CH18

# Fundamentals of Corporate Finance + Standard & Poor's Educational Version of Market Insight

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CHAPTER 18 How Much Should a Firm Borrow? Answers to Practice Questions 1. For \$1 of debt income: Corporate tax =\$0 Personal tax = 0.44 × \$1 = \$0.440 Total = \$0.440 For \$1 of equity income, with all capital gains realized immediately: Corporate tax = 0.35 × \$1 = \$0.350 Personal tax = 0.44 × 0.5 × [\$1 – (0.35 × \$1)] + 0.20 × 0.5 × [\$1 – (0.35 × \$1)] = \$0.208 Total = \$0.558 For \$1 of equity income, with all capital gains deferred forever: Corporate tax = 0.35 × \$1 = \$0.350 Personal tax = 0.44 × 0.5 × [\$1 – (0.35 × \$1)] = \$0.143 Total = \$0.493 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: 161 ) 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 - - - - [

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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. 3. The book value of Pfizer’s assets is \$21,529 million. With a 40 percent book debt ratio: Long-term debt + Other long-term liabilities = 0.40 × \$21,529 = \$8,612 This is [\$8,612 – (\$2,123 + \$4,330)] = \$2,159 more than shown in Table 18.3(a). The corporate tax rate is 35 percent, so firm value increases by: 0.35 × \$2,159 = \$756 million The market value of the firm is now: (\$296,247 + \$756) = \$297,003 million. The market value balance sheet is: Net working capital \$5,206 \$4,282 Long-term debt Market value of long-term assets 291,797 4,330 Other long-term liabilities 288,391 Equity Total Assets \$297,003 \$297,003 Firm market value 4. Answers here will vary depending on the company chosen. 162 ) 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
5. The value of interest tax shields is determined by:

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CH18 - CHAPTER 18 How Much Should a Firm Borrow Answers to Practice Questions 1 For \$1 of debt income Corporate tax = \$0 Personal tax = 0.44 \$1 =

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