Question

Bruce Wayne is raising capital to renovate a workspace underneath Wayne Enterprises. He

needs $10m in order to complete renovations. The current capital structure of Wayne Enterprises
includes $100m in debt with a YTM of 5%. Wayne Enterprises also has common stock
outstanding with a market value of $300m. The firm is taxed at a rate of 30%. The stock’s beta
is 1.4 today. The risk free rate is currently 3%, while the market risk premium is 6%. Assuming
Mr. Wayne wishes to borrow all the money he needs for the renovations at the current YTM on
the existing debt, how much will the cost of capital change, measured in basis points, due to the
transaction? Assume the market value of equity does not change in the transaction.

Answer 1

The cost of capital will change by 175 basis points due to the transaction.

Step-by-step explanation:

To calculate the cost of capital change due to the transaction, we need to calculate the new cost of debt and the weighted average cost of capital (WACC) after the transaction.

First, we calculate the new cost of debt. Since Mr. Wayne wishes to borrow all the money he needs for the renovations at the current YTM on the existing debt, the cost of debt remains the same at 5%.

Next, we calculate the WACC. The WACC is the weighted average of the cost of debt and the cost of equity, where the weights are the market values of debt and equity. In this case, the market value of debt is $100m, and the market value of equity is $300m. Therefore, the weights are 100m/(100m+300m) = 0.25 for debt and 300m/(100m+300m) = 0.75 for equity.

The cost of equity can be calculated using the CAPM (Capital Asset Pricing Model) formula: Cost of Equity = Risk-Free Rate + Beta * Market Risk Premium. In this case, the risk-free rate is 3% and the market risk premium is 6%. Therefore, the cost of equity = 3% + 1.4 * 6% = 11.4%.

Now, we can calculate the WACC using the formula: WACC = Weight of Debt * Cost of Debt + Weight of Equity * Cost of Equity. Plugging in the values, we get WACC = 0.25 * 5% + 0.75 * 11.4% = 8.775%.

To calculate the change in the cost of capital, we subtract the new WACC from the old WACC and multiply by 10,000 to get the change in basis points. The old WACC is 8.6% (calculated using the same formula with the old weights). Therefore, the change in the cost of capital = (8.775% - 8.6%) * 10,000 = 175 basis points.