# FN2 Ron Muller MODULE 4: CAPITAL STRUCTURE QUESTION 1

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1 MODULE 4: CAPITAL STRUCTURE QUESTION 1 Gadget Corp. manufactures gadgets. The average selling price of this finished product is \$200 per unit. The variable cost for these units is \$125. Gadget Corp. incurs fixed costs of \$600,000 per year. Determine the following: a) Breakeven point in units. b) The company s profit/loss if it produced and sold: 12,000 units, 15,000 units or 20,000 units. c) Degree of operating leverage for units produced and sold in part b). 1

2 QUESTION 1 SOLUTION a) BEP (units) = fixed costs/contribution margin = 600,000/( ) = 8,000 units b) BREAKEVEN 12,000 UNITS 15,000 UNITS 20,000 UNITS Sales (200 per/u) 1,600,000 2,400,000 3,000,000 4,000,000 Variable costs 1,000,000 1,500,000 1,875,000 2,500,000 Contr margin 600, ,000 1,125,000 1,500,000 Fixed costs 600, , , ,000 EBIT 0 300, , ,000 c) Degree of operating leverage: Breakeven = undefined 12,000 units = 900/300 =3.0 15,000 units = 1,125/525 = ,000 units = 1,500/900 =

3 QUESTION 2 A company has \$10 million of perpetual operating earnings, an all-equity capital structure, and a 40% tax rate. It has an equity beta of Management is considering a proposal to issue \$15 million of 10% perpetual debt and to retire outstanding shares with the debt proceeds. The risk-free rate of interest is 6% and the expected return on the market portfolio of risky assets is 13%. Required: a. Calculate the cost of equity of the unlevered firm. b. Calculate the value of the unlevered firm. c. According to the MM propositions, what value will the firm have if it proceeds with the debt issue? d. Calculate the cost of equity and the weighted average cost of capital for the levered firm. e. Should the refinancing proposal be accepted? Explain your answer. f. List three market imperfections, other than taxes, that might limit the use of debt financing in practice. 3

4 QUESTION 2 SOLUTION a. Using the CAPM formula: k e = (13 6) = 17.2% b. Look at the formula sheet V U = 10,000,000 (1 -.4) = 34,883, c. Look at the formula sheet for the formula for the value of a levered firm. V L = 34,883, (15,000,000) = 40,883,721 d. Look at the formula sheet for the formula for the cost of equity of a levered firm. k e = ( ) (1 -.40) (.58) =.1971 or 19.71% You must calculate the D/E ratio, and it equals: 15,000,000/ (40,883,721-15,000,000) = 0.58 WACC =.10 (1 -.40) (15,000,000/40,883,721) (25,883,721/40,883,721) = =.1468 or 14.68% e. The levered firm is more valuable and has a lower weighted average cost of capital versus the same firm without leverage. The company should therefore proceed with the debt issue. f. Market imperfections other than taxes that might limit the use of debt financing include: - bankruptcy costs, agency costs and institutional restrictions. 4

5 QUESTION 3 ABC Corp. has \$60 million of outstanding 6% debt and 3,000,000 outstanding common shares valued at \$15. The terms of its outstanding preferred share issue are as follows: Preferred shares outstanding 1,000,000 Face value per share \$40 Quarterly dividend \$1 A reduction in interest rates since the preferred shares were issued will enable ABC to refinance the preferred shares at more favourable terms. New preferred shares can be sold at \$40 if quarterly dividends are \$0.80. ABC Corp. has also decided that it requires an estimated \$10 million of additional long-term financing. ABC s tax rate is 40%. Required: a) Identify one advantage and one disadvantage of preferred share financing rather than debt financing for the issuing firm. b) What is the EBIT indifference level between preferred share financing and debt financing? c) Assume that the existing preferred share issue is refinanced. Also, assume that as another option, ABC Corp. could sell \$10 million worth of additional common shares at \$15 per share to raise funds, rather than increase its outstanding debt or preferred shares. There would be no floatation costs associated with the new common share issue. i) What is the EBIT indifference level between common share financing and debt financing? ii) What is the EBIT indifference level between common share financing and preferred share financing? 5

