Major Points



CAPITAL STRUCTURE: PROBLEM SET

(copyright © 2018 Joseph W. Trefzger)

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1. Alberta Appliances is considering a new investment project: producing the Portable Perfect Chicken Chum,

a small rotisserie grill that plugs into a car’s cigarette lighter. The Chums are expected to be sold for $135 each.

The variable cost (materials, production wages, power to run the machines, etc.) of producing each unit is expected to be $94. Cash outlays for building rent, management salaries, and other fixed annual operating costs are expected to be $2,600,000 each year. Alberta also would have to buy manufacturing machinery at a cost of $13,250,000. This equipment is expected to have a 10-year life (equal to the life of the project), and then to have no salvage value. What is the grill project’s annual operating (sometimes called accounting) break-even point? If Alberta’s weighted average cost of capital is 11.25% per year, what is the project’s annual financial break-even point?

2. In its most recent operating year, British Columbia Lumber Products sold 450,000 folding tables. Its total fixed operating costs (in an accounting sense) were $3,500,000, and variable cost per unit produced was $27.75. The tables were sold to houseware stores for $46 each. British Columbia paid $765,000 in interest during the year. Compute the company’s degree of operating leverage (DOL), degree of financial leverage (DFL), and degree of total leverage (DTL, also called degree of combined leverage DCL), and interpret these values.

3. The managers of Canada Consolidated Copper are analyzing the company’s capital structure. They feel that the costs of various components of the financing mix (debt, preferred stock, and common stock) would be as follows, under the indicated capital structure possibilities:

Proportion Cost of Proportion Cost of

Proportion Pre-Tax from Preferred Preferred from Common Common

from Lenders Cost of Debt Stockholders Stock Stockholders Stock

(D/V or wd) (kd) (P/V or wp) (kp) (E/V or wc) (ke)

0 N/A .10 6.0% .90 14.5%

.20 8% .10 7.5% .70 16.5%

.40 10% .10 9.5% .50 18.0%

.60 14% .10 15.0% .30 28.0%

.80 26% .10 30.0% .10 52.0%

Compute the weighted-average cost of capital (WACC) under each of the representative capital structures shown

(do not forget to adjust the cost of debt to reflect the expected income tax savings under Canada’s 34% marginal income tax rate). Which financing mix results in the lowest WACC and is, therefore, our estimate of the optimal capital structure? Why does that outcome seem to occur?

4. The treasurer of Hudson Bay Handbrakes, Inc. is trying to decide what the company’s optimal capital structure would be. Hudson Bay has $100,000 in total assets, and expects operating income, or EBIT (a figure largely unaffected by the chosen capital structure) to be $8,000 in each of the next several years. The company’s common stock sells for a market price of $10 per share. The treasurer believes that Hudson Bay would pay an 8% annual interest rate on borrowed money under any capital structure choice. A simple “EBIT/EPS” analysis the treasurer performs results in the projections shown below.

Debt Ratio 0% 25% 50% 75% 99%

Amount of Debt $0 $25,000 $50,000 $75,000 $99,000

Amount of Equity $100,000 $75,000 $50,000 $25,000 $ 1,000

Shares of $10 Common Stock 10,000 7,500 5,000 2,500 100

Operating Income (EBIT) $8,000 $8,000 $8,000 $8,000 $8,000

Minus Interest (8% x debt) $ 000 $2,000 $4,000 $6,000 $7,920

Net Income (ignoring tax) $8,000 $6,000 $4,000 $2,000 $ 800

Net Income/Equity = ROE 8% 8% 8% 8% 8%

Net Income/Shares = EPS $.80 $.80 $.80 $.80 $.80

(Income taxes are ignored in this analysis.) Based on these projections, it seems that any selected capital structure would lead to the same level of return on equity (ROE) and earnings per share (EPS), two important measures of financial return to the owners whose wealth the firm’s managers are supposed to maximize. Is this finding realistic; is capital structure irrelevant? Why does financial leverage here have a neutral (rather than a positive or negative) effect? In other words, what has caused projected ROE and EPS to be the same, in this situation, for any debt ratio?

