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CHAPTER 16CAPITAL STRUCTURE DECISIONS: PART II (Difficulty: E = Easy, M = Medium, and T = Tough) True/False Easy: (16.1) Taxes and capital structure Answer: a Diff: E 1 . In a world with no taxes, MM show that a firm’s capital structure does not affect the firm’s value. However, when taxes are considered, MM show a positive relationship between debt and value, i.e., its value rises as its debt is increased. a. True b. False (16.1) Taxes and capital structure Answer: b Diff: E 2 . According to MM, in a world without taxes the optimal capital structure for a firm is approximately 100% debt financing. a. True b. False (16.1) MM models Answer: a Diff: E 3 . MM showed that in a world with taxes, a firm’s optimal capital structure would be almost 100% debt. a. True b. False (16.1) MM models Answer: a Diff: E 4 . MM showed that in a world without taxes, a firm’s value is not affected by its capital structure. a. True b. False (16.2) Miller model Answer: a Diff: E 5 . The Miller model begins with the MM model with taxes and then adds personal taxes. a. True b. False (16.2) Miller model Answer: b Diff: E 6 . The Miller model begins with the MM model without corporate taxes and then adds personal taxes. Chapter 16: Capital Structure Decisions: Part II Page 3 a.4) MM extension with growth Answer: a Diff: M 10 . a. True b. the appropriate discount rate for the tax shield is the unlevered cost of equity. but with zero personal taxes. Other things held constant. True b. but with zero corporate taxes. The MM model is the same as the Miller model. False (16. False (16. In the MM extension with growth. False (16.5) Financial leverage Answer: a Diff: E 7 . an increase in financial leverage will increase a firm's market (or systematic) risk as measured by its beta coefficient. True b.4) MM extension with growth Answer: b Diff: M 11 . the appropriate discount rate for the tax shield is the after-tax cost of debt. a.2) MM models Answer: a Diff: M 8 .4) MM extension with growth Answer: b Diff: M 12 . False (16. In the MM extension with growth. a. True b. True b. False (16.a. In the MM extension with growth. a. False (16.5) Equity as an option Page 4 Answer: a Diff: M Chapter 16: Capital Structure Decisions: Part II . The MM model with corporate taxes is the same as the Miller model. True b. a. True b. False Medium: (16. the appropriate discount rate for the tax shield is the WACC.2) MM models Answer: b Diff: M 9 . True b. a. its equity can be viewed as an option on the total value of the firm with an exercise price equal to the face value of the debt. When a firm has risky debt.13 . False Chapter 16: Capital Structure Decisions: Part II Page 5 . a. Under MM with corporate taxes. e. c. the value of a levered firm exceeds the value of the unlevered firm by the product of the tax rate times the market value dollar amount of debt. Which of the following statements concerning capital structure theory is NOT CORRECT? a. (16. False Multiple Choice: Conceptual Medium: (16. personal taxes decrease the value of using corporate debt. c.2) Miller model Answer: b Diff: M 15 . rs increases with leverage. (16.3) MM and Miller Answer: d Diff: M 16 . its debt can be viewed as an option on the total value of the firm with an exercise price equal to the face value of the equity.5) Equity as an option Answer: b Diff: M 14 . personal taxes increase the value of using corporate debt. equity costs increase with financial leverage. Under MM with zero taxes.4) MM extension with growth Page 6 Conceptual Questions Answer: d Diff: M Chapter 17: Cap Structure: Ext’ns . financial leverage has no effect on a firm’s value. The major contribution of Miller's theory is that it demonstrates that personal taxes decrease the value of using corporate debt. True b. Under MM with corporate taxes. d. b. debt costs increase with financial leverage. d. When a firm has risky debt. Under MM with corporate taxes. b.