Sapp Trucking’s balance sheet shows a total of noncallable $45 million long-term debt with a coupon rate of 7.00% and a yield to maturity of 6.00%. This debt currently has a market value of $50 million. The balance sheet also shows that the company has 10 million shares of common stock, and the book value of the common equity (common stock plus retained earnings) is $65 million. The current stock price is $21.00 per share; stockholders' required return, rs, is 14.00%; and the firm's tax rate is 40%. The CFO thinks the WACC should be based on market value weights, but the president thinks book weights are more appropriate. What is the difference between these two WACCs.
The answer I came up with is 2.16% but I don't know if I'm right.
2.36
To determine the difference between the Weighted Average Cost of Capital (WACC) based on market value weights and book value weights, we need to calculate both WACCs first.
First, let's calculate the WACC based on market value weights:
1. Calculate the market value of equity:
Market value of equity = Number of shares × Stock price
Market value of equity = 10 million shares × $21.00
Market value of equity = $210 million
2. Calculate the market value of debt:
Market value of debt = Current market value of long-term debt
Market value of debt = $50 million
3. Calculate the total market value of the firm:
Total market value = Market value of equity + Market value of debt
Total market value = $210 million + $50 million
Total market value = $260 million
4. Calculate the proportion of equity:
Proportion of equity = Market value of equity / Total market value
Proportion of equity = $210 million / $260 million
Proportion of equity ≈ 0.8077, or 80.77%
5. Calculate the proportion of debt:
Proportion of debt = Market value of debt / Total market value
Proportion of debt = $50 million / $260 million
Proportion of debt ≈ 0.1923, or 19.23%
6. Calculate the after-tax cost of debt:
After-tax cost of debt = Yield to maturity × (1 - Tax rate)
After-tax cost of debt = 6.00% × (1 - 0.40)
After-tax cost of debt = 6.00% × 0.60
After-tax cost of debt = 3.60%
7. Calculate the WACC based on market value weights:
WACC = (Proportion of equity × Cost of equity) + (Proportion of debt × After-tax cost of debt)
WACC = (0.8077 × 14.00%) + (0.1923 × 3.60%)
WACC ≈ 11.33%
Now let's calculate the WACC based on book value weights:
1. Calculate the book value of equity:
Book value of equity = Common equity = $65 million
2. Calculate the book value of debt:
Book value of debt = Total debt on the balance sheet = $45 million
3. Calculate the total book value of the firm:
Total book value = Book value of equity + Book value of debt
Total book value = $65 million + $45 million
Total book value = $110 million
4. Calculate the proportion of equity:
Proportion of equity = Book value of equity / Total book value
Proportion of equity = $65 million / $110 million
Proportion of equity ≈ 0.5909, or 59.09%
5. Calculate the proportion of debt:
Proportion of debt = Book value of debt / Total book value
Proportion of debt = $45 million / $110 million
Proportion of debt ≈ 0.4091, or 40.91%
6. Calculate the WACC based on book value weights:
WACC = (Proportion of equity × Cost of equity) + (Proportion of debt × After-tax cost of debt)
WACC = (0.5909 × 14.00%) + (0.4091 × 3.60%)
WACC ≈ 9.43%
Now, to find the difference between the two WACCs:
Difference = WACC based on market value weights - WACC based on book value weights
Difference = 11.33% - 9.43%
Difference ≈ 1.90%
Therefore, the difference between the two WACCs is approximately 1.90%.
To find the difference between the two WACCs, we first need to calculate the WACC using market value weights and book value weights separately.
1. WACC using market value weights:
To calculate the WACC using market value weights, we need to determine the weights for debt and equity based on their market values.
Market value of debt = $50 million
Market value of equity = Current stock price * Number of shares = $21.00 * 10 million = $210 million
Weight of debt = Market value of debt / (Market value of debt + Market value of equity) = 50 / (50 + 210) = 0.1923 or 19.23%
Weight of equity = Market value of equity / (Market value of debt + Market value of equity) = 210 / (50 + 210) = 0.8077 or 80.77%
Next, we calculate the cost of debt and cost of equity:
Cost of debt = Yield to maturity = 6.00%
Cost of equity = Stockholders' required return = 14.00%
Finally, we can calculate the WACC using market value weights:
WACC (market value weights) = (Weight of debt * Cost of debt) + (Weight of equity * Cost of equity)
= (0.1923 * 6.00%) + (0.8077 * 14.00%)
= 1.1538% + 11.3238%
= 12.4776%
2. WACC using book value weights:
To calculate the WACC using book value weights, we need to determine the weights for debt and equity based on their book values.
Book value of debt = Total long-term debt = $45 million
Book value of equity = Book value of common equity = $65 million
Weight of debt = Book value of debt / (Book value of debt + Book value of equity) = 45 / (45 + 65) = 0.4091 or 40.91%
Weight of equity = Book value of equity / (Book value of debt + Book value of equity) = 65 / (45 + 65) = 0.5909 or 59.09%
Next, we calculate the cost of debt and cost of equity (same as before):
Cost of debt = Yield to maturity = 6.00%
Cost of equity = Stockholders' required return = 14.00%
Finally, we can calculate the WACC using book value weights:
WACC (book value weights) = (Weight of debt * Cost of debt) + (Weight of equity * Cost of equity)
= (0.4091 * 6.00%) + (0.5909 * 14.00%)
= 2.4546% + 8.2736%
= 10.7282%
Now, to find the difference between the two WACCs:
Difference = WACC (market value weights) - WACC (book value weights)
= 12.4776% - 10.7282%
= 1.7494% or approximately 1.75%
Thus, the difference between the two WACCs is approximately 1.75%.