**Problem 15-1** : Break-even Quantity: Shapland Inc. has fixed operating costs of $550,000 and variable costs of $41 per unit. If it sells the product for $85 per unit, what is the break-even quantity?

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**Problem 15-2**: Unlevered Beta: Counts Accounting has a beta of 1.40. The tax rate is 35%, and Counts is financed with 40% debt. What is Counts’ unlevered beta? Round your answer to two decimal places.

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Premium for Financial Risk: Ethier Enterprise has an unlevered beta of 1.25. Ethier is financed with 50% debt and has a levered beta of 1.75. If the risk free rate is 3.5% and the market risk premium is 7%, how much is the additional premium that Ethier’s shareholders require to be compensated for financial risk? Round your answer to two decimal places.

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Problem 15-4 Value of Equity after Recapitalization

Nichols Corporation’s value of operations is equal to $400 million after a recapitalization (the firm had no debt before the recap). It raised $180 million in new debt and used this to buy back stock. Nichols had no short-term investments before or after the recap. After the recap, wd = 45%. What is S (the value of equity after the recap)? Enter your answer in millions of dollars.

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**Problem 15-5** Stock Price After Recapitalization

Lee Manufacturing’s value of operations is equal to $900 million after a recapitalization (the firm had no debt before the recap). Lee raised $514.29 million in new debt and used this to buy back stock. Lee had no short-term investments before or after the recap. After the recap, wd = 4/7. The firm had 35 million shares before the recap. What is P (the stock price after the recap)? Round your answer to the nearest cent.

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Problem 15-6 Shares Remaining After Recapitalization Dye Trucking raised $200 million in new debt and used this to buy back stock. After the recap, Dye’s stock price is $5.25. If Dye had 65 million shares of stock before the recap, how many shares does it have after the recap? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Round your answer to two decimal places.

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Problem 15-7 Break-even Point Schweser Satellites Inc. produces satellite earth stations that sell for $95,000 each. The firm’s fixed costs, F, are $1.5 million, 50 earth stations are produced and sold each year, profits total $400,000; and the firm’s assets (all equity financed) are $4 million. The firm estimates that it can change its production process, adding $3.5 million to investment and $410,000 to fixed operating costs. This change will (1) reduce variable costs per unit by $12,000 and (2) increase output by 20 units, but (3) the sales price on all units will have to be lowered to $89,000 to permit sales of the additional output. The firm has tax loss carryforwards that render its tax rate zero, its cost of equity is 15%, and it uses no debt.

a. What is the incremental profit? To get a rough idea of the project’s profitability, what is the project’s expected rate of return for the next year (defined as the incremental profit divided by the investment)? Round your answer to two decimal places.

The incremental profit is %

b. Would the firm’s break-even point increase or decrease if it made the change? By how much? Enter your answer as positive number if it increases or negative number if it decreases.

The break-even point changes by units.

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**Problem 15-10** Optimal Capital Structure with Hamada

Beckman Engineering and Associates (BEA) is considering a change in its capital structure. BEA currently has $20 million in debt carrying a rate of 6%, and its stock price is $30 per share with 2 million shares outstanding. BEA is a zero growth firm and pays out all of its earnings as dividends. The firm’s EBIT is $12.401 million, and it faces a 30% federal-plus-state tax rate. The market risk premium is 5%, and the risk-free rate is 4%. BEA is considering increasing its debt level to a capital structure with 50% debt, based on market values, and repurchasing shares with the extra money that it borrows. BEA will have to retire the old debt in order to issue new debt, and the rate on the new debt will be 10%. BEA has a beta of 1.1.

a. What is BEA’s unlevered beta before restructuring? Use market value D/S (which is the same as wd/ws) when unlevering. Round your answer to three decimal places.

Unlevered beta is

b. What are BEA’s new beta after releveraging and cost of equity if it has 50% debt? Round your answers to two decimal places.

The new beta is .

The new cost of equity is %.

c. What is BEA’s WACC after releveraging? Round your answer to two decimal places.

BEA’s WACC after releveraging is %.

d. What is its total value of the firm with 50 % debt? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Round your answer to two decimal places.

The total value of the firm with 50% debt is $ million.