(16. and this increase exactly offsets the tax benefits of debt financing. financial distress and agency costs reduce the value of using corporate debt. the effect of business risk is automatically incorporated because rsL is a function of rsU. The major contribution of the Miller model is that it demonstrates that a. e. Which of the following statements concerning the MM extension with growth is NOT CORRECT? a. The total value of the firm increases with the amount of debt. the WACC is less than the WACC under MM’s original (with tax) assumptions. e.17 . b. The tax shields should be discounted at the unlevered cost of equity. For a given D/S. For a given D/S. the levered cost of equity is greater than the levered cost of equity under MM’s original (with tax) assumptions. c. Chapter 16: Capital Structure Decisions: Part II Page 7 . d. The value of a growing tax shield is greater than the value of a constant tax shield. d. what would Firm L's total value be if it had no debt? Page 8 Chapter 16: Capital Structure Decisions: Part II . Which of the following statements concerning the MM extension with growth is NOT CORRECT? a.6% 13.4% 12.4) MM extension with growth Answer: e Diff: M 19 . Firm L has debt with a market value of $200. The firm's equity has a market value of $300. e. and its tax rate is 40%.4) MM extension with growth Answer: a Diff: M 18 . c. c.0% 12. c. e. A similar firm with no debt has a cost of equity of 12%. The total value of the firm increases with the amount of debt.4) MM extension with growth Answer: c Diff: M 21 . the WACC is greater than the WACC under MM’s original (with tax) assumptions. For a given D/S. e. and its tax rate is 40%. Multiple Choice: Problems Medium: (16.000. 11. The tax shields should be discounted at the cost of debt. Under the MM extension with growth. For a given D/S.(16. the levered cost of equity is greater than the levered cost of equity under MM’s original (with tax) assumptions. its earnings are growing at a 5% rate. The value of a growing tax shield is greater than the value of a constant tax shield. Under the MM extension with growth. For a given D/S. The firm's equity has a market value of $300. d. The total value of the firm is independent of the amount of debt it uses. For a given D/S. Which of the following statements concerning the MM extension with growth is NOT CORRECT? a. b. what is Firm L's cost of equity? a.4) MM extension with growth Answer: e Diff: M 20 .000 and a yield of 9%.000.3% 14. d. b.000 and a yield of 9%. Firm L has debt with a market value of $200.0% (16. its earnings are growing at a rate of 5%. b. (16. The value of a growing tax shield is greater than the value of a constant tax shield. A similar firm with no debt has a cost of equity of 12%. the WACC is greater than the WACC under MM’s original (with tax) assumptions. The tax shields should be discounted at the unlevered cost of equity. the levered cost of equity is greater than the levered cost of equity under MM’s original (with tax) assumptions. What is the firm's cost of equity? a. c.000 and a corporate tax rate of 30%.8% 32.4) MM extension with growth Answer: b Diff: M 22 .0%. d. d. Answer: e Diff: E 21.000 of 12.500 $646.250 $710.0% debt. with a yield of 9%.3% 25. c.143 $124. and the cost of equity to