Tutorial+solutions+Week+8

# Tutorial+solutions+Week+8 - Chapter 8 The Rationale for...

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Chapter 8 The Rationale for Hedging Currency Risk Answers to Conceptual Questions 8.1 Describe the conditions that can lead to tax schedule convexity. Tax schedule convexity can arise from any of the following: a) progressive taxation in which larger taxable income receives a higher tax rate, b) tax-loss carryforwards or carrybacks, c) Alternative Minimum Tax (AMT) rules, d) investment tax credits. 8.2 Define financial distress. Give examples of direct and indirect costs of financial distress. Financial distress refers to the additional financial troubles facing firms when the value of equity approaches zero. Direct costs are incurred during bankruptcy proceedings. Indirect costs include lower revenues or higher operating/financial costs. 8.3 What is an agency conflict? How can agency costs be reduced? Agency conflicts arise as managers act in their own interests rather than those of shareholders. Agency costs are the costs of aligning managers’ and shareholders’ objectives. Although currency risk may be diversifiable to shareholders, managers are undiversified and care about currency risk. Allowing managers to hedge exposure to currency risk may reduce agency conflicts. Problem Solutions 8.1 a. Expected taxable income is (½)(\$250,000) + (½)(–\$250,000) = \$0. E[PV(taxes)|unhedged] = (½)(\$125,000)–(½)(\$125,000)/(1.25) = \$12,500. The present value of current taxes is \$125,000. The present value of the tax shield received in one year is only (\$125,000)/(1.25) = \$100,000. E[PV(taxes)|hedged] = Tax rate times expected taxable income = (½)(\$0) = \$0, an expected tax savings of \$12,500. b. Expected taxable income is (½)(\$250,000) + (½)(–\$250,000) = \$0. E[PV(taxes)|unhedged] = (½)(\$125,000)–(½)(\$125,000)/(1.00) = \$0. E[PV(taxes)|hedged] = (tax rate) times (expected taxable income) = (½)(\$0) = \$0. The present value of the tax shield from tax loss carryforwards increases at lower discount rates. If the discount rate is zero, time doesn’t matter and future tax shields have the same magnitude as current tax payments. c. Expected taxable income is (½)(\$250,000) + (½)(–\$250,000) = \$0. E[PV(taxes)|unhedged] = (½)(\$125,000)–(½)(\$125,000)/(1.25) 2 = \$22,500. The present value of current taxes is \$125,000. The present value of the tax shield received in one year is only (\$125,000)/(1.25) 2 = \$80,000. E[PV(taxes)|hedged] = (tax rate) times (expected taxable income) = (0.50)(\$0) = \$0, a savings in expected tax payments of \$22,500.

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8.2 a. b. Expected taxes with no hedging: (½) [(R500,000)(0.20)] + (½)[(R1,000,000)(0.20) + (R500,000)(0.40)] = (½) (R100,000) + (½) (R400,000) = R250,000. c. Expected taxes with hedging: (R1,000,000)(0.20) = R200,000 < R250,000. d. Hedging allows Widget to minimize its expected tax liability. This increase in expected future cash flows to equity results in an increase in equity value. 8.3 a. At \$6,000 in taxable income, debt receives \$4,000 and equity receives nothing. At \$16,000 in taxable income, debt receives \$10,000 and equity receives \$6,000. b. Firm value as a combination of debt plus equity: c. Unhedged E[V Bonds ] = (½)(\$6,000–\$2,000) + (½)(\$10,000) = \$7,000 Taxes 20% tax rate 40% tax rate R0 R2,000,000 R1,000,000 R500,000 R1,500,000 Taxable income R200,000 R250,000 V Bonds + V Stock = V Bonds + Stock += \$10,000 \$10,000 \$10,000 \$6,000 \$16,000 Firm value
+ E[V Stock ] = (½)(\$0) + (½)(\$6,000) = \$3,000 E[V Firm ] = (½)(\$6,000–\$2,000) + (½)(\$16,000) = \$10,000 Hedged E[V Bonds ] = \$10,000 + E[V Stock ] = \$1,000 E[V Firm ] = \$11,000 Firm value rises from \$10,000 when unhedged to \$11,000 when hedged. Hedging results in a \$3,000 increase in the value of debt and a \$2,000 decrease in the value of equity, for a net gain of \$1,000. The \$1,000 net gain is captured by avoiding the ½ probability of a

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Tutorial+solutions+Week+8 - Chapter 8 The Rationale for...

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