Firm Has Determined Its Optimal Capital Structure

Firmhas Determined Its Optimal Capital Structure Which Is Compose

A firm has established its optimal capital structure, comprising long-term debt, preferred stock, and common equity, with target market value proportions of 30%, 5%, and 65%, respectively. The objective is to calculate the firm's weighted average cost of capital (WACC) based on provided data about each source of capital, including their costs and flotation costs, considering that the firm has exhausted all retained earnings.

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The calculation of the weighted average cost of capital (WACC) is fundamental for understanding a firm's cost of funding and its implication on valuation, investment decisions, and financial strategy. It incorporates the costs associated with different sources of capital, weighted by their respective proportions in the firm's target capital structure. In this analysis, we will determine the WACC for a firm with specified proportions of debt, preferred stock, and common equity, considering the costs associated with each, as well as tax effects where applicable.

Cost of Debt

The firm's debt involves issuing 20-year bonds with a par value of $1,000, a coupon rate of 9%, and a market price of $980. Flotation costs amount to 2% of the face value, plus an additional discount fee of $20, which effectively raises the cost of debt. To determine the firm's after-tax cost of debt, we first need to compute the yield to maturity (YTM) on the bonds, incorporating flotation costs and discounts.

The net proceeds from issuing the bonds are calculated as:

• Gross proceeds: $980
• Less flotation costs (2% of $1,000): $20

Therefore, the net proceeds per bond are:

$980 - $20 = $960

The bond pays an annual coupon of 9% of par value: $90 annually. To find the YTM, we consider the cash flows: $90 annual interest, $1,000 face value at maturity, and the net proceeds of $960.

Using the approximate YTM formula or a financial calculator, the YTM can be estimated. For simplicity, an approximation is performed with the following formula:

YTM ≈ (Coupon Payment + (Face Value - Price) / Years) / ((Face Value + Price) / 2)

YTM ≈ ($90 + ($1,000 - $960) / 20) / (($1,000 + $960) / 2)

YTM ≈ ($90 + $2) / $980 ≈ $92 / $980 ≈ 0.0939 or 9.39%

Adjusting for flotation costs, the effective cost of debt after flotation costs is approximately 9.39%. Because interest expense is tax-deductible, the after-tax cost of debt is:

After-tax cost of debt = YTM × (1 - Tax rate) = 9.39% × (1 - 0.40) = 5.63%

Cost of Preferred Stock

The firm can issue preferred stock at a price of $65 per share with an $8 annual dividend. The flotation cost per share is $3. Therefore, the net proceeds per preferred share are:

$65 - $3 = $62

The cost of preferred stock (Kp) is calculated as the dividend divided by the net issue price:

Kp = $8 / $62 ≈ 0.1290 or 12.90%

Cost of Common Equity

The firm's current stock price is $40 per share. The expected dividend next year is $5.07, with dividends growing at a constant rate. Five years ago, the dividend was $3.45, indicating a growth rate (g) that can be derived via the Dividend Discount Model (DDM):

g = [(Dividend today / Dividend five years ago)^{1/5}] - 1

g = ($5.07 / $3.45)^{1/5} - 1 ≈ (1.4696)^{0.2} - 1 ≈ 1.077 - 1 ≈ 0.077 or 7.7%

The cost of equity (Ke) is calculated using the Gordon Growth model:

Ke = (Dividend / Price) + g = ($5.07 / $40) + 0.077 ≈ 0.12675 + 0.077 ≈ 0.20375 or 20.38%

For new common equity issuance, the firm must underprice the stock by $1 and pay flotation costs of $1 per share, meaning the net proceeds per share will be:

$40 - $1 - $1 = $38

The cost of new equity (Ke) considering flotation costs is:

Ke = (Next year's dividend / Net proceeds) + g = ($5.07 * (1 + g)) / $38 + g

Next year's dividend = $5.07 (1 + 0.077) ≈ $5.07 1.077 ≈ $5.463

Ke = $5.463 / $38 + 0.077 ≈ 0.1438 + 0.077 ≈ 0.2208 or 22.08%

Calculating WACC

Now, integrating the costs with the target capital structure proportions:

• Weight of debt (Wd): 30%
• Weight of preferred stock (Wp): 5%
• Weight of equity (We): 65%

The WACC formula is:

WACC = (Wd × after-tax cost of debt) + (Wp × cost of preferred stock) + (We × cost of equity)

Applying the values:

WACC = (0.30 × 5.63%) + (0.05 × 12.90%) + (0.65 × 20.38%)

WACC = (0.30 × 0.0563) + (0.05 × 0.1290) + (0.65 × 0.2038)

WACC = 0.01689 + 0.00645 + 0.13237 ≈ 0.1557 or 15.57%

Thus, the firm's weighted average cost of capital is approximately 15.57%, which reflects the blended cost of its sources of financing, accounting for taxes and flotation costs, aligned with the target capital structure.

Conclusion

The calculated WACC of 15.57% provides crucial insights into the firm's cost of capital under its optimal capital structure. This rate serves as a benchmark for investment appraisal, valuation, and financial strategy decisions. Ensuring the WACC accurately reflects current market conditions and capital costs is essential for effective financial management and maximizing shareholder value.

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