# Answer 3 we see that v l v u 213 2 013 billion since

This preview shows pages 17–18. Sign up to view the full content.

ANSWER (3): We see that V L – V U = \$2.13 – \$2 = \$0.13 billion . Since this value is just G L , we can show that G L for the personal tax view is greater than the G L for the corporate tax view. For the corporate tax view, we have: G L = TD = T(CPN / r d ) = 0.2(50 / 0.05) = \$0.2 billion . Thus, the corporate tax view gives a value that is \$0.2 – \$0.13 = \$0.07 billion or \$70,000 million more . Most of the difference can be explained by the fact debtholders now pay taxes. Note that even without considering the impact of (1 – α ), we have: (1 – T d )CPN / r d = (1 – 0.85)\$50M / 0.05 = \$850 million. For the corporate tax view, this value would be \$1 billion because debtholders do not pay personal taxes. 74. Consider the following definitions. The gain to leverage (G L ) equals leveraged firm value (V L ) minus unleveraged firm value (V U ). V L equals leveraged equity value (E L ) plus debt value (D). E L equals (1 – T e )(1 – T)( – CPN) / r L where T e is the applicable tax rate on equity income, T is the firm's applicable corporate tax rate, is the uncertain perpetual before-tax cash flow for unleveraged equity owners, CPN is the perpetual before-tax cash flow for debt owners, and r L is the endogenously determined cost of leveraged equity. V U is unleveraged equity value (E U ) and equals (1 – T e )(1 – T) / r where r is the exogenous cost of unleveraged equity. D is (1 – T d )CPN / r d where T d is the applicable tax rate on debt income, and r d is the cost of debt. Given these definitions answer the below questions. (1) Substitute the definitions of E L and D into the formula for V L and then substitute this expression into the definition for G L . After doing this, use algebra to see if you can get gain to leverage = G L = [1 – α r d / r L ]D – [1 – (r / r L )]E U where α = (1 – T e )(1 – T) / (1 – T d ). NOTE. The derivation is unimpeded regardless of whether r d is the exogenous riskless rate or is endogenously determined by the choice of D. (2) Why might this expression for gain to leverage be more valuable than other expressions? ANSWER (1): Substituting the definitions of E L and D into the formula for V L gives: V L = E L + D = [(1 – T e )(1 – T)( – CPN) / r L ] + D. Substituting this expression along with the definition V U = E U into the definition G L = V L – V U gives: G L = [(1 – T e )(1 – T)( – CPN) / r L ] + D – E U . Multiplying out the first component and rearranging: G L = D – [(1 – T e )(1 – T)CPN / r L ] – E U + [(1 – T e )(1 – T) / r L ]. Multiplying the second component by (1 – T d )r d / (1 – T d )r d = 1 and noting that this is equivalent to – {(1 – T e )(1 – T)r d / (1 – T d )r L }(1 – T d )CPN / r d which is – [(1 – T e )(1 – T)r d / (1 – T d )r L ]D, and factoring out D: G L = [1 – {(1 – T e )(1 – T)r d / (1 – T d )r L }D – E U + [(1 – T e )(1 – T) / r L ]. Multiplying the last component by r / r = 1 and noting this equals (r / r L )(1 – T e )(1 – T) / r which is (r / r L )E U , and factoring out E U : G L = [1 – {(1 – T e )(1 – T}r d / (1 – T d )r L }]D – [1 – (r / r L )]E U .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern