Your Firm Is Considering A New Investment Proposal
Your Firm Is Considering A New Investment Proposal And Would Like To C
Your firm is considering a new investment proposal and would like to calculate its weighted average cost of capital. To help this, compute the cost of capital for the firm for the following: a. A bond that has a $1,000 par value (face value) and a contract or a coupon interest rate of 12.2%. The bond is currently selling for a price of $1,129 and will mature in 10 years. The firm’s tax rate is 34%. b. If the firm’s bonds are not frequently traded, how would you go about determining a cost of debt for this company? c. A new common stock issue that paid $1.78 dividend last year. The par value of the stock is $16 and the firm’s dividends per share have grown at a rate of 8.9% per year. The growth rate is expected to continue in the foreseeable future. The price of the stock now is $27.56. d. A preferred stock paying a 13.1% dividend on $122 par value. The preferred shares are currently selling for $150.55. e. A bond selling to yield 12.1% for the purchaser of the bond. The borrowing firm faces a tax rate of 34%.
Paper For Above instruction
Calculating the weighted average cost of capital (WACC) is vital for firms planning new investments, as it represents the minimum return required to satisfy investors and lenders. This analysis involves determining the cost of each component of capital—debt, equity, and preferred stock—and weighting them per their proportions in the firm’s capital structure. Here, each component's calculation is discussed in detail, with a focus on practical application and considerations for non-traded bonds.
1. Cost of Debt for a Traded Bond
The first step involves calculating the yield to maturity (YTM) for a bond with a face value of $1,000, a coupon rate of 12.2%, selling at $1,129, and maturing in 10 years. The bond's annual coupon payment is computed as:
\[ C = 0.122 \times 1000 = \$122 \]
The current market price is:
\[ P = \$1,129 \]
The YTM can be estimated using the present value formula for bonds:
\[ P = \sum_{t=1}^{n} \frac{C}{(1 + r)^t} + \frac{FV}{(1 + r)^n} \]
Where:
- \( P \) = current bond price
- \( C \) = annual coupon payment
- \( FV \) = face value
- \( r \) = YTM or cost of debt
- \( n \) = number of years to maturity
Using a financial calculator or iterative methods, the YTM approximates to about 10.0%. Given the tax rate of 34%, the after-tax cost of debt is:
\[ \text{After-tax cost of debt} = r \times (1 - \text{Tax rate}) = 10.0\% \times (1 - 0.34) = 6.6\% \]
This reflects the actual cost to the firm of issuing debt with these conditions.
2. Determining Cost of Debt for Non-Traded Bonds
When bonds are not actively traded, estimating the cost of debt becomes more complex. One approach is to analyze similar bonds in the market with comparable credit ratings, maturities, and risk characteristics, then approximate the yield using:
- Comparable Bond Approach: Identify similar bonds and use their yields as benchmarks.
- Credit Rating and Spread Method: Use the company's credit rating to find the average spread over the risk-free rate, then add it to a risk-free rate such as the yield on U.S. Treasuries.
- Build-Up Method: Add risk premiums to a risk-free rate, including liquidity, default, and industry risk premiums.
Ultimately, selecting the appropriate method depends on the available market data, bond characteristics, and the company's creditworthiness.
3. Cost of Equity via the Dividend Discount Model (DDM)
For common stock issues, the cost of equity can be estimated using the Gordon Growth (Dividend Discount) Model:
\[ r_e = \frac{D_1}{P_0} + g \]
Where:
- \( D_1 = D_0 \times (1 + g) = 1.78 \times (1 + 0.089) = \$1.94 \)
- \( P_0 = \$27.56 \)
- \( g = 8.9\% \)
Plugging in values:
\[ r_e = \frac{\$1.94}{\$27.56} + 0.089 \approx 0.0703 + 0.089 = 15.03\% \]
The estimated cost of equity is approximately 15.03%.
4. Cost of Preferred Stock
Preferred stock issuances pay a fixed dividend based on the par value. The cost of preferred stock is:
\[ r_{ps} = \frac{D_{ps}}{P_{ps}} \]
Where:
- \( D_{ps} = 13.1\% \times 122 = \$15.98 \)
- \( P_{ps} = \$150.55 \)
Thus:
\[ r_{ps} = \frac{\$15.98}{\$150.55} \approx 10.63\% \]
Because dividends on preferred stock are not tax-deductible, this rate remains unadjusted for taxes.
5. Yield-to-Maturity for a Bond with 12.1% Yield
If a bond is trading at a yield of 12.1% to the purchaser, the firm's pre-tax cost of debt from this bond is directly 12.1%. Adjusted for taxes:
\[ \text{After-tax cost} = 12.1\% \times (1 - 0.34) \approx 7.99\% \]
This rate reflects the effective cost to the firm when issuing similar debt.
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In conclusion, calculating each component's cost of capital provides the foundation for an accurate WACC figure, which firms use to evaluate investment projects. Accurate estimation requires careful analysis of market data, appropriate models, and considerations of tax impacts. Depending on market conditions and data availability, firms may need to adapt methodologies, especially for non-traded debt instruments. Applying these principles ensures that investment decisions align with the company's financial strategy and risk appetite.
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