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You are given the following information concerning Melbourne, Inc.:

**Debt:**
- 7,500 bonds with a 6.8 percent coupon rate.
- 11 years to maturity, quoted price of 97.9.
- Par value is $1,000.
- These bonds pay interest semiannually.

**Common Stock:**
- 284,000 shares selling for $68 per share.
- Beta: 1.04
- Expected dividend next year: $2.62
- Dividend growth rate: 2.5 percent per year indefinitely.
- Use CAPM to calculate the cost of common stock.

**Preferred Stock:**
- 9,000 shares of $8 preferred stock selling at $88 per share.

**Market Information:**
- Expected return: 14.6 percent.
- Risk-free rate: 4.1 percent.

**Company Information:**
- Tax rate: 21 percent.

**Calculate the following:**
1. Market value of the firm.
2. Cost of equity.
3. Cost of debt.
4. Cost of preferred stock.
5. WACC for this firm.

Answer :

To calculate the market value of the firm, we need to sum up the values of the debt, common stock, and preferred stock.

1. Debt: The market value of debt can be calculated by multiplying the number of bonds by the quoted price per bond. In this case, there are 7,500 bonds with a quoted price of 97.9, so the market value of debt is 7,500 * 97.9 = $734,250.

2. Common stock: The market value of common stock can be calculated by multiplying the number of shares by the price per share. In this case, there are 284,000 shares of common stock selling for $68 per share, so the market value of common stock is 284,000 * $68 = $19,312,000.

3. Preferred stock: The market value of preferred stock can be calculated by multiplying the number of shares by the price per share. In this case, there are 9,000 shares of preferred stock selling for $88 per share, so the market value of preferred stock is 9,000 * $88 = $792,000.

Adding up the market values of debt, common stock, and preferred stock, we get:

Market value of the firm = $734,250 + $19,312,000 + $792,000 = $20,838,250.

To calculate the cost of equity using the Capital Asset Pricing Model (CAPM), we need the risk-free rate, the expected market return, and the beta of the stock.

The risk-free rate is given as 4.1 percent and the expected market return is 14.6 percent.

The cost of equity (Ke) can be calculated using the formula:

Ke = Risk-free rate + Beta * (Expected market return - Risk-free rate).

In this case, the beta of the stock is given as 1.04.

Ke = 4.1% + 1.04 * (14.6% - 4.1%) = 4.1% + 1.04 * 10.5% = 4.1% + 10.92% = 15.02%.

So, the cost of equity is 15.02%.

Next, let's calculate the cost of debt. The cost of debt is the yield to maturity (YTM) of the bonds. The YTM is not given directly, but we can calculate it using the following steps:

1. Find the semiannual coupon payment by multiplying the coupon rate (6.8%) by the par value ($1,000) and dividing by 2, since the bonds pay interest semiannually. So, the semiannual coupon payment is 6.8% * $1,000 / 2 = $34.

2. Find the number of semiannual periods by multiplying the number of years to maturity (11) by 2, since the bonds pay interest semiannually. So, the number of semiannual periods is 11 * 2 = 22.

3. Find the present value of the bond by discounting the future cash flows (coupon payments and par value) at the YTM. The present value of the bond is equal to the quoted price (97.9% of par value).

Using a financial calculator or spreadsheet software, we can find that the YTM is approximately 3.58% (rounded to two decimal places).

So, the cost of debt is 3.58%.

Finally, let's calculate the cost of preferred stock. The cost of preferred stock can be calculated by dividing the annual dividend by the market price per share. In this case, the annual dividend is $8 and the market price per share is $88.

Cost of preferred stock = $8 / $88 = 0.0909 or 9.09%.

Lastly, to calculate the Weighted Average Cost of Capital (WACC), we need to weight the costs of debt, equity, and preferred stock by their respective market values and sum them up.

WACC = (Market value of debt / Total market value of the firm) * Cost of debt + (Market value of equity / Total market value of the firm) * Cost of equity + (Market value of preferred stock / Total market value of the firm) * Cost of preferred stock.

Plugging in the values, we get:

WACC = [tex]($734,250 / $20,838,250) * 3.58% + ($19,312,000 / $20,838,250) * 15.02% + ($792,000 / $20,838,250) * 9.09%.[/tex]

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