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INSTRUCTOR: Mr. Konstantinos Kanellopoulos, MSc (L.S.E.), M.B.A.

COURSE: FIN-210-50-S13 Finance

SEMESTER: II, 2013

Tutorial 4 – for tutor

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

11th 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:

ks = Cost of retained earnings

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

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

ke = Cost of new equity

= [pic]/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:

[pic]

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

Multiple Choice Questions

1. The optimal capital structure is the one that maximizes __________, and this will always be lower than the debt/equity ratio that maximizes __________.

|a. |expected EPS; the firm's stock price |

|b. |net income, expected EPS |

|c. |book value of the firm; net income |

|d. |the firm's stock price; expected EPS CORRECT |

2. If a given change in sales results in a larger relative change in EPS then we can definitely say that the firm has

|a. |a degree of financial leverage greater than one. |

|b. |a degree of operating leverage less than one. |

|c. |a degree of total leverage less than one. CORRECT |

|d. |a degree of total leverage greater than one. |

Problem 1

Brown Products is a new firm just starting operations. The firm will produce backpacks that will sell for $22.00 each. Fixed costs are $500,000 per year, and variable costs are $2.00 per unit of production. The company expects to sell 50,000 backpacks per year, and its marginal tax rate is 40 percent. Brown needs $2 million to build facilities, obtain working capital, and start operations. If Brown borrows part of the money, the interest charges will depend on the amount borrowed as follows:

Percentage of Debt Interest Rate on Total

Amount Borrowed in Capital Structure Amount Borrowed  

$ 200,000 10% 9.00%

400,000 20 9.50

600,000 30 10.00

800,000 40 15.00

1,000,000 50 19.00

1,200,000 60 26.00

Assume that stock can be sold at a price of $20 per share on the initial offering, regardless of how much debt the company uses. Then after the company begins operating, its price will be determined as a multiple of its earnings per share. The multiple (or the P/E ratio) will depend upon the capital structure as follows:

Debt/Assets P/E Debt/Assets P/E

0.0 12.5 40.0 8.0

10.0 12.0 50.0 6.0

20.0 11.5 60.0 5.0

30.0 10.0

What is Brown’s optimal capital structure, which maximizes stock price, as measured by the debt/assets ratio?

Solution to Problem 1

The first step is to calculate EBIT:

Sales in dollars [50,000($22)] $1,100,000

Less: Fixed costs (500,000)

Variable costs [50,000($2)] (100,000)

EBIT $ 500,000

The second step is to calculate the EPS at each debt/assets ratio using the formula:

EPS = [pic].

Recognize (1) that I = Interest charges = (Dollars of debt)(Interest rate at each D/A ratio), and (2) that shares outstanding = (Assets – Debt)/Initial price per share = ($2,000,000 – Debt)/$20.00.

D/A EPS D/A EPS

0% $3.00 40% $3.80

10 3.21 50 3.72

20 3.47 60 2.82

30 3.77

Finally, the third step is to calculate the stock price at each debt/assets ratio using the following formula: Price = (P/E)(EPS).

D/A Price D/A Price

0% $37.50 40% $30.40

10 38.52 50 22.32

20 39.91 60 14.10

30 37.70

Thus, a debt/assets ratio of 20 percent maximizes stock price. This is the optimal capital structure.

Problem 2

The Strasburg Company plans to raise a net amount of $270 million to finance new equipment and working capital in early 2011. Two alternatives are being considered: Common stock can be sold to net $60 per share, or bonds yielding 12 percent can be issued. The balance sheet and income statement of the Strasburg Company prior to financing are as follows:

The Strasburg Company: Balance Sheet as of December 31, 2010

(millions of dollars)

__________

Current assets $900.00

Net fixed assets 450.00

___________

Total assets $1,350.00

Accounts payable $172.50

Notes payable to bank $255.00

Other current liabilities $255.00

__________

Total current liabilities $652.50

Long-term debt (10%) 300.00

Common Stock, ($3 par) 60.00

Retained earnings 337.50

___________

Total liabilities and equity $1,350.00

The Strasburg Company: Income Statement for year ended December 31, 2010 (millions of dollars)

Sales $2,475.00

Operating costs (2,227.50)

__________

Earnings before interest and taxes $247.50

Interest on short-term debt (15.00)

Interest on long-term debt (30.00)

___________

Earnings before taxes (EBT) $202.50

Taxes (40%) (81.00)

___________

Net income $121.50

The probability distribution for annual sales is as follows:

Probability Annual Sales (millions of dollars)

0.30 $2,250

0.40 2,700

0.30 3,150

Assuming that EBIT is equal to 10 percent of sales, calculate earnings per share under both the debt financing and the stock financing alternatives at each possible level of sales. Then calculate expected earnings per share and σEPS under both debt and stock financing. Also calculate the debt-to-total assets ratio and the times-interest-earned (TIE) ratio at the expected sales level under each alternative. The old debt will remain outstanding. Which financing method do you recommend?

Solution to Problem 2

Use of debt ($ millions):

Probability 0.3 0.4 0.3

Sales $2,250.0 $2,700.0 $3,150.0

EBIT (10%) 225.0 270.0 315.0

Interest* ( 77.4) ( 77.4) ( 77.4)

EBT 147.6 192.6 237.6

Taxes (40%) ( 59.0) ( 77.0) ( 95.0)

Net income $ 88.6 $ 115.6 $ 142.6

Earnings per share

(20 million shares) $ 4.43 $ 5.78 $ 7.13

*Interest on debt = ($270 x 0.12) + Current interest expense

= $32.4 + ($15 + $30) = $77.4

Expected EPS = (0.30)($4.43) + (0.40)($5.78) + (0.30)($7.13) = $5.78 if debt is used.

[pic]

Expected Sales = 0.3($2,250) + 0.4($2,700) + 0.3($3,150) = $2,700. At Sales = $2,700, EBIT = $270.

[pic]

Debt/Assets = ($652.50 + $300 + $270)/($1,350 + $270) = 75.5%.

Use of stock (Millions of dollars):

Probability 0.3 0.4 0.3

Sales $2,250.0 $2,700.0 $3,150.0

EBIT 225.0 270.0 315.0

Interest (45.0) (45.0) (45.0)

EBT 180.0 225.0 270.0

Taxes (40%) (72.0) (90.0) (108.0)

Net income $ 108.0 $ 135.0 $ 162.0

Earnings per share

(24.5 million shares)* $ 4.41 $ 5.51 $ 6.61

*Number of shares = ($270 million/$60) + 20 million

= 4.5 million + 20 million = 24.5 million.

EPSEquity = (0.30)($4.41) + (0.40)($5.51) + (0.30)($6.61) = $5.51.

[pic]

[pic]

Debt/Assets = ($652.50 + $300)/($1,350 + $270) = 58.8%

Under Debt financing the expected EPS is $5.78, the standard deviation is $1.05, the CV is 0.18, and the debt ratio increases to 75.5%. (The debt ratio had been 70.6 percent.) Under Equity financing the expected EPS is $5.51, the standard deviation is $0.85, the CV is 0.15, and the debt ratio decreases to 58.8 percent. At this interest rate, debt financing provides a higher expected EPS than equity financing; however, the debt ratio is significantly higher under the debt financing situation as compared with the equity financing situation. Because EPS is not significantly greater under debt financing, but the risk is noticeably greater, equity financing should be recommended.

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