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Here is the condensed balance sheet for Skye Computer Company (in thousands of dollars): Skye Computer's earnings per share last year were \(\$ 3.20 ;\) the stock sells for \(\$ 55,\) and last year's dividend was \(\$ 2.10 .\) A flotation cost of 10 percent would be required to issue new common stock. Skye's preferred stock pays a dividend of \(\$ 3.30\) per share, and new preferred could be sold at a price to net the company \(\$ 30\) per share. Security analysts are projecting that the common dividend will grow at a rate of 9 percent per year. The firm can issue additional long-term debt at an interest rate (or before-tax cost) of 10 percent, and its marginal tax rate is 35 percent. The market risk premium is 5 percent, the risk-free rate is 6 percent, and Skye's beta is \(1.516 .\) In its cost of capital calculations, the company considers only long-term capital, hence it disregards current liabilities for this purpose. a. Calculate the cost of each capital component, that is, the after-tax cost of debt, the cost of preferred stock, the cost of equity from retained earnings, and the cost of newly issued common stock. Use the DCF method to find the cost of common equity. b. Now calculate the cost of common equity from retained earnings using the CAPM method. c. What is the cost of new common stock, based on the CAPM? (Hint: Find the difference between \(k_{c}\) and \(k_{s}\) as determined by the \(D C F\) method, and add that differential to the CAPM value for \(\left.k_{s} .\right)\) d. If Skye Computer continues to use the same capital structure, what is the firm's WACC assuming (1) that it uses only retained earnings for equity and (2) that it expands so rapidly that it must issue new common stock? e. Suppose Skye is evaluating three projects with the following characteristics: Each project has a cost of \(\$ 1\) million. They will all be financed using the target mix of long-term debt, preferred stock, and common equity. The cost of the common equity for each project should be based on the beta estimated for the project. All equity will come from retained earnings. Equity invested in Project A would have a beta of 0.5 and an expected return of 9.0 percent. Equity invested in Project \(\mathrm{B}\) would have a beta of 1.0 and an expected return of 10.0 percent. Equity invested in Project \(C\) would have a beta of 2.0 and an expected return of 11.0 percent. Analyze the company's situation and explain why each project should be accepted or rejected.

Step by step solution

01

Calculate After-Tax Cost of Debt

The formula to calculate the after-tax cost of debt is: \( k_d = i(1 - T) \), where \( i \) is the interest rate and \( T \) is the tax rate. Here, \( i = 0.10 \) and \( T = 0.35 \).\[ k_d = 0.10(1 - 0.35) = 0.065 \text{ or } 6.5\% \].

02

Calculate Cost of Preferred Stock

The formula for the cost of preferred stock is: \( k_{ps} = \frac{D_{ps}}{P_0} \), where \( D_{ps} \) is the dividend and \( P_0 \) is the net price after flotation costs.Given \( D_{ps} = 3.30 \) and \( P_0 = 30 \), we have\[ k_{ps} = \frac{3.30}{30} = 0.11 \text{ or } 11\% \].

03

Calculate Cost of Equity using DCF Method

The Dividend Discount Model (DCF) formula is \( k_{s} = \frac{D_1}{P_0} + g \), where \( D_1 = D_0(1+g) \) is the expected dividend, \( P_0 \) is the stock price, and \( g \) is the growth rate.Given \( D_0 = 2.10 \), \( P_0 = 55 \), and \( g = 0.09 \), we calculate \( D_1 \):\[ D_1 = 2.10(1 + 0.09) = 2.289 \].Then,\[ k_s = \frac{2.289}{55} + 0.09 = 0.1316 + 0.09 = 0.2216 \text{ or } 22.16\% \].

04

Calculate Cost of Equity using CAPM

The CAPM formula is \( k_s = r_f + \beta (r_m - r_f) \), where \( r_f \) is the risk-free rate, \( \beta \) is the beta of the stock, and \( r_m - r_f \) is the market risk premium.Given \( r_f = 0.06 \), \( \beta = 1.516 \), and \( r_m - r_f = 0.05 \), we find:\[ k_s = 0.06 + 1.516(0.05) = 0.1378 \text{ or } 13.78\% \].

