Question

Firm C currently has 250,000 shares outstanding with current market value of $42.00 per share and generates an annual EBIT of $1,250,000. Firm C also has $1 million of debt outstanding. The current cost of equity is 8 percent and the current cost of debt is 5 percent. The firm is considering issuing another $2 million of debt and using the proceeds of the debt issue to repurchase shares (a pure capital structure change). It is estimated that the cost of the new debt will be 5.5 percent and that the cost of equity will rise to 8.48 percent with the additional debt. The marginal tax rate is 30 percent.

a. Before capitalization, what is the firm’s weighted average cost of capital? Answer in decimal form

b. What will the firm’s market value be after the announcement of the new debt issue?

Answer 1

a. The calculation of the weighted average cost of capital is shown below:

But before that we need to do the following calculatoions

After tax cost of debt = Cost of debt * (1 - Marginal Tax rate)

= 5% * (1 - 0.30)

= 5% * 0.70

= 3.55 %

Now the total equity is

Value of the equity = Share Price * Total shares outstanding

= $42 * 250,000 shares

= $10,500,000

= $10.50 million

And, the debt is $1 million

So, the total capital is

= $10.50 million + 1 million

= $11.50 million

As we know that

WACC = (Weight of debt * Post tax-Cost of Debt) + (Weight of equity * Cost of equity)

Weight of debt = Total Debt / Total Capital

= 1 / 11.50

= 0.09

And, Weight of Equity is

= 1- Weight of debt

= 1- 0.09

= 0.91

Now the WACC is

WACC = (0.09 * 3.55%) + (0.91 * 8%) 0.3195

WACC = 7.60%

b. Now the market value after annoucing the new debit issue is

But before that

The interest on total debt is

Interest expense = 5% on old debt + 5.5% on new debt

= (5% * 1,000,000) + (5.5% * 2,000,000)

= $50,00 + $110,000

= $160,000

Now the value of equity is

= (EBIT - Interest)* (1-Tax Rate) / (Cost of equity)

              = (1,250,000 - $160,000) * (1 - 0.30) / (8.48%)

              = $8,997,642

So, the total market value is

= Debt + equity

= $1,000,000 + $2,000,000 + $8,997,642

= $11,997,642