are falling. Also, its pit is getting deeper each year, so its costs are rising. As a result, the company's earnings and dividends are declining at the constant rate of 5 percent per year. If \(\mathrm{D}_{0}=\$ 5\) and \(\mathrm{k}_{\mathrm{s}}=15 \%,\) what is the value of Martell Mining's stock?

Robert Balik and Carol Kiefer are senior vice-presidents of the Mutual of Chicago Insurance Company. They are co-directors of the company's pension fund management division, with Balik having responsibility for fixed income securities (primarily bonds) and Kiefer being responsible for equity investments. A major new client, the California League of Cities, has requested that Mutual of Chicago present an investment seminar to the mayors of the represented cities, and Balik and Kiefer, who will make the actual presentation, have asked you to help them. To illustrate the common stock valuation process, Balik and Kiefer have asked you to analyze the Bon Temps Company, an employment agency that supplies word processor operators and computer programmers to businesses with temporarily heavy workloads. You are to answer the following questions. a. Describe briefly the legal rights and privileges of common stockholders. b. (1) Write out a formula that can be used to value any stock, regardless of its dividend pattern. (2) What is a constant growth stock? How are constant growth stocks valued? (3) What happens if a company has a constant g that exceeds its \(\mathrm{k}_{\mathrm{s}}\) ? Will many stocks have expected \(\mathrm{g}>\mathrm{k}_{\mathrm{s}}\) in the short run (that is, for the next few years)? In the long run (that is, forever)? c. Assume that Bon Temps has a beta coefficient of \(1.2,\) that the risk-free rate (the yield on T-bonds) is 7 percent, and that the required rate of return on the market is 12 percent. What is the required rate of return on the firm's stock? d. Assume that Bon Temps is a constant growth company whose last dividend (D \(_{0},\) which was paid yesterday) was \(\$ 2.00\) and whose dividend is expected to grow indefinitely at a 6 percent rate. (1) What is the firm's expected dividend stream over the next 3 years? (2) What is the firm's current stock price? (3) What is the stock's expected value 1 year from now? (4) What are the expected dividend yield, the capital gains yield, and the total return during the first year? e. Now assume that the stock is currently selling at \(\$ 30.29\) What is the expected rate of return on the stock? f. What would the stock price be if its dividends were expected to have zero growth? g. Now assume that Bon Temps is expected to experience supernormal growth of 30 percent for the next 3 years, then to return to its long-run constant growth rate of 6 percent. What is the stock's value under these conditions? What is its expected dividend yield and capital gains yield in Year 1? Year 4? h. Suppose Bon Temps is expected to experience zero growth during the first 3 years and then to resume its steady-state growth of 6 percent in the fourth year. What is the stock's value now? What is its expected dividend yield and its capital gains yield in Year 1? Year 4? i. Finally, assume that Bon Temps' earnings and dividends are expected to decline by a constant 6 percent per year, that is, \(g=-6 \% .\) Why would anyone be willing to buy such a stock, and at what price should it sell? What would be the dividend yield and capital gains yield in each year? j. Bon Temps embarks on an aggressive expansion that requires additional capital. Management decides to finance the expansion by borrowing \(\$ 40\) million and by halting dividend payments to increase retained earnings. The projected free cash flows for the next 3 years are \(-\$ 5\) million, \(\$ 10\) million, and \(\$ 20\) million. After the third year, free cash flow is projected to grow at a constant 6 percent. The overall cost of capital is 10 percent. What is Bon Temps' total value? If it has 10 million shares of stock and \(\$ 40\) million total debt, what is the price per share? k. What does market equilibrium mean? 1\. If equilibrium does not exist, how will it be established? m. What is the Efficient Markets Hypothesis, what are its three forms, and what are its implications? n. Phyfe Company recently issued preferred stock. It pays an annual dividend of \(\$ 5,\) and the issue price was \(\$ 50\) per share. What is the expected return to an investor on this preferred stock?

Hart Enterprises recently paid a dividend, \(\mathrm{D}_{0},\) of \(\$ 1.25 .\) The company expects to have supernormal growth of 20 percent for 2 years before the dividend is expected to grow at a constant rate of 5 percent. The firm's cost of equity is 10 percent. a. What year is the terminal, or horizon, date? b. What is the firm's horizon, or terminal, value? c. What is the firm's intrinsic value today, \(\hat{\mathrm{P}}_{0}\) ?

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?
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
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.