Question

Question: Delta Corporation has the following capital structure:

	Cost (after tax)	Weights	Weighted cost
Debt	8.1%	35%	2.84
Preferred stock (Kp)	9.6	5	0.48
Common equity (Ke) (retained earnings)	10.1	60	6.06
Weighted average cost of capital (Ka)			9.38%

a. If the firm has \(18 million in retained earnings, at what size capital structure will the firm run out of retained earnings?

b. The 8.1 percent cost of debt referred to earlier applies only to the first \)14 million of debt. After that the cost of debt will go up. At what size capital structure will there be a change in the cost of debt?

Short answer

Answer

1. $30 million.
2. $40 million.

Step-by-step solution

Definition of Retained Earnings

The income of the business entity that is kept aside for re-investment in the business entity or to make dividend payments in future periods is known as retained earnings.

Calculation of capital structure at which the firm will run out of retained earnings

The weight of the common equity represents the retained earnings in the capital structure, which is 60% of the total capital structure. Therefore, the size of the capital structure at which the firm will run out of retained earnings is calculated as:

$$\begin{gathered} \mathit{Y}\mathbf{=}\frac{\mathbf{R}\mathbf{e}\mathbf{t}\mathbf{a}\mathbf{i}\mathbf{n}\mathbf{e}\mathbf{d}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{n}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{s}}{\mathbf{W}\mathbf{e}\mathbf{i}\mathbf{g}\mathbf{h}\mathbf{t}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{m}\mathbf{o}\mathbf{n}\mathbf{e}\mathbf{q}\mathbf{u}\mathbf{i}\mathbf{t}\mathbf{y}} \\ \mathbf{=}\frac{\mathbf{\$}\mathbf{18}}{\mathbf{60}\mathbf{\%}} \\ \mathbf{=}\mathbf{\$}\mathbf{30}\mathbf{}\mathit{m}\mathit{i}\mathit{l}\mathit{l}\mathit{i}\mathit{o}\mathit{n} \end{gathered}$$

Capital structure at which there is a change in the cost of debt

The cost of debt only applied to the first $14 million. Therefore, the capital structure at which the cost of debt will change will be calculated as follows:

$$\begin{gathered} \mathit{Z}\mathbf{=}\frac{\mathbf{D}\mathbf{e}\mathbf{b}\mathbf{t}}{\mathbf{W}\mathbf{e}\mathbf{i}\mathbf{g}\mathbf{h}\mathbf{t}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{D}\mathbf{e}\mathbf{b}\mathbf{t}} \\ \mathbf{=}\frac{\mathbf{\$}\mathbf{14}}{\mathbf{35}\mathbf{\%}} \\ \mathbf{=}\mathbf{\$}\mathbf{40}\mathbf{}\mathit{m}\mathit{i}\mathit{l}\mathit{l}\mathit{i}\mathit{o}\mathit{n} \end{gathered}$$