a firm wants to create a weighted average cost of capital (WACC) of 10.4 percent. The firm's cost of equity is 14.5 percent and its pre-tax cost of debt is 8.5 percent. The tax rate is 34 percent. What does the debt weight need to be for the firm to achieve its target WACC?

To find the debt weight needed for the firm to achieve its target WACC, we need to use the formula for WACC:

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

Where:
- Equity is the market value of the firm's equity
- Total Value is the sum of the market value of equity and the market value of debt
- Debt is the market value of the firm's debt
- Tax Rate is the corporate tax rate
- Cost of Equity is the return required by equity investors
- Cost of Debt is the return required by debt investors

In this case, we have the following information:

WACC = 10.4%
Cost of Equity = 14.5%
Pre-tax Cost of Debt = 8.5%
Tax Rate = 34%

Let's assume the market value of equity is E, the market value of debt is D, and the total value is V.

Now we can rearrange the formula to solve for the debt weight:

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

10.4% = (E / V) * 14.5% + (D / V) * (1 - 34%) * 8.5%

Simplifying further:

0.104 = 0.145 * (E / V) + 0.66 * (D / V) * 0.085

To find the debt weight (D / V), we substitute (E / V) with (1 - D / V) in the equation:

0.104 = 0.145 * (1 - D / V) + 0.66 * (D / V) * 0.085

Now we solve for (D / V):

0.104 = 0.145 - 0.145 * (D / V) + 0.0561 * (D / V)

0.145 * (D / V) + 0.0561 * (D / V) = 0.145 - 0.104

0.2011 * (D / V) = 0.041

(D / V) = 0.041 / 0.2011

(D / V) ≈ 0.204

Therefore, the debt weight (D / V) needed for the firm to achieve its target WACC of 10.4% is approximately 0.204 or 20.4%.