Delta Corporation has the following capital structure: Cost (aftertax) Weights Weighted Cost Debt (Kd) 6.2 % 25 % 1.55 % Preferred stock (Kp) 5.5 25 1.38 Common equity (Ke) (retained earnings) 15.5 50 7.75 Weighted average cost of capital (Ka) 10.68 % a. If the firm has $22 million in retained earnings, at what size capital structure will the firm run out of retained earnings

the  firm run out of retained earnings at $44 million

Explanation:

The equity capital is the retained earnings. From the question given 50% is the amount of equity  capital the firm must maintain to keep a balance between fixed income securities and  ownership interest.

But equity capital in the form of retained earnings cannot grow  as the firm’s capital needs expand because retained earnings is limited to the  amount of past and present earnings that can be redeployed into the investment projects.

Delta Corporation has $22 million of retained  earnings. Since retained earnings is to represent 50% of  the capital structure:

Y =  Retained earnings / weight of common equity (retained earnings)

where;

Y represents the size of the capital structure that retained earnings will support

Retained earnings=  $22 million  and  

weight of common equity = 50% = 0.5

Therefore Y  = $22 million/0.5 = $44 million.

After the first $44 million, retained earnings will no longer be  available to provide the 60 percent equity position in the capital structure. After $44 million, common equity capital will be in the form of new  common stock rather than retained earnings.

Also to calculate the size of the capital structure in which lower-cost debt can be  utilized (Z)

Z = Amount of lower cost debt / Weight of debt

in this case, weight of debt = 25%= 0.25,  if the cost of debt referred to earlier applies only to the first $25 million of debt

Z = $25 million/ 0.25 = $100 million

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