The following information has been presented to you about the Gibson Corporation. $$\begin{array} { l c }
\text { Total assets } & \$ 3,000 \text { millionTax rate } &25\%\
\text { Operating income (EB TT) } & \$ 800 \text { millionDebt ratio } &0\%\
\text { Interest expense } & \$ 0 \text { millionW } \mathrm { ACC } &10\%\
\text { Net income } & \$ 480 \text { millionM/B ratio } &1.00×\
\text { Share price } & \$ 32.00 \mathrm { EPS } = \text { DPS }&\$3.20
\end{array}$$ The company has no growth opportunities (g = 0), so the company pays out all of its earnings as dividends (EPS = DPS).The consultant believes that if the company moves to a capital structure financed with 20% debt and 80% equity (based on market values) that the cost of equity will increase to 11% and that the pre-tax cost of debt will be 8%.If the company makes this change, what would be the total market value (in millions) of the firm?
A) $4,400
B) $4,800
C) $5,200
D) $5,400
E) $6,000

Question

The following information has been presented to you about the Gibson Corporation. $$\begin{array} { l c } 
\text { Total assets } & \$ 3,000 \text { millionTax rate } &25\%\
\text { Operating income (EB TT) } & \$ 800 \text { millionDebt ratio } &0\%\
\text { Interest expense } & \$ 0 \text { millionW } \mathrm { ACC } &10\%\
\text { Net income } & \$ 480 \text { millionM/B ratio } &1.00×\
\text { Share price } & \$ 32.00 \mathrm { EPS } = \text { DPS }&\$3.20
\end{array}$$ The company has no growth opportunities (g = 0), so the company pays out all of its earnings as dividends (EPS = DPS).The consultant believes that if the company moves to a capital structure financed with 20% debt and 80% equity (based on market values) that the cost of equity will increase to 11% and that the pre-tax cost of debt will be 8%.If the company makes this change, what would be the total market value (in millions) of the firm?
A) $4,400
B) $4,800
C) $5,200
D) $5,400
E) $6,000

Quizplus · Accepted Answer

To calculate the total market value of the firm after the change in capital structure, we can use the Modigliani and Miller Proposition II with taxes, which suggests that the value of the leveraged firm equals the value of the unleveraged firm plus the tax shield on debt.First, calculate the unleveraged firm value (VU). Since the company pays out all of its earnings as dividends and there is no growth, the value of the firm can be calculated using the dividend discount model (DDM) for a no-growth firm, which simplifies to $V = \frac{D}{r}$, where $D$ is the dividend per share and $r$ is the required rate of return (cost of equity for an unleveraged firm).Given that the EPS = DPS = $3.20 and the cost of equity (WACC for an unleveraged firm) is 10%, the value of the unleveraged firm is:$$VU = \frac{3.20}{0.10} = 32 \text{ per share}$$Given the share price is $32, the market value per share does not change, indicating that the calculation aligns with the given share price, confirming the approach. However, to find the total market value of the firm, we should consider the net income and the cost of equity.The net income is $480 million, and the cost of equity is 10%, so the total market value of the unleveraged firm (VU) can also be calculated as:$$VU = \frac{\text{Net Income}}{\text{Cost of Equity}} = \frac{480}{0.10} = 4800 \text{ million}$$However, this calculation does not directly lead to the correct answer because it does not account for the change in capital structure. The correct approach involves calculating the value of the leveraged firm (VL) using the tax shield benefit.With 20% debt, the firm plans to have a capital structure that includes a tax shield. The tax shield on debt is calculated as $TD = tc \times D$, where $tc$ is the corporate tax rate and $D$ is the amount of debt. The corporate tax rate is 25%, and if the firm moves to 20% debt based on market values, we need to calculate the new value with the tax shield.The mistake in the initial calculation is not accounting for the new capital structure and the tax shield. The correct approach involves using the new WACC under the leveraged structure to find the value of the firm, considering the tax shield.Given the lack of direct information to calculate the leveraged value with the provided data and the approach leading to confusion, the correct answer involves understanding that the value of the firm increases due to the tax shield on debt, but without the exact calculation provided in the initial response, pointing directly to the correct choice is challenging based on the initial explanation. The key is recognizing that the value of the firm is expected to increase due to the tax benefits of debt, and the correct answer would involve recalculating based on the new capital structure and the tax shield, which was not accurately completed in the initial response.

The Following Information Has Been Presented to You About the Gibson