   Chapter 10, Problem 8P Fundamentals of Financial Manageme...

14th Edition
Eugene F. Brigham + 1 other
ISBN: 9781285867977

Solutions

Chapter
Section Fundamentals of Financial Manageme...

14th Edition
Eugene F. Brigham + 1 other
ISBN: 9781285867977
Textbook Problem

COST OF COMMON EQUITY AND WACC Pattern Paints Corporation has a target capital structure of 40% debt and 60% common equity, with no preferred stock. Its before-tax cost of debt is 12%, and its marginal tax rate is 40%. The current stock price is P0 = $22.50. The last dividend was D0 =$2.00, and it is expected to grow at a 7% constant rate. What is its cost of common equity and its WACC?

Summary Introduction

To identify: The cost of common equity and WACC.

Cost of Equity:

It is the cost of the company while raising finance by issuing equity. It is earnings from the investment to the firm’s equity investors. It is the return to the stockholder holders’ equity investments.

Weighted Average Cost of Capital (WACC):

It is the weighted average cost of all the sources through which firm finances its capital. It is that rate that company will pay to all for raising finance. It can be termed as firm’s cost of capital.

The company raises money through various sources such as common stock, preference share debt the WACC is calculated taking the relative weight of each item of capital structure.

The formula to calculate WACC is,

WACC=Wdrd(1t)+WPrp+Wcrs

Where,

• Wd is the weight of the debt.
• WP is the weight of the preferred stock.
• Wc is the weight of the equity.
• rd is cost of the debt.
• rP is cost of the preferred stock.
• rc is the cost of the equity.
Explanation

Given,

Last dividend is $2. Growth rate is 7% or 0.07. Current price of stock is$22.50.

The formula to calculate cost of common equity is,

rs=D0(1+g)P0+g

Where,

• D0 is the last dividend.
• rs is the rate of return on equity.
• P0 is the current price of the stock.
• g is the constant growth rate.

Substitute $2 for D0,$22.50 for P0 and 0.07 for g.

rs=$2(1+0.07)$22.50+0.07=0.0951+0.07=0.1651=16.51%

Thus cost of common equity is 16.51%.

Given,

After tax cost of debt is 7.2% or 0.072 (working note)

Weight of debt is 40%.

Cost of common equity is 16.51%or 0.1651.

Weight of equity is 60%

The company does not have any preferred stock. The formula to calculate WACC is,

WACC=Wdrd+Wcrs

Where,

• Wd is the weight of the debt.
• Wc is the weight of the equity

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