6 QUESTION 3 SOLUTION a) Advantage of preferred share financing rather than debt financing for the issuing firm: - preferred shares are less risky to issue than bonds, as the issuer has more flexibility on whether or not to declare a dividend versus debt interest and principal payments, which are not discretionary. Disadvantage of preferred share financing rather than debt financing for the issuing firm: - preferred shares are usually more expensive because dividend payments are not a tax deductible expense. b) This is somewhat of a trick question! As you will see from the calculation below, there is no point of indifference between debt and preferred. Debt Preferred EBIT EBIT Interest, existing 60,000,000 x 6% (3,600,000) (3,600,000) New debt 10,000,000 x 6% (600,000) 0 NIBT EBIT 4,200,000 EBIT 3,600,000 40% NIAT.60(EBIT-4,200,000).60(EBIT-3,600,000) Less: Preferred share dividend (3,200,000) (4,000,000) Earnings available to common s/h s.6(ebit)-5,720,000.6(ebit)-6,160,000 Note that for the Debt column, preferred dividends are calculated as: 1,000,000 existing preferred shares x (.80/quarter x 4) = 3,200,000 For the Preferred share column, we have 1,000,000 existing shares + 10,000,000/40 new shares = 1,250,000 Dividends = 1,250,000 x 3.20 = 4,000,000. Indifference point:.6(ebit) 5.720,000 =.6(EBIT) 6,160,000 3,000,000 3,000,000.6(EBIT) 5,720,000 =.6(EBIT) 6,160,000 0EBIT = -440,000 Conclusion: There is no indifference point in this instance. Debt appears better. 6

7 c) i) Debt v. Common shares Debt Common EBIT EBIT Interest, existing 60,000,000 x 6% (3,600,000) (3,600,000) New debt 10,000,000 x 6% (600,000) 0 NIBT EBIT 4,200,000 EBIT 3,600,000 40% NIAT.60(EBIT-4,200,000).60(EBIT-3,600,000) Less: Preferred share dividend (3,200,000) (3,200,000) Earnings available to common s/h s.6(ebit)-5,720,000.6(ebit)-5,360,000 Number of common shares = 3,000, ,000,000/15 = 3,666,667 Indifference point:.6(ebit) 5.720,000 =.6(EBIT) 5,360,000 3,000,000 3,666,667.6(EBIT) 5,720,000 =.6(EBIT) 5,360, EBIT 20,973,335 = 1.8EBIT 16,080,000.40EBIT = 4,893,335 EBIT = 12,233,338, and EPS =.54. For example, If EBIT > 12,233,338, say15,000,000, then EPS debt = 1.09 and EPS common = 0.99, therefore Debt is better. If EBIT < 12,233,338, say 10,000,000, then EPS debt = 0.09 and EPS common = 0.17, therefore Common is better. 7

8 c) ii) Common v. Preferred shares Common Preferred EBIT EBIT Interest, existing 60,000,000 x 6% (3,600,000) (3,600,000) NIBT EBIT 3,600,000 EBIT 3,600,000 40% NIAT.60(EBIT-3,600,000).60(EBIT-3,600,000) Less: Preferred share dividend (3,200,000) (4,000,000) Earnings available to common s/h s.6(ebit)-5,360,000.6(ebit)-6,160,000 Indifference point:.6(ebit) 5,360,000 =.6(EBIT) 6,160,000 3,666,667 3,000,000.6(EBIT) 5,360,000 =.6(EBIT) 6,160, EBIT 16,080,000 = 2.2EBIT 22,586,669.40EBIT = 6,506,669 EBIT = 16,266,673, and EPS = For example, If EBIT > 16,266,673, say 20,000,000, then EPS preferred = 1.95 and EPS common = 1.81, therefore Preferred is better. If EBIT < 16,266,673, say 10,000,000, then EPS preferred = and EPS common = 0.17, therefore Common is better. 8

9 QUESTION 4 BC Minerals, an unlevered firm, is expecting cash flows to be as indicated in Exhibit 1 forever. The firm s shareholders expect 20% return per year. The firm pays out all of its earnings after interest and taxes and dividends. Exhibit 1 State of the economy Bad Fair Good Very Good Probability EBIT (\$millions) \$1.00 \$1.50 \$2.50 \$3.00 Required: a) In a world of no taxes, what is the firm s value? b) If BC Minerals tax rate is 32%, what is the value of the firm to its shareholders? c) BC Minerals decides to use leverage in its capital structure. It sells bonds to raise \$3.06 million at 8% yield. The money is used to purchase outstanding shares. What is the market value of BC Minerals after the bond issue? d) What is BC Minerals debt-to-equity ratio and the required rate of return to shareholders? e) If personal taxes on dividends are 30%, while personal taxes on interest income are 50%, what is the value of BC Minerals? f) What should be the tax rate on dividends to make taxes irrelevant to the firm s value? 9

