/*! 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 3 Percy Motors has a target capita... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Percy Motors has a target capital structure of 40 percent debt and 60 percent common equity, with no preferred stock. The yield to maturity on the company's outstanding bonds is 9 percent, and its tax rate is 40 percent. Percy's CFO estimates that the company's WACC is 9.96 percent. What is Percy's cost of common equity?

Short Answer

Expert verified
Percy's cost of common equity is 13%.

Step by step solution

01

Identify the given data

The exercise gives us the following data: target capital structure with 40% debt and 60% equity, yield to maturity on bonds as 9%, a tax rate of 40%, and a weighted average cost of capital (WACC) of 9.96%.
02

Write the formula for WACC

The WACC is calculated using the formula: \[WACC = w_d \times r_d \times (1 - T) + w_e \times r_e\]where \(w_d\) is the weight of debt, \(r_d\) is the cost of debt (bond yield), \(T\) is the tax rate, \(w_e\) is the weight of equity, and \(r_e\) is the cost of equity.
03

Substitute known values in the WACC formula

Substitute the known values into the WACC formula: \[9.96\% = 0.4 \times 9\% \times (1 - 0.4) + 0.6 \times r_e\] Here, \(w_d = 0.4\), \(r_d = 9\%\), \(T = 0.4\), \(w_e = 0.6\).
04

Calculate the after-tax cost of debt

First, calculate the after-tax cost of debt: \[0.4 \times 9\% \times (1 - 0.4) = 0.0216 \, \text{or} \, 2.16\%\] This is the contribution of debt to the WACC.
05

Solve for the cost of equity \(r_e\)

Substitute the after-tax cost of debt back into the WACC equation and solve for \(r_e\): \[9.96\% = 2.16\% + 0.6 \times r_e\] \[9.96\% - 2.16\% = 0.6 \times r_e\] \[7.8\% = 0.6 \times r_e\] \[r_e = \frac{7.8\%}{0.6} = 13\%\]
06

Conclusion

The cost of common equity \(r_e\) has been calculated as 13%. This is the required return on Percy's equity investments given the company's target capital structure.

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.

Cost of Equity
The cost of equity represents the return a company needs to provide to its shareholders to compensate them for their investment risk. It is a crucial part of a company's Weighted Average Cost of Capital (WACC), which measures a firm's cost of financing from all sources, including equity. In the exercise about Percy Motors, we use the formula for WACC to find the cost of equity, denoted as \(r_e\).

When investors allocate funds to a company, they expect a certain rate of return reflecting the risk of their investment. The calculated cost of equity for Percy Motors was found to be 13%.

This percentage is crucial for decision-makers, as it serves as a benchmark for evaluating investment opportunities. If a potential investment is projected to generate returns above this rate, it may be considered profitable.
  • It forms part of a strategic guide for optimizing capital structure decisions.
  • It influences dividend decisions and share repurchase strategies.
  • An understanding of cost equity can aid investors in comparative analyses with other firms.
Understanding the cost of equity helps ensure investments meet or exceed expected returns, thus sustaining the company's growth and competitive advantage.
Capital Structure
The capital structure of a company is the mix of different forms of capital it uses for its operations and growth, primarily debt and equity. For Percy Motors, their target capital structure consists of 40% debt and 60% equity.

This strategic mix affects the overall cost of capital, since each component has different cost implications. Equity is typically more expensive than debt because equity investors assume more risk, expecting higher returns. Debt, such as bonds, has a fixed cost but offers a tax shield through deductible interest expenses.

  • Capital structure decisions impact financial risk and business risk.
  • Debt reduces taxable income due to interest payments, known as the 'tax shield.'
  • The chosen structure should align with corporate strategy and market conditions.
For firms like Percy Motors, balancing debt and equity is critical in maintaining financial health and maximizing returns for shareholders.
Yield to Maturity
Yield to maturity (YTM) is the total return anticipated on a bond if the bond is held until it matures. Used by investors as a key measure, YTM accounts for the bond's current market price, par value, coupon interest rate, and time to maturity.

In the Percy Motors example, the bonds have a yield to maturity of 9%. This indicates what investors expect to earn annually from the bond until it matures.

  • It assumes all payments are reinvested at the same rate.
  • Serves as an estimate for evaluating bond performance.
  • Helps in comparing bonds with varying terms and credit risks.
YTM is essential for calculating the after-tax cost of debt in WACC, which affects the overall cost structure of capital. It's a predictive measure allowing investors and the company to make informed financial strategies.
Tax Rate
The tax rate influences numerous financial decisions and calculations for businesses. It is used in calculating the after-tax cost of debt, an element of the Weighted Average Cost of Capital (WACC). Percy Motors operates with a tax rate of 40%.

This rate directly affects how the cost of debt is computed, since interest payments on debt are tax-deductible, thus lowering the real cost to the firm. Known as the 'tax shield,' this benefit is crucial for optimizing overall capital costs.

  • The tax rate impacts after-tax earnings available to equity holders.
  • Higher tax rates may encourage corporations to rely on debt financing.
  • It influences corporate strategies, like capital investment and dividends.
Understanding the tax rate's role in financial calculations helps in strategic planning and improving a company's financial efficiency. Percy Motors leverages its tax rate to optimize its WACC and improve stakeholder value.

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

Sidman Products' common stock currently sells for \(\$ 60\) a share. The firm is expected to earn \(\$ 5.40\) per share this year and to pay a year-end dividend of \(\$ 3.60,\) and it finances only with common equity. a. If investors require a 9 percent return, what is the expected growth rate? 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 \(\text { rate } )(\mathrm{ROE}) .]\)

The Bouchard Company's EPS was \(\$ 6.50\) in \(2005,\) up from \(\$ 4.42\) in \(2000 .\) The company pays out 40 percent of its earnings as dividends, and its common stock sells for \(\$ 36\) a. Calculate the past growth rate in earnings. (Hint: This is a 5-year growth period.) b. The last dividend was \(\mathrm{D}_{0}=0.4(\$ 6.50)=\$ 2.60 .\) Calculate the next expected dividend, \(\mathrm{D}_{1},\) assuming that the past growth rate continues. c. What is Bouchard's cost of retained earnings, \(r_{s} ?\)

The earnings, dividends, and common 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 it will pay a dividend of \(\$ 2.14\) at the end of the current year. a. Using the DCF 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 \(r_{s}\) be based on the bondyield-plus-risk-premium approach, using the midpoint of the risk premium range? d. Assuming you have equal confidence in the inputs used for the three approaches, what is your estimate of Carpetto's cost of common equity?

Trivoli Industries plans to issue a \(\$ 100\) par perpetual preferred stock with an 11 percent dividend. It is currently selling for \(\$ 97.00\) but flotation costs will be 5 percent of the market price, so the net price will be \(\$ 92.15\) per share. What is the cost of the preferred stock, including flotation?

After-tax cost of debt The Heuser Company's currently outstanding bonds have a 10 percent coupon and a 12 percent yield to maturity. Heuser believes it could issue new bonds at par that would provide a similar yield to maturity. If its marginal tax rate is 35 percent, what is Heuser's after-tax cost of debt?

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.