05

Calculate Cost of New Common Stock using CAPM

Using the differential from Step 3 and Step 4, find the cost of new equity \( k_{e} = k_s + \Delta k \).The differential \( \Delta k \) from DCF is \(0.2216 - 0.1378 = 0.0838 \) or 8.38%.Add this to the CAPM value:\[ k_e = 0.1378 + 0.0838 = 0.2216 \text{ or } 22.16\% \].

06

Calculate Skye's WACC (Retained Earnings)

WACC is calculated as a weighted average of costs of each capital component:WACC = \( w_d k_d + w_{ps} k_{ps} + w_s k_s \).Assuming weights \( w_d = 0.30, w_{ps} = 0.20, \) and \( w_s = 0.50 \) (sample values for illustration, actual values required):\[ \text{WACC} = 0.30(0.065) + 0.20(0.11) + 0.50(0.1378) = 0.0911 \text{ or } 9.11\% \].

07

Calculate Skye's WACC (New Common Stock)

Use new cost of stock from Step 5, \( k_e = 0.2216 \):\[ \text{WACC} = 0.30(0.065) + 0.20(0.11) + 0.50(0.2216) = 0.1283 \text{ or } 12.83\% \].

08

Decision on Projects A, B, and C

Evaluate against project expected returns:- Project A: \( \beta = 0.5, \text{return } 9\% \) vs WACC (9.11%) — Reject.- Project B: \( \beta = 1.0, \text{return } 10\% \) vs WACC (9.11%) — Accept.- Project C: \( \beta = 2.0, \text{return } 11\% \) vs WACC (12.83%) — Reject.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

After-Tax Cost of Debt

Understanding the after-tax cost of debt is important for calculating a firm's overall cost of capital. Debt is often cheaper than equity because interest payments on debt are tax-deductible. This deduction lowers the actual cost of borrowing for the company. The formula to determine the after-tax cost of debt is:\[ k_d = i(1 - T) \]where:

• \( k_d \) is the after-tax cost of debt,
• \( i \) is the interest rate on the debt, and
• \( T \) is the company’s tax rate.

In the context of Skye Computer, the interest rate \( i \) is 10%, and the tax rate \( T \) is 35%. Using these numbers, the after-tax cost of debt calculates to be 6.5%. This calculation shows how tax benefits make debt an attractive option for financing.

Cost of Preferred Stock

Preferred stock is a unique financial instrument that pays dividends. These dividends are often fixed, similar to debt interest. However, unlike debt, preferred stock dividends are not tax-deductible. The cost of raising funds through preferred stock is crucial in the overall calculation of the cost of capital. The formula is:\[ k_{ps} = \frac{D_{ps}}{P_0} \]where:

• \( D_{ps} \) is the annual preferred dividend,
• \( P_0 \) is the net issuing price per share,

For Skye Computer, \( D_{ps} \) is \(3.30, and \( P_0 \) is \)30. This results in a preferred stock cost of 11%. Although preferred stock typically has a higher cost compared to debt due to its position in the capital structure, it offers stability because of its fixed dividend nature.

DCF Method

The Discounted Cash Flow (DCF) method is used to calculate the cost of equity for common stock, representing investor expectations. It is based on future dividends adjusted for growth expectations:\[ k_s = \frac{D_1}{P_0} + g \]where:

• \( D_1 \) is the expected future dividend,
• \( P_0 \) is the current price of the stock,
• \( g \) is the growth rate,

In this case, Skye Computer has a calculated expected dividend \( D_1 \) at \(2.289, a stock price \( P_0 \) at \)55, and a growth rate \( g \) of 9%. Consequently, the cost of equity via the DCF method is 22.16%. This approach emphasizes dividend growth and the current market price, serving as insights into market expectations.

CAPM Method

The Capital Asset Pricing Model (CAPM) method calculates the cost of equity by gauging the risk involved. Unlike the DCF method, CAPM considers a company's beta (volatility relative to the market):\[ k_s = r_f + \beta(r_m - r_f) \]where:

• \( r_f \) is the risk-free rate (typically government bond yield),
• \( \beta \) is the beta value of the stock,
• \( r_m - r_f \) is the market risk premium,

For Skye Computer, with \( r_f \) at 6%, \( \beta \) at 1.516, and a market risk premium of 5%, the CAPM-calculated cost of equity is 13.78%. This method highlights the stock’s volatility and the market's role in equity cost calculation, focusing heavily on the systematic risk faced by equity investors.