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# 1 what is the gain to leveraged if t 03 and d 2

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(1) What is the gain to leveraged if T = 0.3 and D = \$2 billion? What is G L if T falls to 0.2? (2) What is the gain to leveraged if T = 0.3, CPN = \$50 million, and r d = 0.05? What is G L if T falls to 0.2? (3) Is this equation complete? For example, exactly what variables are missing from this equation? ANSWER (1): G L = TD = 0.3(\$2 billion) = \$600 million . If T falls to 0.2 then G L = TD = 0.2(\$2 billion) = \$400 million . ANSWER (2): G L = TD = T(CPN / r d ) = 0.3(\$50 million / 0.05) = 0.3(\$1 billion) = \$300 million . If T falls to 0.2 then G L = 0.2(\$50 million / 0.05) = 0.2(\$1 billion) = \$200 million . ANSWER (3): This equation is incomplete since it ignores possible effects stemming from either personal taxes or leverage costs such as agency and financial distress (including bankrupctcy). In particular, this equation does not contain the personal tax rates on equity and debt income and the required rates of return on equity. This equation also assumes that the cost of debt is not influenced by the amount of debt issued in which case debt is riskless (or at least unchanging). 71. Acme, Inc. currently has no debt and has an unleveraged value (V U ) of \$2 billion. It has 100 million shares outstanding. It decides to retire 50 million shares by issuing debt. Its corporate tax rate (T) is 20% and all of the debt can be raised with a coupon rate of 5%. Answer the below questions. (1) Using the corporate tax view of capital structure, what is Acme’s leveraged value (V L ) after its exchange of debt for stock? (2) What would be Acme’s value be if it decided to retire all of its shares? (3) Is your answer in (2) possible? Explain. (4) Realistically, could a firm ever achieve a debt level reaching 100% debt?

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ANSWER (1): According to the corporate tax view of capital, we have: V L = V U + G L = V U + TD = \$2 billion + (0.2)\$1B = \$2.2 billion . ANSWER (2): If Acme decides to retire all of its shares, we have: V L = V U + G L = V U + TD = \$2 billion + (0.2)\$2B = \$2.4 billion . ANSWER (3): This answer is not possible because by definition a company is a legal entity controlled by shareholders. With all debt, we have no shareholders and all debtholders become the new owners. Their payments would no longer be tax deductible. ANSWER (4): Realistically, the capital markets would not lend money to companies with such high debt levels due to the risk involved. Also, stakeholders would not want to take on so much risk. Jobs and livelihood would be threatened. 72. Early advocates of the personal tax view of capital structure argued that personal taxes on equity and debt income offset the positive corporate tax shield. The gain to leverage (G L ) is captured by the following equation: G L = [1 – α ]D where α = (1 – T e )(1 – T) / (1 – T d ); T e = the personal tax rate applicable to income from equity; T d = personal tax rate applicable to income from debt; T = applicable corporate tax rate; D = (1 – T d )CPN / r d ; CPN = perpetual before-tax cash flow for debt owners; and, r d is the required rate of return for debt or the cost of debt (which is considered riskless or at least assumed not to change with increasing debt levels). Answer the following questions using the above the gain to leverage equation.
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