The Following Information Applies To Questions 4 Through 8

The Following Information Applies To Questions 4 Through 8the Jones C

The following information applies to questions 4 through 8. The Jones Corporation has the following capital structure on its books: Bonds, 8% (now selling at par) $800,000; Preferred stock, $5.00 par value, $450,000; Common stock, $500,000; Retained earnings, $250,000. The total capital is $2,000,000. Dividends on common stock are currently $4 per share and are expected to grow at a constant rate of 10 percent. The market price per share of common stock is $44, and the preferred stock is selling at $50 per share. Flotation costs on new issues of common stock are 8 percent. The interest on the bonds is paid annually. Jones Corporation's tax rate is 40 percent.

Paper For Above instruction

The assessment of a company's cost of capital involves several components, each corresponding to different sources of financing, including debt, preferred stock, retained earnings, and newly issued common stock. Accurately estimating these costs is crucial for effective capital budgeting and financial decision-making. This paper discusses the calculation methods for each component, specifically focusing on Jones Corporation based on the provided data.

Cost of Debt

The cost of debt pertains to the effective rate a company pays on its borrowed funds, considering its current market conditions and the tax shield benefit. Since Jones Corporation's bonds are 8% fixed-rate and are presently selling at par, the yield to maturity (YTM) closely matches the coupon rate. The bonds pay interest annually, and the company's tax rate influences the effective cost of debt due to tax deductibility of interest expenses.

The pre-tax cost of debt is thus 8%. After accounting for the tax shield, the after-tax cost is calculated as:

Cost of Debt = 8% × (1 – 0.40) = 4.8%

This indicates that the effective annual cost of debt to the company, considering tax benefits, is 4.8%.

Cost of Preferred Stock

The cost of preferred stock is determined by dividing the dividend per preferred share by the net issuing price (considering any flotation costs). Since the preferred stock has a par value of $5.00 and is selling at $50 per share, the dividend is typically expressed as a percentage of par; here, the dividend yield is misunderstood initially. However, there is no stated dividend rate for preferred stock, but given the context of the question, the dividend is usually specified or can be inferred from a dividend rate. Assuming the preferred stock pays a fixed dividend, which is typical, the dividend per share is calculated based on the par value or given dividend rate—yet the problem states the preferred stock's selling price at $50 per share and the face value at $5, indicating potentially a dividend rate of 5% of par, unless otherwise specified.

Alternatively, in many cases, the dividend rate must be explicitly given. If not, a typical approach is to assume a preferred stock dividend rate or use the yield from the sale price and dividend, but since no dividend amount per preferred stock is provided, a common assumption is a dividend yield of 5% of par, equaling $0.25 per share.

Given the lack of explicit dividend figures, a reasonable approximation uses the dividend yield. Assuming the preferred stock pays a dividend rate of 5% on its par value, the dividend per share is:

$5.00 × 5% = $0.25

However, since the stock's market price is $50, given typical preferred stocks pay dividends equivalent to a set percentage based on the face value, the yield is calculated as:

\(\frac{\$0.25}{\$50} = 0.005 = 0.5\%\)

But considering the market price is significantly higher than par and typical preferred dividends are fixed, the more precise approach defaults to using the dividend rate on the preferred stock or the given data. If the dividend rate is unspecified, the cost of preferred stock can be approximated as the dividend divided by the market price minus flotation costs.

Alternatively, without explicit dividend, assuming a typical preferred dividend yield of around 5%, then the cost of preferred stock becomes:

\(\frac{\text{Dividend}}{\text{Market Price}}\) = \(\frac{\$0.25}{\$50}\) = 0.5%

However, for accurate calculations, if the dividend rate is provided or typical, the cost of preferred stock generally is computed as:

\(\text{Cost of Preferred Stock} = \frac{\text{Dividend per share}}{\text{Net issue price}}\)

This yields approximately 5%, assuming a fixed dividend rate at par. Considering the market price of $50 and flotation costs of 8%, the net price for issuing new preferred stock is:

\$50 × (1 – 0.08) = \$46

Thus, the cost of preferred stock is:

\(\frac{\$0.25}{\$46}\) ≈ 0.543, or 5.43%

In conclusion, the approximate cost of preferred stock for Jones Corporation is 5.43%.

Cost of Retained Earnings

The cost of retained earnings is typically estimated using the dividend growth model, also known as the Gordon Growth Model, which relates the current dividend, the stock price, and the growth rate of dividends.

This is calculated as:

\(\text{Cost of Retained Earnings} = \frac{\text{Dividend per share} \times (1 + g)}{\text{Market price}} + g\)

Where:

  • Dividend per share (D₁) = $4
  • Growth rate (g) = 10% or 0.10
  • Market price (P₀) = $44

Applying the formula:

\(\frac{\$4 \times (1 + 0.10)}{\$44} + 0.10 = \frac{\$4.40}{\$44} + 0.10 ≈ 0.10 + 0.10 = 0.20,\text{or} 20%\)

This indicates that the cost of retained earnings is approximately 20%, reflecting the expected return investors require given the dividend growth prospects.

Cost of Newly Issued Common Stock

The cost of issuing new common stock accounts for flotation costs and is calculated using the dividend growth model adjusted for these costs. The formula becomes:

\(\text{Cost of New Common Stock} = \frac{\text{Dividend per share} \times (1 + g)}{\text{Net issuing price}} + g\)

The net price after accounting for flotation costs is:

\$44 × (1 – 0.08) = \$40.48

Substituting values:

\(\frac{\$4 \times (1 + 0.10)}{\$40.48} + 0.10 = \frac{\$4.40}{\$40.48} + 0.10 ≈ 0.1086 + 0.10 = 0.2086,\text{or} 20.86%\)

This suggests that the cost of issuing new common stock, considering flotation costs, is approximately 20.86%.

Weighted Average Cost of Capital (WACC)

The WACC integrates all sources of capital, weighted by their proportion in the overall capital structure, and adjusts the cost of debt for taxes. The formula is:

\(\text{WACC} = \frac{E}{V} \times \text{Re} + \frac{D}{V} \times \text{Rd} \times (1 - T) + \frac{P}{V} \times \text{Rp}\)

Where:

  • E = Market value of equity (common stock) = $500,000
  • D = Market value of debt (bonds) = $800,000
  • P = Market value of preferred stock = $450,000
  • V = Total value = $1,750,000

The respective costs are:

  • Re (cost of equity, retained earnings) ≈ 20%
  • Rd (cost of debt after tax) = 4.8% (from earlier)
  • Rp (cost of preferred stock) ≈ 5.43%

Calculating the weightings:

\(\frac{\$500,000}{\$1,750,000} ≈ 0.2857,\)

\(\frac{\$800,000}{\$1,750,000} ≈ 0.4571,\)

\(\frac{\$450,000}{\$1,750,000} ≈ 0.2571

The WACC becomes:

WACC ≈ 0.2857 × 20% + 0.4571 × 4.8% + 0.2571 × 5.43% ≈ 0.0571 + 0.0219 + 0.0140 ≈ 0.093, or 9.3%

Therefore, the weighted average cost of capital for Jones Corporation is approximately 9.3%.

Conclusion

In conclusion, accurately determining each component's cost is essential for strategic financial management. The calculations highlight that the company's cost of debt is relatively low after tax adjustments, while the costs of equity and preferred stock are higher due to market expectations and dividend requirements. The WACC, at around 9.3%, serves as a critical benchmark for investment decisions, ensuring that projects undertaken generate sufficient returns to cover the weighted cost of capital, thus maximizing shareholder value.

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