The Impact of Capital Structure Change on Beckman Engineering and Associates (BEA): Unlevered Beta, Cost of Equity, WACC, and Firm Value Analysis

QUESTION

Beckman Engineering and Associates (BEA) is considering a change in its capital structure. BEA currently has $20 million in debt carrying a rate of 7%, and its stock price is $40 per share with 2 million shares outstanding. BEA is a zero growth firm and pays out all of its earnings as dividends. The firm’s EBIT is $12.321 million, and it faces a 40% federal-plus-state tax rate. The market risk premium is 4%, and the risk-free rate is 6%. BEA is considering increasing its debt level to a capital structure with 30% debt, based on market values, and repurchasing shares with the extra money that it borrows. BEA will have to retire the old debt in order to issue new debt, and the rate on the new debt will be 7%. BEA has a beta of 0.8.

1. What is BEA’s unlevered beta? Use market value D/S (which is the same as w_d/w_s) when unlevering. Do not round intermediate calculations. Round your answer to two decimal places.
2. What are BEA’s new beta and cost of equity if it has 30% debt? Do not round intermediate calculations. Round your answers to two decimal places.
   Beta:
   Cost of equity:   %
3. What are BEA’s WACC and total value of the firm with 30% debt? Do not round intermediate calculations. Round your answer to two decimal places.
   %

ANSWER

To determine BEA’s unlevered beta, we need to follow these steps:

1. Calculate the leveraged beta (βL) using the current capital structure:

Using the formula for leveraged beta:

\[ \beta_L = \beta_U \left(1 + \frac{1 – Tc}{D/S}\right) \]

Where:
– βL = Leveraged beta
– βU = Unleveraged beta
– Tc = Corporate tax rate
– D/S = Debt-to-equity ratio (market value)

Given:
– βL = 0.8 (BEA’s beta)
– Tc = 40% (tax rate)
– D/S = Market value of debt / Market value of equity

Market value of equity (E) = Stock price per share * Number of shares outstanding
Market value of debt (D) = $20 million (current debt)

Market value of equity = $40 per share * 2 million shares = $80 million

Now, we can calculate D/S:

\[ D/S = \frac{20,000,000}{80,000,000} = 0.25 \]

Now, we can solve for βU:

\[ 0.8 = βU \left(1 + \frac{1 – 0.4}{0.25}\right) \]

Simplifying the equation:

\[ 0.8 = βU \left(1 + \frac{0.6}{0.25}\right) \]
\[ 0.8 = βU \left(1 + 2.4\right) \]
\[ 0.8 = 3.4βU \]

Now, isolate βU:

\[ βU = \frac{0.8}{3.4} \approx 0.24 \]

So, BEA’s unlevered beta (βU) is approximately 0.24.

Next, let’s calculate BEA’s new beta and cost of equity with 30% debt:

2. Calculate the new leveraged beta (βL-new) with 30% debt:

Given:
– New debt-to-equity ratio (D/S-new) = 30% = 0.30

We can use the formula for leveraged beta again:

\[ \beta_L\text{-new} = \beta_U \left(1 + \frac{1 – Tc}{D/S\text{-new}}\right) \]

Substitute the values:

\[ \beta_L\text{-new} = 0.24 \left(1 + \frac{1 – 0.4}{0.30}\right) \]

\[ \beta_L\text{-new} = 0.24 \left(1 + \frac{0.6}{0.30}\right) \]

\[ \beta_L\text{-new} = 0.24 \cdot 3 \]

\[ \beta_L\text{-new} = 0.72 \]

3. Calculate the cost of equity using the new beta:

The cost of equity can be calculated using the Capital Asset Pricing Model (CAPM):

\[ \text{Cost of Equity} = Rf + \beta_L\text{-new} \times (\text{Market Risk Premium}) \]

Given:
– Risk-free rate (Rf) = 6%
– Market Risk Premium = 4%

\[ \text{Cost of Equity} = 0.06 + 0.72 \times 0.04 = 0.06 + 0.0288 = 0.0888 \]

The cost of equity with 30% debt is approximately 8.88%.

Now, let’s calculate BEA’s weighted average cost of capital (WACC) and the total value of the firm with 30% debt:

4. Calculate the WACC with 30% debt:

WACC is the weighted average of the cost of equity and the after-tax cost of debt (since interest is tax-deductible):

\[ \text{WACC} = \frac{E}{V} \times \text{Cost of Equity} + \frac{D}{V} \times \text{After-Tax Cost of Debt} \]

Where:
– E = Market value of equity
– D = Market value of debt
– V = Total firm value (E + D)

We already calculated βL-new and the cost of equity. Now, calculate the after-tax cost of debt:

Given:
– Rate on the new debt = 7%
– Tc = 40% (tax rate)

After-Tax Cost of Debt = 7% * (1 – 0.4) = 4.2%

Now, calculate the market value of debt with 30% debt:

Market value of debt (D-new) = Total firm value (V) * Debt-to-equity ratio (D/S-new)

Market value of equity (E) remains the same.

\[ D\text{-new} = V \times 0.30 \]

Total firm value (V) = E + D-new

Substitute the values:

\[ D\text{-new} = (80,000,000 + D\text{-new}) \times 0.30 \]

\[ 0.7D\text{-new} = 80,000,000 \]

\[ D\text{-new} = \frac{80,000,000}{0.7} \]

Now, we can calculate V:

\[ V = E + D\text{-new} = 80,000,000 + \frac{80,000,000}{0.7} \]

Now, we can calculate WACC:

\[ \text{WACC} = \frac{80,000,000}{80,000,000 + \frac{80,000,000}{0.7}} \times 0.0888 + \frac{\frac{80,000,000}{0.7}}{80,000,000 + \frac{80,000,000}{0.7}} \times 0.042 \]

Simplify and calculate WACC:

\[ \text{WACC} = \frac{80,000,000}{80,000,000 + 114,285,714.29} \times 0.0888 + \frac{114,285,714.29}{80,000,000 + 114,285,714.29} \times 0.042 \]

\[ \text{WACC} \approx 0.0537 + 0.0336 \]

\[ \text{WACC} \approx 0.0873 \]

The WACC with 30% debt is approximately 8.73%.

5. Calculate the total value of the firm with 30% debt:

Total firm value (V) with 30% debt = Market value of equity (E) + Market value of debt (D-new)

Substitute the values:

\[ V\text{-new} = 80,000,000 + \frac{80,000,000}{0.7} \]

Now, calculate V-new:

\[ V\text{-new} = 80,000,000 + 114,285,714.29 \]

\[ V\text{-new} \approx 194,285,714.29 \]

The total value of the firm