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 company is analyzing the effects of different levels of debt on its cost of capital and earnings per share. The company currently has no debt and is considering issuing $2,000,000 in debt at an interest rate of 8%.

To determine the optimal capital structure, the company needs to calculate the cost of debt, cost of equity, and weighted average cost of capital (WACC) at different levels of debt. The cost of debt can be calculated using the formula:

Cost of Debt = Interest Rate x (1 - Tax Rate)

Cost of Debt = 8% x (1 - 0.40) = 4.8%

Next, the cost of equity can be calculated using the Capital Asset Pricing Model (CAPM) formula:

Cost of Equity = Risk-Free Rate + Beta x (Market Return - Risk-Free Rate)

Assuming a risk-free rate of 3%, a beta of 1.2, and a market return of 10%, the cost of equity would be:

Cost of Equity = 3% + 1.2 x (10% - 3%) = 10.8%

The WACC can then be calculated using the formula:

WACC = (E/V) x Re + (D/V) x Rd x (1 - Tax Rate)

Where:
E = Market value of equity
V = Total value of the firm (E + D)
Re = Cost of equity
D = Market value of debt
Rd = Cost of debt

Assuming the market value of equity is $10,000,000 and the market value of debt is $2,000,000, the total value of the firm would be $12,000,000. Plugging in the values, the WACC would be:

WACC = ($10,000,000 / $12,000,000) x 10.8% + ($2,000,000 / $12,000,000) x 4.8% x (1 - 0.40) = 9.4%

By analyzing the WACC at different levels of debt, the company can determine the optimal capital structure that minimizes the cost of capital and maximizes earnings per share.

Capital Structure and Cost of Capital

Medallion Cooling Systems, Inc. has the following capital structure:

- Debt: $0 (assumed)
- Preferred Stock: $200,000
- Common Equity: $9,800,000

Cost of Preferred Stock:

The cost of preferred stock (rPS) can be calculated using the following formula:

```
rPS = Preferred Dividends / Market Value of Preferred Stock
```

Since the market value of the preferred stock is not provided, we cannot calculate rPS.

Cost of Common Equity:

The cost of common equity (rE) can be estimated using the Capital Asset Pricing Model (CAPM):

```
rE = rRF + β - (rM - rRF)
```

where:

- rRF is the risk-free rate (assumed to be 3%)
- β is the beta of the company's common stock (assumed to be 1.2)
- rM is the expected return on the market (assumed to be 8%)

Therefore,

```
rE = 0.03 + 1.2 - (0.08 - 0.03) = 0.114 = 11.4%
```

Weighted Average Cost of Capital (WACC):

The WACC can be calculated using the following formula:

```
WACC = (Weight of Debt - rD) + (Weight of Preferred Stock - rPS) + (Weight of Common Equity - rE)
```

where:

- Weight of Debt = Debt / Total Assets = $0 / $10,000,000 = 0
- Weight of Preferred Stock = Preferred Dividends / Total Assets = $200,000 / $10,000,000 = 0.02
- Weight of Common Equity = Common Equity / Total Assets = $9,800,000 / $10,000,000 = 0.98

Therefore,

```
WACC = (0 - rD) + (0.02 - rPS) + (0.98 - 0.114) = 11.26%
```

Optimal Capital Structure

The optimal capital structure minimizes the WACC. Since the company is assumed to have no debt, the optimal capital structure is to have no debt and all equity financing. This would result in a WACC of 11.4%, which is the cost of common equity.