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5. Labrador Electric, Ltd. plans to invest in new equipment so it can produce heavy-duty electrical extension cords. The equipment costs $2,850,000 and has an expected life of 8 years, which is also the expected life of the project. There is no expected salvage value for the equipment at the end of year 8. Fixed operating costs paid in cash each year (rent and management salaries, for example) are expected to be $465,000 annually. The variable cost of producing the cords is expected to be $2.67 per unit, and Labrador expects to sell each cord to a retailer for $3.89. What is the project’s annual operating (sometimes called accounting) break-even point? If the company’s annual weighted average cost of capital is 9.75%, what is the project’s annual financial break-even point?

6. One of Manitoba Confections’ many fine candy products is chocolate-covered Sophomore Mints. Five million

boxes are sold each year, at a price of $.43 per box, to retailers (who then sell them to customers for a higher price). The variable cost of producing each box is $.17. Total fixed operating costs (in an accounting sense) incurred

in producing the mints are $480,000 per year, and mint production accounts for $310,000 each year in interest payments. Compute Manitoba’s degree of operating leverage (DOL), degree of financial leverage (DFL), and degree of total leverage (DTL, also called degree of combined leverage DCL), and interpret these values. If sales increase by 30% in the coming year, what would we expect the change in net income to be?

7. Maple Leaf Navigation Equipment, Inc.’s operating results have been very stable over the past few years.

In each recent year the balance sheet has shown $65 million in assets, the income statement has shown operating income (EBIT) of $12 million, and the average federal-plus-state income tax rate has been 38%. The only major change has been a recent increase in the company’s debt/assets ratio (a financing issue that does not directly affect operating performance). The proportion of assets paid for with debt financing was recently increased from 40% (at which Maple Leaf paid a 7.5% average annual interest rate) to 55% (with an accompanying increase to 9.5% in the average annual interest rate, reflecting lenders’ perception that they face greater risk). Because this increase in debt financing increased Maple Leaf’s return on equity (ROE), some managers have proposed further increasing the debt ratio, to 70%. If the increase to this high level of debt would cause the average annual interest rate to rise to 16%, should the proposed change be made?

8. The managers of New Brunswick Nutrients, a company with $10 million in assets, are investigating what their firm’s capital structure should be. The current financing mix is somewhat heavily “leveraged,” with a 60% debt ratio ($6 million in debt financing, $4 million in equity from 80,000 shares of common stock valued at $50 per share). Under one alternative structure being considered, the company would move to a 40% debt ratio (create 40,000 new $50 shares and use the proceeds to pay off $2 million worth of debt, leaving $4 million in debt and $6 million in equity). Under a second alternative, New Brunswick would move to a low 20% debt ratio (create 80,000 new

$50 shares and use the proceeds to pay off $4 million in debt, leaving $2 million in debt and $8 million in equity). Operating income, or EBIT (which is largely unaffected by capital structure), is expected to be $900,000 per year under any chosen financing mix, and New Brunswick’s average federal-plus-state income tax rate is 32%. If the average annual interest rate paid on debt under any capital structure alternative would be 10%, what would return

on equity (ROE) and earnings per share (EPS) be under each of the three capital structure alternatives? What if the average annual interest rate were instead 8%, or 9%?

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9. Each professional grade premium fishing rod manufactured by Newfoundland Premium Reel (NPR) is sold to sporting goods retailers at a $226 price. The variable cost per unit is $159.50, and the operation incurs $5,970,000 in yearly fixed costs ($3,970,000 in annual fixed payments and $2 million per year in straight-line depreciation on equipment that had a $14 million purchase cost and a seven-year expected life), as long as the year’s production

does not exceed 125,000 units. How much annual net income does NPR earn, in an accrual accounting sense, if

it produces and sells 100,000 units? How much does it lose if it makes and sells only 75,000 units? What is the operating (also called accounting) break-even point? What change would we see in the operating break-even point if the price at which NPR sells each unit were to rise to $240, while all costs remained unchanged? What change would we see if the selling price were to rise to $240, but at the same time variable cost per unit rose to $176?

10. Northwest Territories Fabricating is buying new equipment so it can manufacture tiny high-carbon steel pins for industrial use. The equipment costs $4,000,000. The market for the pins is expected to remain strong for six years, and at the end of year six the equipment is expected to have a $400,000 salvage value. Fixed operating costs paid in cash are expected to be $1,100,000 each year. The variable cost of producing a pound of pins, which the company expects to sell for $12.99, is $8.00. Northwest’s managers feel that the weighted average cost of capital for a project like this one is 14.5%. Compute the annual operating (or accounting) and financial break-even points.

