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Brealey. Myers. Allen Chapter 18 Solution - CHAPTER 18 How...

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146 CHAPTER 18 How Much Should a Firm Borrow? Answers to Practice Questions 1. a. T c is the corporate tax rate, T p is the personal tax rate on interest income and T pE is the effective personal tax rate on equity income. In the U.K., T c = 30% and T p = 40%. T pE is less than 40% because the effective capital gains tax rate for the John Peel Group is zero. If, for example, T pE = 20%, then: (1 – T pE ) × (1 – T c ) = 0.80 × 0.70 = 0.56 and: 1 – T p = 0.60 Here, a lower debt ratio reduces the sum of corporate and personal taxes. If T pE = 14.3% then: (1 – T pE ) × (1 – T c ) = 0.857 × 0.70 = 0.600 If the effective tax rate on equity income is 14.3% or higher, then a lower debt ratio reduces the sum of corporate and personal taxes. Since the John Peel Group shareholders are in the top U.K. tax bracket, indicating relatively high income, it seems likely that T pE is relatively high; the annual allowance of £8,000 is relatively low for high-income taxpayers, so that the bulk of their equity income is in the form of cash dividends. b. As discussed in Chapter 16, an increase in cash dividend payout, holding capital investment and debt constant, must be financed by issuing new shares; the capital loss to existing shareholders resulting from the new issue exactly offsets the increased cash dividend. For the John Peel Group shareholders, the increased dividend is taxed at 40% but the capital loss is apparently not tax deductible. Therefore, an increase in cash dividend payout increases the sum of corporate and personal taxes. The John Peel Group should maintain a low dividend payout ratio and use internally generated funds as its primary source of financing.
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147 2. Consider a firm that is levered, has perpetual expected cash flow X, and has an interest rate for debt of r D . The personal and corporate tax rates are T p and T c , respectively. The cash flow to stockholders each year is: (X - r D D)(1 - T c )(1 - T p ) Therefore, the value of the stockholders’ position is: where r is the opportunity cost of capital for an all-equity-financed firm. If the stockholders borrow D at the same rate r D , and invest in the unlevered firm, their cash flow each year is: The value of the stockholders’ position is then: The difference in stockholder wealth, for investment in the same assets, is: V L – V U = DT c This is the change in stockholder wealth predicted by MM. If individuals could not deduct interest for personal tax purposes, then: Then: So the value of the shareholders’ position in the levered firm is relatively greater when no personal interest deduction is allowed. ) T (1 ) (r ) T (1 ) T (1 D) ( ) (r ) T (1 (r) ) T (1 ) T (1 (X) V p D p c D p p c L = )] T (1 D) ( ) T (1 (r) ) T (1 ) T (1 (X) V c p p c L = [ )] T (1 D) ( ) r ( )] T (1 ) T (1 [(X) p D p c [ ) T (1 ) (r ) T (1 D) ( ) (r ) T (1 (r) ) T (1 ) T (1 (X) V p D p D p p c U = D ) T (1 (r) ) T (1 ) T (1 (X) V p p c U = ) T (1 ) (r D) )( (r ) T (1 (r) ) T (1 ) T (1 (X) V p D D p p c U = ) T (1 ) (r )] T (1 ) T (1 D) )( r ( [ D) ( ) (r V V p D p c D D U L = + = ) T (1 T D ) T D ( V V p p c U L
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148 3. The book value of Pfizer’s assets is $97,652 million.
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