10 QUESTION 4 SOLUTION a) The expected EBIT is equal to: (\$1.0 x 0.15) + (\$1.5 x 0.35) + (\$2.5 x 0.35) (\$3.0 x 0.15) = \$ \$ \$ \$0.450 = \$2.0 million The value of the unlevered firm is equal to: V U = EBIT / k U = \$2.0 /.20 = \$10 million b) When the firm pays taxes, the value of the unlevered firm is given by: V U = [EBIT X (1-T C )] / k U = (\$2.0 X 0.68) / 0.20 = \$6.8 million c) The value of the levered firm is given by: V L = V U + T C D = \$6.8 + (0.32 X \$3.06) = \$6.8 + \$ = \$ million d) The value of equity is equal to the total value of the firm, minus the value of debt. Thus: E = \$ \$3.06 = \$ million The debt-to-equity ratio = \$3.06 / \$ = 64.84% The required rate of return on equity is equal to: = [ ] [0.6484] [1-.032] = 25.29% e) Equation 4-13 calculates the market value of the levered firm in the presence of corporate and personal taxes. Therefore: V U = \$2.0 X (1-0.32) X (1-.30) / 0.20 = \$4.76 million V L = \$ [ 1- (1-0.32)(1-0.3)] X \$3.06 (1-0.5) = \$ \$ = \$ million 10

11 f) It is necessary to find T S which will make V L = V U. This occurs if: [1-(1-T C )(1-T S )] = 0 (1-T D ) FN2 Ron Muller This condition simplifies to: (1-T C )(1-T S ) = 1 (1-T D ) or simply: (1-T C ) X (1-T S ) = 1-TD (1-0.32) X (1-T S ) = Therefore: 1-T S = 0.50 / 0.68 or T S = 26.47% 11

12 QUESTION 5 The capital structure of Humpty Corporation is depicted in the Exhibit below. Other companies in the firm s industry rely less heavily on debt than Humpty, and the industry norm is a debt-to-firm-value ratio of 30%. Humpty is assessing the implications of altering its capital structure to match the norm in its industry. Humpty could alter its capital structure by issuing shares and using the proceeds to pay down debt, which costs 8% per annum. The corporate tax rate is 45%. EXHIBIT Capital Structure of Humpty Corporation Market value of equity (100,000 outstanding shares) \$ 4,000,000 Market value of current liabilities 780,000 Market value of long-term debt 2,350,000 Required a. Calculate the total debt-to-value ratio for Humpty, at the current time. b. How much long-term debt would Humpty have to pay down to achieve the industry average debt-to-value ratio? In your solution, consider how firm value will be affected by the tax shields associated with debt financing. Prove that your answer does indeed result in the desired debt-to-value ratio. Show your calculations. c. Determine the value of outstanding equity after the capital structure has been altered. Will the value per share go up, or down, as a result of the restructuring? Explain briefly. 12

13 QUESTION 5 SOLUTION In this question, a firm alters its capital structure to match the industry norm. Students must take into account the impact of the debt tax shield on firm value when assessing how much debt to retire and must consider how equity value will be affected. a. Total debt-to-value ratio for Humpty at the current time: Total debt/total value = (780, ,350,000) / (780, ,350, ,000,000) = 3,130,000 / 7,130,000 = or 43.9% b. To reduce the total debt-to-value ratio to the industry norm of 30%, Humpty would have to issue shares and use the proceeds to pay down some of its debt. With less debt, there will be less debt tax shields and this will reduce market value somewhat. New firm value = Current market value of firm Tax rate Debt reduction = 7,130, Change in debt New amount of debt = Current debt Change in debt = 3,130,000 Change in debt New debt / new value = 30% (3,130,000 change in debt) / (7,130, change in debt) = ,130,000 change in debt = 0.3 (7,130, change in debt) 3,130,000 change in debt = 2,139, change in debt 991,000 = change in debt Change in debt = 991,000 / = 1,145,665 New debt level = 3,130,000 1,145,665 = 1,984,335 New firm value = 7,130, (1,145,665) = 6,614,451 New debt-to-value ratio = 1,984,335 / 6,614,451 = 30% The firm must pay down \$1,145,665 of debt in order to achieve the desired 30% debt-to-value ratio. c. Market value of outstanding equity after altering the capital structure: Value of equity = New firm value Value of debt = 6,614,451 1,984,335 = 4,630,116 Although the total value of equity has increased, the per share value will be lower. Equity was issued to raise the funds (resulting in a higher number of shares outstanding) to retire the debt, and less debt results in lower tax shields so value is lost. 13