11. Nova Scotia Paper Company’s degree of operating leverage (DOL) is 1.29, and its degree of financial leverage is 1.46. What is its degree of total leverage (DTL, also called degree of combined leverage DCL)? How do we interpret these values? What would the DOL be if Nova Scotia were producing at its operating break-even point?

12. Responding to some directors’ concerns that they are making too little use of debt financing, the managers of Nunavut Natural Flavorings are reviewing the company’s capital structure. The $96,000,000 in assets are currently financed with 15% debt and 85% common equity. Two other capital structure possibilities being considered would involve 35% debt or 70% debt (with the remainder from common equity). Nunavut common stock sells in the market for $135 per share. The company’s operating income, or EBIT (which is largely unaffected by capital structure), is expected to be $10,560,000 per year, over the next few years, no matter what financing mix is employed; and income tax is paid at a 38% combined federal-plus-state average rate. If the average annual interest rate Nunavut pays for debt financing, regardless of its capital structure choice, would be 7%, what would return on equity (ROE) and earnings per share (EPS) be under each of the three capital structure possibilities being considered? What if the company instead paid a 14%, or 11%, average annual interest rate?

13. Mr. Ontario owns 6,720 of the 3.36 million outstanding shares of common stock in Prince Edward Island Corporation (PEIC). Each share is worth $25 (we will treat market and book values as being the same). The company has $120 million in assets, financed 30% with debt and 70% with common equity. PEIC’s managers, who feel the firm could benefit from making greater proportional use of borrowed money, have considered increasing the debt ratio to 44%. The average annual interest rate PEIC pays on debt has been 6.85%, a figure that would not be expected to change even if debt financing increased. EBIT (which is essentially unaffected by the capital structure) is expected to be $9,500,000 annually in each of the next several years, and for purposes of this analysis we ignore income taxes. How much financial return does PEIC generate for Mr. Ontario each year, under the current capital structure? How much financial return would it generate for him each year if the proposed change were made, and Mr. Ontario kept all of his shares? How might he return to a position financially equivalent (in terms of risk and total financial return) to the one he was in before the change? How does this situation relate to Modigliani & Miller’s capital structure irrelevance ideas?

14. Ms. Quebec owns 625 of the 12,500 outstanding shares of common stock in Saskatchewan School Services. Each share is worth $12 (we will treat market and book values as being the same). One feature that attracted Ms. Quebec to the stock was Saskatchewan’s aggressive use of debt financing; the company’s $375,000 in assets have been financed 60% with debt and 40% with common equity. Saskatchewan’s managers, on the other hand, fear that the company is overburdened with debt, and they have decided to reduce the debt ratio to 36%. The average annual interest rate Saskatchewan pays on debt has been 8.75%, a figure that would not be expected to change even if debt financing were reduced. EBIT (which is essentially unaffected by the capital structure) is expected to be $46,500 annually in each of the next several years, and for purposes of this analysis we ignore income taxes. How much total financial return (her proportional share of net income) does Saskatchewan generate for Ms. Quebec each year, under the current capital structure? How much total financial return will it generate for her each year after the change

is made, if she holds the same number of shares after the change? How might she return to a position financially equivalent (in terms of risk and total financial return) to the one she was in before the change? How does this situation relate to Modigliani & Miller’s capital structure irrelevance ideas?

15. Yukon Yogurt, Inc. sells 15,000 cases of yogurt to food stores each year for $39 per case. The variable cost (labor, electricity, materials) of producing each case is $34, and accrual-based annual fixed operating costs are $50,000 ($40,000 in cash-based fixed costs such as rent, and $10,000 in annual straight-line depreciation on equipment with a $70,000 cost and a 7-year expected life). Consultants feel that Yukon could reduce the variable cost of producing each case (primarily overtime labor and wasted materials) by switching to a more capital-intensive production process, in which accrual-based annual fixed operating costs would rise to $60,000 ($40,000 cash-based, $20,000 annual straight-line depreciation on costlier equipment with a $140,000 cost and a 7-year life). Because they believe that the more efficient equipment would allow variable cost to fall to $33.00 or even $32.50 per case, the consultants conclude that the switch should unquestionably be made. Are they correct? If you, as Yukon’s chief financial officer, feel that using the more expensive equipment would bring variable costs down only to $33.50 per case, should you approve the change?

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