an unlevered firm in the same risk class is 16.903 Multi-part: (The following data apply to Problems 23 through 25. what is the value of your firm’s tax shield.875 (16.667. and its tax rate is 40%. c. $92. If the effective personal tax rate on stock income is TS = 20%.750 $587.e.1) MM with tax Answer: c Diff: E 23 .850 (16.2) Miller model Answer: e Diff: T 25 .457 $136.a. Under the MM extension with growth. e.571 $102. Your firm has debt worth $200.000 $437. d.857 $113. (16.421 $377. A similar firm with no debt has a cost of equity of 12%.. and equity worth $300.1) MM with tax 24 . e. b. b. e. 16. b. $358.143 $417. e.0% (16.) The problems MUST be The Kimberly Corporation is a zero growth firm with an expected EBIT of $100.000. how much value does the use of debt add? a.875 $528.000. d. what is the implied personal tax rate on debt income? a.286 $397. i. kept together. c.9% 28. What is the value of the firm according to MM with corporate taxes? a. Kimberly uses $500.0% 23. b.4% Chapter 16: Capital Structure Decisions: Part II Page 9 . It is growing at a 5% rate. Assume that the firm's gain from leverage according to the Miller model is $126. $475. e. Page 10 18.0% Chapter 16: Capital Structure Decisions: Part II .b.5% 25. d.2% 20.2% 22. c. 000. Gomez must reinvest 20% of its EBIT in net operating assets.567.533 $1.760.721 $1. e. $254. e. b.000 $1.77 b.936.280 $182.000 $1. $228. According to the MM extension with growth.(The following data apply to Problems 26 through 28. b. what is Gomez’s unlevered value? a.440. In order to support growth.19 Chapter 16: Capital Structure Decisions: Part II Page 11 . (16.606. and the risk-free rate is 5%.. Gomez has $300.646.400 $192. d.9720 and N(d2) = 0. c. and its tax rate is 40%.889 (The following data apply to Problems 29 through 31.296.000 $1. and a similar company with no debt has a cost of equity of 11%.5) Equity as an option Answer: d Diff: M 29 .529. $156.9050. Inc.) The problems MUST be Gomez computer systems has an EBIT of $200. has total value (debt plus equity) of $500 million and $200 million face value of 1-year zero coupon debt.000 in 8% debt outstanding. c.4) MM extension with growth Answer: e Diff: M 26 . c. The volatility () of Trumbull’s total value is 0. What is the value (in millions) of Trumbull’s equity if it is viewed as an option? a. (16. a growth rate of 6%. e.000 $1.4) MM extension with growth Answer: c Diff: M 27 .492.) The problems MUST be Trumbull. $1.4) MM extension with growth Answer: a Diff: M 28 . According to the MM extension with growth.000 (16.000 $1.600.385 $164. kept together. d. b. According to the MM extension with growth. what is the value of Gomez’s tax shield? a. what is Gomez’s value of equity? a.000 (16.300 $1. d. $1.60.616 $173. Assume that N(d1) = 0. kept together. b. e.82 (16.04% 6. What is the yield on Trumbull’s debt? a.57 $186. $313.43 d.19 $204. e.81 e.19 (16. c.42% Chapter 16: Capital Structure Decisions: Part II . $345. What is the value (in millions) of Trumbull’s debt if its equity is viewed as an option? a. d. c.36% 6.29 $247.70% 7.81 $225. d. b. Page 12 Answer: e Diff: M 6. $282.05% 7. $167.5) Equity as an option 31 .c.5) Equity as an option Answer: b Diff: M 30 . CHAPTER 16 ANSWERS AND SOLUTIONS Chapter 16: Capital Structure Decisions: Part II Page 13 . 000 – $102.(16.(16. so VU = VTotal – VTS = D + S – VTS.(16.2) Miller model Answer: b Diff: E 7.000 rsU : 12% g: 5% rsL = rsU + (rsU – rd)(D/S) = 12% + (12% – 9%)($200.4) MM extension with growth Debt: $200.(16.000) = 14. Value tax shelter = VTS = rdTD/(r sU – g) = 0.(16.2) MM models Answer: b Diff: M 10.