14 QUESTION 6 Q1. According to the traditional view of capital structure, which of the following best describes the optimal debt level for firms? 1) Zero debt 2) 100% debt 3) A high percentage of debt, but below 100% 4) A very low proportion of debt financing (below 15%) Q2. Which of the following statements correctly describe the impact of financial leverage under market conditions that are perfect except for the presence of corporate taxes? i) A levered firm is more valuable than an unlevered firm. ii) Firm value is maximized at 100% debt financing. iii) The weighted average cost of capital rises as leverage increases. 1) i) only 2) ii) only 3) iii) only 4) i) and ii) only 5) i), ii) and iii) Q3. Which of the following statements correctly applies to the weighted-average cost of capital (WACC)? 1) The explicit cost of preferred stock is greater than that for debt. 2) The financing mix must be represented by book-value weights when calculating WACC 3) A multi-divisional firm must use a single discount rate for project selection. i) 1 only ii) 2 only iii) 3 only iv) 2 and 3 only v) 1, 2, and 3 Q4. Which of the following factors is not used to evaluate a firm s leverage? i) Debt/equity ratio. ii) Current debt/total assets ratio. iii) Credit ratings of the firm s debt. iv) Return on equity. v) Restrictions on a bank loan. Q5. Which of the following conditions increase(s) the value of an unleveraged firm? 1) Change to a levered capital structure. 2) Projects are accepted if NPV = 0. 3) Dividends are scheduled to increase at 5% annually. i) 1 only ii) 2 only iii) 1 and 2 only iv) 1 and 3 only v) 1, 2 and 3 14

15 Q6. Which of the following statements applies to financial risk? 1) Financial risk to the shareholders can be defined as total risk to the shareholders of the levered firm minus total risk of the unlevered firm. 2) A firm with high financial leverage is likely to have high business risk because the two offset each other. 3) Financial risk is the total risk generated by the nature of the firm s assets and business. 4) Shareholders benefit from financial leverage as long as the interest costs of acquiring money exceed the return on borrowed money. Q7. Which of the following are direct costs of bankruptcy? i) The cost of searching for new suppliers. ii) Losses due to forced sale of assets at below market prices. iii) Deterioration of property due to lack of maintenance. 1) i) only 2) ii) only 3) ii) and iii) 4) i) and iii) Q8. Which of the following statements correctly describes the degree of operating leverage of a company? i) It measures the sensitivity of operating income to changes in sales volume. ii) It is a constant and is invariant to the level of sales at which it is measured. iii) It is one element of the business-risk of a firm. 1) i) only 2) ii) only 3) i) and iii) 4) ii) and iii) Q9. Which one of the following does not prevail when evaluating debt and preferred stock as alternative methods of financing? i) EPS is equal for both alternatives at the EBIT-EPS indifference point. ii) Sinking fund is not considered. iii) EPS is calculated using earnings after preferred dividends are paid. iv) The weighted average cost of capital is calculated taking into account the after tax cost of each method of financing. v) Debt holders have a senior claim. 15

16 Q10. According to capital structure theory, in the presence of both corporate and personal taxes, which of the following interpretations of the formula below is correct? (1 TD) = (1 TC)(1 TS) where TD = tax rate on interest income TC = corporate tax rate TS = personal tax rate on income from shares 1) When this equality holds, firms should not use debt in their capital structures. 2) When the left-hand side is less than the right-hand side, investors prefer bonds, so it is optimal for firms to include bonds in their capital structure. 3) When the left-hand side is less than the right-hand side, investors prefer dividends and capital gains, so firms should use all equity financing. 4) When this equality holds, firms should have 100% debt financing. 16

17 QUESTION 6 SOLUTIONS 1 (3) 2 (4) 3 (i) 4 (iv) 5 (iv) 6 (1) 7 (3) 8 (3) 9 (i) 10 (3) 17

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