Design Interiors has a cost of equity of 14.9 percent and a pretax cost of debt of 8.6 percent. The firm's target weighted average cost of capital is 11 percent and its tax rate is 34 percent. What is the firm's target debt-equity ratio?

0.73

Explanation:

Given that

WACC = 11%

Tax rate = 34%

Cost of equity = 14.9 %

Cost of debt = 8.6%

Recall that

WACC = (cost of equity × % of equity) + (cost of debt × % of debt) + ( 1 - tax rate)

We are to find

Cost of debt and cost of equity

Let

Cost of debt be x

Cost of equity be (1 - x)

Thus,

0.11 = (1 - x)(0.149) + (x)(0.086)(1 - 0.34)

x = 0.4228

Therefore,

Debt-equity ratio

= Cost of debt/cost of equity

= 0.4228/(1 - 0.4228)

= 0.73

0.733 is the firm’s target debit-equity ratio

Explanation:

In this question, we are asked to calculate the firm’s debt-equity ratio.

To calculate this, we proceed as follows;

WACC = (Weight of equity * Cost of equity)+ (Weight of Debt* cost of debt)+ (1 - tax rate)

We identify the following;

WACC = 11%

Weight of equity = x

Cost of equity = 14.9%

Weight of debt = 1 - weight of equity = 1 - x

After tax cost of debt = 34%

11= x*14.9 + (1-x)*8.6*(1-34%)

11 = 14.9x + 5.676(1-x)

11 = 14.9x + 5.676 -5.676x

11-5.676 = 14.9x - 5.676x

5.324 = 9.224x

x = 5.324/9.224 = 0.577

Weight of equity = 0.577

Weight of Debt = 1-0.577 = 0.423

Firm's target debt-equity ratio = Weight of Debt /Weight of equity

Firm's target debt-equity ratio = 0.423/0.577= 0.733

Firm's target debt-equity ratio = 0.733

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