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Chapter 16 Appendix Solutions

# Chapter 16 Appendix Solutions - Chapter 16 Appendix The...

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Chapter 16 Appendix: The Miller Model and the Graduated Income Tax 16.17 a. According to the Miller Model, in equilibrium: r B (1 – T C ) = r S where r B = the pre-tax cost of debt (the interest rate) T C = the corporate tax rate r S = the required return on a firm’s equity In this problem: T C = 0.35 r S = 0.11 Therefore, in order for there to be equilibrium: r B (1 – T C ) = r S r B (1 – 0.35) = 0.11 r B = 0.11 / (1 – 0.35) = 0.1692 The equilibrium interest rate is 16.92%. b. In order to determine whether each group would prefer to hold debt or equity, it is necessary to compare the after-personal tax interest rate to the required return on unlevered equity for each of the three groups of investors. A group of investors will prefer to hold the security that offers them the highest rate of return. The required rate of return to equity holders is 11%. Since the effective personal tax rate on equity distributions is zero, personal taxes do not change the required return to equity holders. The market interest rate is 16.92%. The after-personal tax interest rate for investors who face a 10% tax on interest income is 15.23% {= 0.1692 * (1 - 0.10)}. Since the after-personal tax interest rate (15.23%) is greater than the required return on equity (11%), this group is better off holding debt. Investors whose interest income is taxed at 10% will buy debt. The after-personal tax interest rate for investors who face a 20% tax on interest income is 13.54% {= 0.1692 * (1 - 0.20)}. Since the after-tax interest rate (13.54%) is greater than the required return on equity (11%), this group is also better off holding debt. Investors whose interest income is taxed at 20% will buy debt. The after-personal tax rate interest rate for investors who face a 40% tax on interest income is 10.15% {= 0.1692 * (1 - 0.40)}. Since the after-tax interest rate (10.15%) is less than the required return on equity (11%), this group is also better off holding equity. Investors whose interest income is taxed at 40% will buy equity. c. According to the Miller Model, firm value does not vary with capital structure in equilibrium. Therefore, Firm A’s value would be equal to an all-equity financed firm with EBIT of \$1 million in perpetuity. V A = [(EBIT)(1 – T C )] / r S

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= [(\$1,000,000)(1 – 0.35)] / 0.11 = \$5,909,091 The value of Firm A is \$5.91 million. 16.18 a. According to the Miller Model, in equilibrium: r B (1 – T C ) = r S where r B = the pre-tax cost of debt (the interest rate) T C = the corporate tax rate r S = the required return on a firm’s equity In this problem: T C = 0.35 r S = 0.081 Therefore: r B (1 – T C ) = r S r B (1 – 0.35) = 0.081 r B = 0.081 / (1 – 0.35) = 0.1246 The equilibrium market rate of interest is 12.46%. b. In order to determine whether each group would prefer to hold debt or equity, compare the after-personal tax interest rate on debt to the required return on unlevered equity for each of the three groups of investors. A group of investors will prefer to hold the security that offers them the highest rate of return.
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Chapter 16 Appendix Solutions - Chapter 16 Appendix The...

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