/*! 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 1 Calculating cost of Equity The W... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Calculating cost of Equity The Wind Rider Co. just issued a dividend of \(\$ 2.10\) per share on its common stock. The company is expected to maintain a constant 7 percent growth rate in its dividends indefinitely. If the stock sells for \(\$ 40\) a share, what is the company's cost of equity?

Short Answer

Expert verified
The Wind Rider Co.'s cost of equity is approximately 5.62%, which is calculated using the Gordon Growth Model with the given dividend per share, growth rate, and stock price.

Step by step solution

01

Identify the given values

We are given the following information: - Dividend per share (D): $2.10 - Growth rate (g): 7% or 0.07 - Stock price (P): $40
02

Calculate the projected dividend for next year

According to the Gordon Growth Model, the projected dividend for next year (D1) is given by the formula: D1 = D * (1 + g) Where D is the current dividend per share, and g is the dividend growth rate. Using the given values, D1 = $2.10 * (1 + 0.07) D1 = $2.10 * 1.07 D1 = $2.247
03

Calculate the cost of equity (k)

Now, we have the projected dividend for next year (D1) and the stock price (P). We can calculate the cost of equity (k) using the formula: k = D1 / P Plugging in the values, k = \(2.247 / \)40 k = 0.056175 To express the cost of equity as a percentage, we can multiply it by 100: k = 0.056175 * 100 k = 5.6175%
04

Present the result

The Wind Rider Co.'s cost of equity is approximately 5.62%.

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.

Gordon Growth Model
The Gordon Growth Model, also known as the Dividend Discount Model, is a popular method used for valuing a stock, particularly when a company experiences constant growth in dividends. This model is simple yet powerful, as it helps investors estimate the present value of a stock based on the future series of dividends that the stock will provide.
To use this model, you'll need to know:
  • The current dividend per share (D)
  • The expected constant growth rate of dividends (g)
  • The stock's current market price (P)

The formula for the price of a stock using the Gordon Growth Model is:\[ P = \frac{D1}{k - g} \]where:
  • P is the current stock price
  • D1 is the dividend expected next year
  • k is the cost of equity
  • g is the growth rate

This model is particularly useful for firms with stable dividend growth rates, making it ideal for companies with predictable and stable earnings.
Dividend Growth Rate
The dividend growth rate is a critical component in valuing stocks using the Gordon Growth Model. It represents how quickly a company's dividends are expected to grow over time. Typically expressed as a percentage, the growth rate is integral in forecasting future dividends, a key factor in investment decisions.
Here's why it's important:
  • Helps in future dividend projections
  • Influences the valuation of a stock
  • Shows the potential for income growth for investors

To compute the future dividend using this rate from a current dividend (D0), the calculation is:\[ D1 = D0 \times (1 + g) \]where g is the growth rate.
A higher growth rate may suggest that a company is reinvesting in its operations profitably, leading to potentially higher returns for investors. However, unrealistic growth rates can lead to overvaluation, so it must be determined carefully.
Stock Valuation
Stock valuation is essential when assessing the worth of a company's shares. The goal is to determine an appropriate price of the stock based on current and future dividends, intrinsic value, and the company's financial performance.
Here are a few methods used in stock valuation:
  • Dividend Discount Model: Uses future expected dividends and discount rates to determine stock price.
  • Price-Earnings Ratio (P/E): Relates the company's current share price to its per-share earnings.
  • Discounted Cash Flow (DCF): Estimates a stock's value using its expected future cash flows.

The Gordon Growth Model is a specific type of Dividend Discount Model often used for steady companies with predictable dividend growth. Stock valuation techniques require understanding both quantitative data (like financial statements) and qualitative factors (like management quality). The result helps in making an informed investment decision on whether to buy, sell, or hold a stock.
Financial Calculations
Financial calculations are fundamental to investing and stock valuation. They involve various formulas and arithmetic methods to determine key financial metrics that aid in decision-making.
Key aspects of financial calculations include:
  • Cost of Equity: Represents the return a company requires to decide whether to proceed with a capital project. Calculated using models like CAPM or, as shown, the Gordon Growth Model.
  • Current and Future Dividends: Projecting dividends helps assess future income potential from an investment.
  • Growth Rates: Critical in predicting a company's future performance and sustainability.

For accurate financial analysis, understanding how to perform these calculations is crucial. In the step by step solution provided, we calculated the cost of equity for Wind Rider Co. by predicting next year's dividend and using the stock price. Such calculations are essential for strategic financial planning and investment analysis.

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

Calculating cost of Equity The Tubby Ball Corporation's common stock has a beta of \(1.15 .\) If the risk-free rate is 5 percent and the expected return on the market is 12 percent, what is Tubby Ball's cost of equity capital?

Calculating cost of Debt Jiminy's Cricket Farm issued a 30 -year, 9 percent semiannual bond 8 years ago. The bond currently sells for 105 percent of its face value. The company's tax rate is 35 percent. a. What is the pretax cost of debt? b. What is the aftertax cost of debt? c. Which is more relevant, the pretax or the aftertax cost of debt? Why?

An all-equity firm is considering the following projects $$\begin{array}{|ccc|} \hline \text { Project } & \text { Beta } & \text { Expected Return } \\ \hline \mathrm{W} & .70 & 11 \% \\ \mathrm{X} & .95 & 13 \\ \mathrm{Y} & 1.05 & 14 \\ \mathrm{Z} & 1.60 & 16 \\ \hline \end{array}$$ The T-bill rate is 5 percent, and the expected return on the market is 12 percent. a. Which projects have a higher expected return than the firm's 12 percent cost of capital? b. Which projects should be accepted? c. Which projects would be incorrectly accepted or rejected if the firm's overall cost of capital were used as a hurdle rate?

Project Evaluation This is a comprehensive project evaluation problem bringing together much of what you have learned in this and previous chapters. Suppose you have been hired as a financial consultant to Defense Electronics, Inc. (DEI), a large, publicly traded firm that is the market share leader in radar detection systems (RDSs). The company is looking at setting up a manufacturing plant overseas to produce a new line of RDSs. This will be a five-year project. The company bought some land three years ago for \(\$ 6\) million in anticipation of using it as a toxic dump site for waste chemicals, but it built a piping system to safely discard the chemicals instead. The land was appraised last week for \(\$ 9.2\) million. The company wants to build its new manufacturing plant on this land; the plant will cost \(\$ 14\) million to build. The following market data on DEI's securitics are current: DEI uses G. M. Wharton as its lead underwriter. Wharton charges DEI spreads of 9 percent on new common stock issues, 7 percent on new preferred stock issues,

Flotation costs and NPV Photochronograph Corporation (PC) manufactures time series photographic equipment. It is currently at its target debt-equity ratio of \(1.2 .\) It's considering building a new \(\$ 40\) million manufacturing facility. This new plant is expected to generate aftertax cash flows of \(\$ 5.5\) million in perpetuity. There are three financing options: 1\. A new issue of common stock. The flotation costs of the new common stock would be 8 percent of the amount raised. The required return on the company's new equity is 18 percent. 2\. A new issue of 20 -year bonds. The flotation costs of the new bonds would be 3 percent of the proceeds. If the company issues these new bonds at an annual coupon rate of 9 percent, they will sell at par. 3\. Increased use of accounts payable financing. Because this financing is part of the company's ongoing daily business, it has no flotation costs and the company assigns it a cost that is the same as the overall firm WACC. Management has a target ratio of accounts payable to long-term debt of .25 . (Assume there is no difference between the pretax and aftertax accounts payable cost.)

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.