Question

the president and cfo of media corp cannot agree whether to use market value or book value weights in calculating the wacc. the company 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 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 $22.50 per share; stockholders' required return, r s, is 14.00%; and the firm's tax rate is 25%. 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?

Answer 1

We can see here that the WACC calculated using market value weights is 11.18%, while the WACC calculated using book value weights is 9.73%. Thus, the difference between these two WACCs is approximately 1.45% points.

How we arrived at the solution

1. Market Value Weight Approach:

• The market value of the long-term debt = $50 million.

• The market value of the equity can be calculated by multiplying the number of shares by the current stock price: $22.50 × 10 million shares = $225 million.

• The total market value of the firm's capital structure is the sum of the market value of debt and the market value of equity: $50 million + $225 million = $275 million.

• The weight of debt is the market value of debt divided by the total market value of the firm's capital structure: $50 million / $275 million = 0.1818 (approximately 18.18%).

• The weight of equity is the market value of equity divided by the total market value of the firm's capital structure: $225 million / $275 million = 0.8182 (approximately 81.82%).

To calculate the WACC, we need to multiply the weight of debt by the after-tax cost of debt and the weight of equity by the cost of equity. Finally, we sum these two values.

• Given that the cost of debt is 6.00% and the tax rate is 25%, the after-tax cost of debt is: 6.00% × (1 - 0.25) = 4.50%.

• The cost of equity = 14.00%.

• Now, let's calculate the WACC using the market value weights: (0.1818 * 4.50%) + (0.8182 × 14.00%) = 11.18%.

2. Book Value Weight Approach:

• The book value of the long-term debt is $45 million.

• The book value of the equity (common stock plus retained earnings) = $65 million.

• The total book value of the firm's capital structure is the sum of the book value of debt and the book value of equity: $45 million + $65 million = $110 million.

• The weight of debt is the book value of debt divided by the total book value of the firm's capital structure: $45 million / $110 million = 0.4091 (approximately 40.91%).

• The weight of equity is the book value of equity divided by the total book value of the firm's capital structure: $65 million / $110 million = 0.5909 (approximately 59.09%).

• To calculate the WACC, we need to multiply the weight of debt by the after-tax cost of debt and the weight of equity by the cost of equity. Finally, we sum these two values.

• Using the same after-tax cost of debt (4.50%) and cost of equity (14.00%), let's calculate the WACC using the book value weights: (0.4091 × 4.50%) + (0.5909 × 14.00%) = 9.73%.

Thus, WACC = 11.18% - 9.73% = 1.45%.