Solution to Problem 2

INSTRUCTIONS

Students are required to study the following questions and problems indicated and to be able to solve them by themselves.

Although this is not a required part of a coursework, the purpose of the tutorial is twofold: to help the student understand the methodology for solving the problems and to help him/her prepare for the courseworks and/or exams. The utilisation of this resource can be maximised depending on the time and effort each individual student devotes.

Konstantinos Kanellopoulos

11^th April 2013

CHAPTER 11

Problem 1

On January 1, 2005, the total assets of the Dexter Company were $270 million. The firm’s present capital structure, which follows, is considered to be optimal. Assume that there is no short-term debt.

Long-term debt $135,000,000

Common equity 135,000,000

Total liabilities and equity $270,000,000

New bonds will have a 10 percent coupon rate and will be sold at par. Common stock, currently selling at $60 a share, can be sold to net the company $54 a share. Stockholders’ required rate of return is estimated to be 12 percent, consisting of a dividend yield of 4 percent and an expected growth rate of 8 percent. (The next expected dividend is $2.40, so $2.40/$60 = 4%). Retained earnings are estimated to be $13.5 million. The marginal tax rate is 40 percent. Assuming that all asset expansion (gross expenditures for fixed assets plus related working capital) is included in the capital budget, the dollar amount of the capital budget, ignoring depreciation, is $135 million.

a. To maintain the present capital structure, how much of the capital budget must Dexter finance by equity?

b. How much of the new equity funds needed will be generated internally? Externally?

c. Calculate the cost of each of the equity components.

Solution to Problem 1

a. Common equity needed: 0.50($135,000,000) = $67,500,000.

b. Expected internally generated equity (retained earnings) is $13.5 million. External equity needed is as follows:

New equity needed $67,500,000

Retained earnings 13,500,000

External equity needed $54,000,000

c. Cost of equity:

k_s = Cost of retained earnings

= Dividend yield + Growth rate = 12% = 4% + 8% = 12%.

= /P₀ + g = $2.40/$60 + 0.08 = 0.04 + 0.12 = 12.0%.

k_e = Cost of new equity

= /NP + g = $2.40/$54.00 + 0.08 = 0.044 + 0.08 = 0.124 = 12.4%.

Problem 2

A company’s 6 percent coupon rate, semiannual payment, $1,000 par value bond that matures in 30 years sells at a price of $515.16. The company’s marginal tax rate is 40 percent. What is the firm’s component cost of debt for purposes of calculating the WACC? (Hint: Base your answer on the simple rate, not the effective annual rate, EAR.)

Solution to Problem 2

We can use the equation given (Equation 7‑3) in Chapter 7 to find the approximate yield to maturity:

Note that we use the number of years rather than the number of interest payments in this computation, because the “approximate YTM” computation does not consider the time value of money.

Using the calculator, enter these values: N = 60, PV = -515.16, PMT = 30, and FV = 1000, to get I = 6% = periodic rate. The simple rate is 6%(2) = 12%, and the after-tax component cost of debt is 12%(0.6) = 7.2%.

CHAPTER 12

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