Question

Rockwood Enterprises is currently an all equity firm and has just announced plans to expand their current business. In order to fund this expansion, Rockwood will need toraise $100 million in new capital. After the expansion, Rockwood is expected to produce earnings before interest and taxes of $50 million per year in perpetuity. Rockwood has already announced the planned expansion, but has not yet determined how best to fund the expansion. Rockwood currently has 16 million shares outstanding and following the expansion announcement these shares are trading at $25 per share. Rockwood has the ability to borrow at a rate of 5% or to issue new equity at $25 per share. Show mathematically that the stock price of Rockwood does not depend on whether they issue new stock or borrow to fund their expansion.

Answer 1

Step 1: Calculate Number of New Shares and Total Outstanding Shares if Expansion is Finance with Issuance of New Stock

Even after the issuance of new stock, the stock price will continue to be $25 because the positive effect of the announcement of new project has already been factored into the stock price .

The number of new shares and total outstanding shares is calculated as below:

Number of New Shares = Amount to be Raised/Stock Price = 100/25 = 4 million shares

Total Shares Outstanding = Current Shares Outstanding + Number of New Shares = 16 + 4 = 20 million shares

_____

Step 2: Calculate Cost of Equity Capital if Expansion is Financed with Issuance of New Stock

The cost of equity capital if expansion is financed with issuance of new stock is determined as follows:

Cost of Equity Capital (Unlevered) = EPS/Stock Price

where EPS = EBIT/Total Shares Outstanding = 50/20 = $2.50 [we will take EBIT in the calculation of EPS as we interest is not present in a capital structure without debt and no information with respect to tax has been given in the question] and Stock Price = $25 [stock price will continue to be $25]

Using these values in the above formula, we get,

Cost of Equity Capital (Unlevered) = 2.50/25 = 10%

_____

Step 3: Calculate Cost of Equity Capital if Expansion is Financed with Debt

The cost of equity capital if expansion is financed with debt is arrived as below:

Cost of Equity Capital (Levered) = Cost of Equity Capital (Unlevered) + (Cost of Equity Capital (Unlevered) - Cost of Debt)*Debt/Equity

Here, Cost of Equity Capital (Unlevered) = 10%, Cost of Debt = 5%, Debt = $100 and Equity = 500 - 100 = $400

Using these values in the above formula, we get,

Cost of Equity Capital (Levered) = 10% + (10% - 5%)*100/400 = 11.25%

_____

Step 4: Calculate EPS and Stock Price if Expansion is Financed with Debt

The EPS and stock price if expansion is financed with debt is calculated as follows:

EPS = (EBIT - Interest)/Current Number of Outstanding Shares = (50 - 5%*100)/16 = $2.8125

Stock Price = EPS/Cost of Equity Capital (Levered) = 2.8125/11.25% = $25 per share

As can be seen from the above calculation that the stock price comes out to be $25 per share if the expansion is financed with the use of debt which is same as if the expansion has been financed with the issuance of new stock. Therefore, it can be concluded that the stock price of Rockwood does not depend on whether they issue new stock or borrow to fund their expansion.