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CH18 - CHAPTER 18 How Much Should a Firm Borrow Answers to...

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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 = .44 ($1 - $0) Total = $.440 For $1 of equity income, with all capital gains realized immediately: Corporate tax = .35 ($1) Personal tax = .44 {.5 [$1 - 35 ($1) ] } + .28 {.5 [$1 - .35($1) ] } Total = $.584 For $1 of equity income, with all capital gains deferred forever: Corporate tax = .35 ($1) Personal tax = .44 {.5 [$1 - .35 ($1) ] } Total = $.493 2. Consider a firm which is levered, has perpetual expected cash flow X, and has an interest rate of r D on its debt. 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 ) which makes the value of the stockholders’ position: 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 in each year is: 189 ) 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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which makes the value of the stockholders’ position: The difference is stockholder wealth, for investment in the same assets, is: This is the change in stockholder wealth predicted by MM. If individuals could not deduct interest, then: and 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 Merck’s assets if $16,408 million. With a 40 percent book debt ratio, debt is $6,563 million, $5,417 million more than shown in Table 18-3a. The corporate tax rate is 35 percent, so firm value increases by $1,896 million. The market value of the firm is now $54,581 million. The market value balance sheet is: Net working capital $1,473 $6,563 Long-term debt Market value of long-term assets 51,212 4,123 Other long-term liabilities Present value of additional tax shields 1,896 43,895 Equity Total Assets $54,581 $54,581 Firm market value 190 ) 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 - - - - = c u L T D V V = - ) 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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Answers here will vary according to the company chosen. However, the general analysis should closely parallel that in the text, Section 18.1. 4. The value of tax shields are determined by: The on-going degree of profitability. The ability to carry-forward and carry-back excess credits The ability to maintain debt levels on an on-going basis. The rates of personal and corporate taxation. The amount of non-interest tax shields 5. When a firm defaults, the cause (absent fraud) is usually an operating problem. Although both shareholders and debtholders are worse off, their expected rate of return is designed to compensate for this risk. As noted in Section 18.3, the combined positions of stock and bondholders in limited liability and unlimited liability firms is the same. The ability to assign the assets to the creditors and not have to repay has value to the shareholders since it is a more efficient transfer of wealth.
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