(16.5) Equity as an option Answer: b Diff: M 15.4) MM extension with growth Answer: a Diff: M 19.000 rd: 9% T: 40% Equity: $300.12 – 0.1) MM models Answer: a Diff: E 5.3) MM and Miller Answer: d Diff: M 17.4) MM extension with growth Answer: a Diff: M 11.(16.000.(16.(16.(16.(16.4) MM extension with growth Answer: b Diff: M 12.(16.2) Miller model Answer: b Diff: M 16.5) Equity as an option Answer: a Diff: M 14.4) MM extension with growth Answer: e Diff: M 20.(16.000/$300.4) MM extension with growth Answer: e Diff: M Answer: c Diff: M Debt: $200.(16.000 rd: 9% T: 40% Equity: $300.1 .05) = $102.4) MM extension with growth Answer: d Diff: M 18.857 = $397. Here is the calculation: VTotal = VU + VTS.2) MM models Answer: a Diff: M 9.143 .(16. A similar firm with no debt should have a smaller value.1) Taxes and capital structure Answer: a Diff: E 2.(16.(16.40)($200.000 = $500.(16.000 + $200.000)/(0.1) Taxes and capital structure Answer: b Diff: E 3.2) Miller model Answer: a Diff: E 6.857 VU = $300.(16.1) MM models Answer: a Diff: E 4.(16.0% 21.4) MM extension with growth Answer: b Diff: M 13.000 rsU : 12% g: 5% Firm L has a total value of $200.(16.5) Financial leverage Answer: a Diff: E 8.09(0.000 + $300. 56 0.500 + 0.56/X = 0.40)($300.25000 Answer: e Diff: M Answer: c Diff: M rsU: 11% T: 40% EBIT retained: 20% VTS = r dTD/(r sU – g) = 0.000 VU = FCF/(r sU – g) = $80.4) MM extension with growth EBIT: $200.12 – 0.000 rd: 12% Tc: 30% Debt: $500.000 .000/(0.(16.000 Debt: $300.000 = $80.500 24. Note also that the firm has $500.4) MM extension with growth Answer: b Diff: M Answer: c Diff: E Answer: e Diff: E Debt: $200.7)/0.74666 = X= Td = 26.500.(16.0% 25.667 [1 – (0.000 rd: 9% rsU: 12% T: 40% g: 5% VTotal = VU + VTS Value tax shelter = VTS = rdTD/(r sU – g) VTS = r dTD/(r sU – g) = 0.000(0.75000 1 − Td 0.22.000)/(0.70 0.09(0.20) = $200.000 [1 – (1 – Tc)(1 – Ts)/(1 – Td)]D = $126. note that the leveraged value of the firm is $587.857 23. the value of its equity must be $87.74667 0.000 rd: 8% g: 6% Diff: T 0.000 − $40.(16.000 Equity: $300.000 rsU: 16% VU = EBIT(1 – T)/r sU = $100.06) = $192.75000 Td = 25. we find the leveraged cost of equity as follows: rsL = rsU + (rsU – rd)(1 – T)(D/S) = 16% + (16% – 12%)(0.20) = $120.000 = $126.16 = $437.000 27.000)/(0.56/-0.1) MM with tax EBIT: $100.000/$87.11 – 0.(16. Therefore.00% (1 − Tc) = (1 − Ts) = (1 − Tc) × (1 − Ts) = Gain/Debt = Gain/Debt − 1 = X = -0.80 0.7)(0.667 Debt: $500.500 as found in Problem 23.(16.3($500.25333 0.08(0.56/X = 0.11 – 0.000) = $587.06) = $1.500 VL = VU + TD = $437.4) MM extension with growth FCF = NOPAT – Net investment in operating assets = EBIT(1 – T) – EBIT(0.60) – $200.40)($200.05) = $102.75000 1 − Td = 0.000 of debt.74667 X = 0.600.8)/X]$500.2) Miller model Tc: 30% Ts: 20% Answer: e Gain from leverage: $126.7)($500.500) = 32.(16.1) MM with tax First.667 1 – 0.000(0.25333 -0.000(0. Using these data. 5) Equity as an option Yield = [(Face Value/Price)1/Maturity] – 1.000 + $192.(16.17 = $313.0 = 7.000 (from above).310485 N(d2) = 0.000 – $300. VTotal = VU + VTS so.9050) = $485.42% .0 = [$200/$186.19] 1 – 1.492.0 Volatility () = 0. VEquity = VU + VTS – Debt.910485 N(d1) = 0.98 − $172.9050 Vs = PN(d1) – Xe-RFtN(d2) = $500(0.81 30.28.(16.0 Debt = X = $200.(16. VTS = $192.9720) – $200e-0.6 rRF = 5% d1 = 1.000 = $1.600.000 29.9720 d2 = 1. VU = $1.000 (from above).5) Equity as an option VDebt = VTotal – VEquity = $500 – $313. VEquity = $1.600.(16.19 31.05(1)(0.5) Equity as an option Total value = P = $500.81 = $186.4) MM extension with growth Answer: a Diff: M Answer: d Diff: M Answer: b Diff: M Answer: e Diff: M VEquity = VTotal – Debt.