Risk-Free Rate Of Return 3%; Market Rate Of Return 8%

If Rrfrisk Free Rate Of Return 3 Rm Market Rate Of Return 8

Determine the required rate of return on the firm’s stock using the Capital Asset Pricing Model (CAPM), given the risk-free rate, market rate of return, and beta. Subsequently, calculate the stock price based on dividend growth assumptions. Then, compute the Weighted Average Cost of Capital (WACC) incorporating bond yields, preferred stock yields, and equity costs, adjusted for the firm's target capital structure and tax considerations.

Paper For Above instruction

The evaluation of a firm's cost of equity and overall capital structure is fundamental to corporate finance decision-making. It enables firms to assess the minimum acceptable return on investments and to appraise projects and investments against these benchmarks. This paper synthesizes the calculation processes of the required rate of return using the Capital Asset Pricing Model (CAPM), the valuation of a growing dividend stock, and the derivation of the Weighted Average Cost of Capital (WACC) incorporated within the firm's strategic financing decisions.

Calculating the Required Rate of Return Using CAPM

The CAPM provides a straightforward method to estimate the required return on equity by considering the risk-free rate, the market risk premium, and the stock’s beta. The formula is:

re = rRF + β (rM - rRF)

Given the data: r_RF = 3%, r_M = 8%, and β = 1.2, the calculation is as follows:

r_e = 3% + 1.2 (8% - 3%) = 3% + 1.2 * 5% = 3% + 6% = 9%

Thus, the required rate of return on the firm's stock, based on the CAPM, is 9%.

Valuation of the Stock Based on Dividend Growth Model

The Dividend Discount Model (DDM), especially the Gordon Growth Model, provides a method to determine stock prices for companies expected to grow dividends at a constant rate. The model is:

P0 = D1 / (re - g)

Where:

• D₁ = dividend next year = $4.3995
• g = dividend growth rate = 4% or 0.04
• r_e = required rate of return from earlier = 9% or 0.09

Calculating the stock price:

P0 = 4.3995 / (0.09 - 0.04) = 4.3995 / 0.05 = $87.99

Hence, the estimated stock price, given the dividend growth assumptions, is approximately $88.00.

Calculating the Weighted Average Cost of Capital (WACC)

The firm's WACC represents the hurdle rate for projects, accommodating the diverse sources of capital: debt, preferred stock, and common equity. It can be calculated with the formula:

WACC = wd rd (1 – T) + wp rp + wc re

Where:

• w_d = weight of debt = 30%
• w_p = weight of preferred stock = 10%
• w_c = weight of common equity = 60%
• T = tax rate = 40%

To find the cost of debt (r_d), we first derive the yield to maturity (YTM) on bonds:

• Bond details: 15-year, 12% coupon, semiannual payments, selling at $1,153.72, face value $1,000
• Approximating YTM involves solving for the interest rate 'i' in the bond pricing formula:

BOND PRICE = ∑(C / (1 + i/2)ⁿ) + Face Value / (1 + i/2)ⁿ

Numerical approximation (using a financial calculator or iterative methods) yields the YTM approximately 9%, which translates into a semiannual yield. Annualized, it is around 9.23%. Adjusting for taxes, the after-tax cost of debt:

rd (after tax) = 9.23% * (1 - 0.4) ≈ 5.54%

Next, the cost of preferred stock (r_p) is calculated as:

rp = Dp / Pp = 10% of $1,000 = $100 dividend; Pp = $1,111

Thus:

rp = 100 / 1,111 ≈ 9.00%

The cost of equity (r_e) based on the stock's expected return with flotation costs incorporated is derived as the required return plus flotation costs. The zero-flotation equity cost is 9%; including a 15% flotation cost means adjusting the price or the cost proportionally. The adjusted cost of new equity considers flotation costs:

re,new = re / (1 - flotation rate) = 0.09 / (1 - 0.15) ≈ 0.1059 or 10.59%

Finally, plugging in all components into the WACC formula:

WACC = 0.30  5.54% + 0.10  9.00% + 0.60 * 10.59% = 1.662% + 0.9% + 6.354% ≈ 8.916%

Therefore, the firm's WACC is approximately 8.92%, serving as the hurdle rate for evaluating investment projects with an average risk profile.

In conclusion, these calculations provide critical insights into the firm's capital costs and offer a comprehensive framework for investment appraisal. The use of the CAPM for determining the required return aligns with market risk perceptions, whereas the dividend growth model offers a valuation method grounded in expected future dividends. The WACC calculation synthesizes the firm's financing mix and provides a requisite hurdle rate for capital budgeting purposes, adjusted for tax shields and flotation costs.

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