Medallion Cooling Systems, Inc., has total assets of $10,000,000, EBIT of $2,000,000, and preferred dividends of $200,000 and is taxed at a rate of 40%. In an effort to determine the optimal capital structure, the firm has assembled data on the cost of debt, the number of shares of common stock for various levels of indebtedness, and the overall required return on investment:

Capital structure No. of common
debt ratio Cost of debt, kd stock shares Required return, ks
0% 0% 200,000 12%
15 8 170,000 13
30 9 140,000 14
45 12 110,000 16
60 15 80,000 20

a. Calculate earnings per share for each level of indebtedness.

b. Use Equation 12.12 and the earnings per share calculated in part a to calculate
a price per share for each level of indebtedness.

c. Choose the optimal capital structure. Justify your choice.

To calculate the earnings per share (EPS) for each level of indebtedness, we need to use the following formula:

EPS = (EBIT - Interest Expense - Preferred Dividends) / Number of Common Stock Shares

Let's calculate the EPS for each level of indebtedness:

a. For 0% debt ratio:
Interest Expense = 0% * $10,000,000 = $0
EPS = ($2,000,000 - $0 - $200,000) / 200,000 = $9

b. For 15% debt ratio:
Interest Expense = 15% * $10,000,000 * 8% = $120,000
EPS = ($2,000,000 - $120,000 - $200,000) / 170,000 ≈ $9.71

c. For 30% debt ratio:
Interest Expense = 30% * $10,000,000 * 9% = $270,000
EPS = ($2,000,000 - $270,000 - $200,000) / 140,000 ≈ $10.64

d. For 45% debt ratio:
Interest Expense = 45% * $10,000,000 * 12% = $540,000
EPS = ($2,000,000 - $540,000 - $200,000) / 110,000 ≈ $13.45

e. For 60% debt ratio:
Interest Expense = 60% * $10,000,000 * 15% = $900,000
EPS = ($2,000,000 - $900,000 - $200,000) / 80,000 = $12.5

Now, let's move to part b to calculate the price per share for each level of indebtedness.

We can use Equation 12.12, which states:

Price per Share = EPS / (required return on equity - growth rate)

The growth rate is not given, so we need to assume a constant growth rate. For simplicity, let's assume a growth rate of 0%.

c. For 0% debt ratio:
Price per Share = $9 / (12% - 0%) = $75

d. For 15% debt ratio:
Price per Share = $9.71 / (13% - 0%) = $74.69

e. For 30% debt ratio:
Price per Share = $10.64 / (14% - 0%) = $76

f. For 45% debt ratio:
Price per Share = $13.45 / (16% - 0%) ≈ $84.06

g. For 60% debt ratio:
Price per Share = $12.5 / (20% - 0%) = $62.5

Now, let's move on to part c to choose the optimal capital structure.

In order to choose the optimal capital structure, we need to consider two factors: EPS and the price per share. Generally, a higher EPS and a lower price per share are preferred.

Based on the calculations, the highest EPS is for the 45% debt ratio ($13.45), and the lowest price per share is for the 60% debt ratio ($62.5).

Considering both factors, it appears that the 45% debt ratio provides the optimal capital structure as it offers a higher EPS and a relatively lower price per share compared to the other levels of indebtedness.

Therefore, the optimal capital structure for Medallion Cooling Systems, Inc. is a 45% debt ratio.