Question

Thomas Co. expects its EBIT to be $250,000 every year forever. The firm can borrow at 5 percent. The company currently has no debt, and its cost of equity is 14 percent. The corporation tax rate for Thomas is 21 percent. (a) What is the value of the firm? (b) What will the value be if the company borrows $300,000 and uses the proceeds to repurchase shares? (c) What is the cost of equity after recapitalization? (d) What is the WACC after recapitalization?

Answer 1

(a) What is the value of the firm?

Value of the firm = Expected EBIT / WACC

Since the company initially has no debt, the WACC is simply the cost of equity:

WACC = Cost of equity = 14%

Value of the firm = $250,000 / 0.14 = $1,785,714

(b) What will the value be if the company borrows $300,000 and uses the proceeds to repurchase shares?

After borrowing $300,000, the new capital structure is:

Debt of $300,000

Equity of $1,785,714

The debt proportion is:

Debt / (Debt + Equity)

= $300,000 / ($300,000 + $1,785,714)

= 0.14

Assuming the cost of debt remains 5% and cost of equity increases to 15%, the new WACC is:

WACCnew = (0.15 * (1 - 0.21)) + (0.05 * 0.14)

= 0.122

The revised firm value is:

Firm valuenew = $250,000 / 0.122

= $2,045,090

(c) Cost of equity after recapitalization = 15% (as assumed)

(d) WACC after recapitalization = 0.122 (calculated above)

In summary:

• (a) Firm value initially= $1,785,714
• (b) Revised firm value after borrowing = $2,045,090
• (c) Cost of equity after recapitalizing = 15%
• (d) WACC after recapitalizing = 0.122

The key corrections are:

Calculating WACC correctly both before and after borrowing

Using a reasonable assumption for the new cost of equity

Using the correct debt proportion to calculate the new WACC

Calculating the revised firm value based on the correct new WACC

Hope this helps! Let me know if you have any other questions.

Answer 2

To calculate the values requested, we'll use the following information:

EBIT (Earnings Before Interest and Taxes) = $250,000
Cost of Equity (Ke) = 14%
Tax Rate = 21%
Debt Interest Rate (Kd) = 5%
Debt Recapitalization Amount = $300,000

Let's calculate the values step by step:

(a) Value of the Firm (Unlevered Firm Value):
The value of the firm without any debt is calculated using the formula for the unlevered firm value:

Value of the Firm = EBIT / Cost of Equity

Using the given values:
Value of the Firm = $250,000 / 0.14 = $1,785,714.29

(b) Value of the Firm after Share Repurchase:
When the firm borrows $300,000 and uses it to repurchase shares, it increases its debt. The value of the firm after the recapitalization is calculated using the adjusted formula:

Value of the Firm = (EBIT * (1 - Tax Rate)) / (Cost of Equity - Debt Interest Rate * (1 - Tax Rate))

Using the given values:
Value of the Firm = ($250,000 * (1 - 0.21)) / (0.14 - 0.05 * (1 - 0.21)) = $1,041,666.67

(c) Cost of Equity after Recapitalization:
The cost of equity after recapitalization is determined by adjusting the cost of equity based on the new capital structure. We can calculate it using the formula:

Cost of Equity = Cost of Equity before Recapitalization * (1 + ((Debt / Equity) * (1 - Tax Rate)))

Using the given values and assuming the original equity is equal to the initial firm value:
Cost of Equity = 0.14 * (1 + (($300,000 / $1,785,714.29) * (1 - 0.21))) = 0.1459 or 14.59%

(d) Weighted Average Cost of Capital (WACC) after Recapitalization:
The WACC after recapitalization is calculated using the new capital structure. We can calculate it using the formula:

WACC = (Equity / Total Value) * Cost of Equity + (Debt / Total Value) * Cost of Debt * (1 - Tax Rate)

Using the given values:
WACC = ($1,041,666.67 / ($1,041,666.67 + $300,000)) * 0.1459 + ($300,000 / ($1,041,666.67 + $300,000)) * 0.05 * (1 - 0.21) = 0.1235 or 12.35%

Therefore:
(a) The value of the firm is $1,785,714.29.
(b) The value of the firm after the share repurchase is $1,041,666.67.
(c) The cost of equity after recapitalization is 14.59%.
(d) The WACC after recapitalization is 12.35%.