A firm's correctly computed capital structure consists of 20% debt, 10% preferred stock, and 70% equity. If new debt of $3 million can be raised at the current interest rate before a higher yield must be paid to investors, at what point will the MCC break upward because of the cost of debt?

Question

Quizplus · Accepted Answer

The MCC will break upward when the cost of debt becomes higher than the weighted average cost of capital (WACC). Since the firm's current capital structure consists of 20% debt, and they can raise $3 million of new debt without increasing the interest rate, the total debt will become (20% x Total Value) + 3 million. Let's assume the total value of the firm is X. 
So the new capital structure will be:
20% (X+3 million) debt
10% preferred stock
70% equity
Let's assume the cost of debt after raising the additional $3 million is 8%, the cost of preferred stock is 10%, and the cost of equity is 15%. Then the WACC will be:
(0.2 x (X+3 million) x 0.08) + (0.1 x X x 0.10) + (0.7 x X x 0.15) = 0.107X + 240,000.
Therefore, the MCC will break upward when the cost of debt is higher than 10.7%. Let Y be the point where the MCC breaks upward. Then, we can set up the following equation:
(0.2 x (Y+3 million) x r) + (0.1 x Y x 0.10) + (0.7 x Y x 0.15) = 0.107Y + 240,000
where r is the interest rate on the new debt. Solving for Y, we get:
Y = $15,000,000
Therefore, the MCC will break upward when the total value of the firm reaches $15,000,000.

A Firm's Correctly Computed Capital Structure Consists of 20% Debt