1. The optimal capital structure is the one that maximizes __________, and this will always be lower than the debt/equity ratio that maximizes __________.
expected EPS; the firm's stock price
net income, expected EPS
book value of the firm; net income
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 degree of financial leverage greater than one.
a degree of operating leverage less than one.
a degree of total leverage less than one. CORRECT
a degree of total leverage greater than one.
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 Borrowedin 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
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 = .
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
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 PriceD/A Price
0% $37.50 40% $30.40
10 38.52 50 22.32
20 39.91 60 14.10
Thus, a debt/assets ratio of 20 percent maximizes stock price. This is the optimal capital structure.
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)
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:
ProbabilityAnnual Sales (millions of dollars)
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?