Homework #3

The purpose of this assignment is to solidify your understanding on the applications of the cost

of capital topics. The scores of this assignment will help in assessing the following learning goal

of the course: “students successfully completing this course will be able to estimate and interpret

the cost of capital of a firm based on different capital structures”.

Instructions:

You are required to use a financial calculator or spreadsheet (Excel) to solve 10 problems related

to the cost of capital. You are required to show the following 3 steps for each problem (sample

questions and solutions are provided for guidance):

(i) Describe and interpret the assumptions related to the problem.

(ii) Apply the appropriate mathematical model to solve the problem.

(iii) Calculate the correct solution to the problem.

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Grading Rubric

Learning Objective

Subcomponent Not Submitted

0

Does Not Meet

Expectations

1

Meets Expectations

2

Exceeds Expectations

3

LO#4: Estimate and interpret the cost of capital of a firm based on different capital structures

The student will make and evaluate important assumptions in identification of appropriate cost of capital measures

No attempt made

Attempts to describe assumptions

Explicitly describes assumptions

Explicitly describes assumptions and provides rationale for why each assumption is appropriate. Show awareness that confidence in final conclusions is limited by the accuracy of the assumptions (e.g., provides descriptions about the assumptions of each of the cost of capital components; lists and describes each variable within the model)

The student will convert relevant information into various mathematical forms (e.g., equations, graphs, words)

No attempt made

Completes conversion of information but resulting mathematical portrayal is inappropriate or inaccurate

Completes conversion of information into mathematical portrayal

Relevant information is expressed in an insightful mathematical portrayal in a way that contributes to a further or deeper understanding (e.g., correct variables are selected and the mathematical model is portrayed with the correct variables)

The student will calculate the cost of each capital structure component and the average cost of capital

No attempt made

Calculations are attempted but are both unsuccessful and not comprehensive

Calculations are attempted to solve the problem but not comprehensive

Calculations attempted are essentially all successful and sufficiently comprehensive to solve the problem. Calculations are also presented elegantly (e.g., provides insights on the interpretation of the cost of capital and its appropriateness within the framework listed in assumptions)

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Sample Questions and Solutions

Sample Question: A company is expected to pay a $3.50 dividend at year-end, the dividends are expected to grow at a constant rate of 6.50% a year, and the common stock currently sells for $62.50 a share. The before-tax cost of debt is 7.50%, and the tax rate is 40%. The target capital structure consists of 40% debt and 60% common equity. What is the company’s WACC if all equity is from retained earnings?

Solution

(i) The problem assumes the stock will have a constant growth of 6.5% forever. The constant growth model is appropriate to use for this problem. The accuracy of the solution depends on the correctness of the constant growth assumption. The cost of equity assumes there will not be any new stock issuance. Therefore, the cost of equity is the cost of retained earnings for the existing shareholders. The cost of debt should be on after-tax basis due to the tax shield provided by the interest expense.

(ii) The cost of equity is based on the following: Kre = (D1/P0) + g • P0 is the current price to be calculated, • D1 is the next period’s dividend, • R is the required return on this stock • g is the constant growth

The cost of debt is based on kd = rd(1-T)

• rd is the before-tax cost of debt • T is the tax rate

The WACC is based on: WACC = wdkd + wrekre

(iii) Cost of retained earnings = (3.5/62.5) + 0.065 = 0.121 or 12.1% Cost of debt = 7.5 x (1-0.4) = 4.5% WACC = (0.4×4.5) + (0.6×12.1) = 9.06%

The average cost of capital for this company based on their existing debt and equity is 9.06%

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Homework Problems

1. A company has $10 million of debt outstanding with a coupon rate of 8%. Currently the yield to maturity on these bonds is 10.5%. If the firm’s tax rate is 40%, what is relevant cost of debt financing to this company?

2. Suppose a company currently has some bonds outstanding in the market. The bonds have 10 years until maturity, they pay a coupon rate of 6% on a semi-annual basis. If the company’s bonds are selling now for $965, what is the YTM? If the company’s tax rate is 40%, what is its cost of debt?

3. A company’s perpetual preferred stock currently trades at $87.50 per share, and it pays an $8.00 annual dividend. What is the firm’s cost of preferred stock?

4. Assume that you have been provided with the following firm data: risk free rate = 4.00%, market risk premium = 5.00%, and beta = 1.15. What is the cost of equity from retained earnings based on the CAPM approach?

5. A company hired you as a consultant to help them estimate its cost of capital. You have been provided with the following data: D1 = $0.80, P0 = $22.50, and g = 5.00% (constant). Based on the DCF approach, what is the cost of equity from retained earnings?

6. The expected dividend is $1.50 for a share of common stock priced at $15. What is the cost of internal common equity if the long-term growth in dividends is projected to be 4% indefinitely?

7. A company is expected to pay a dividend of $1.90 next year. Dividends are expected to grow at a constant rate of 3% per year, and the stock price is currently $12.50. The company’s marginal tax rate is 40%. Compute the cost of internal equity (i.e. retained earnings).

8. You were hired as a consultant to a company, whose target capital structure is 40% debt, 10% preferred, and 50% common equity. The after-tax cost of debt is 6%, the cost of preferred stock is 7.50%, and the cost of retained earnings is 13.25%. The firm will not be issuing any new stock. What is its WACC?

9. A company’s capital structure consists of 40% debt and 60% equity. The before-tax cost of debt is 12%, the cost of retained earnings is 15%, and the tax rate is 40%. What is this company’s WACC?

10. A company plans to maintain its optimal capital structure of 30% debt, 20% preferred stock, and 50% common stock far into the future. The required return on each component is: debt = 10%, preferred stock = 11%, and common stock = 18%. Assuming a 40% marginal tax rate, what is the WACC of this company?

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