Question

River Cruises is an entirely equity-financed company. The current position of the company is as follows: Number of shares 108761 Price per share $ 11 Operating income $ 140,933 Earning per share $ 1.30 The CFO of the company is proposing to issue new debt and repurchase the share using the cash from issuing the debt as follows: Amount of debt issue $ 299,093 Interest rate of debt 8%

i. What is the market value of the company now?

ii. What is the return on equity of the company? Assume that there is no tax.

iii. What will be the value of the company after the proposed change in capital structure (assume no-tax world)?

iv. What will be the return on equity and return on asset (weighted average cost of capital) with the proposed change assuming no-tax world?

v. What will be the value of the company after the proposed changes in capital structure assuming that the company pays 25% tax?

vi. What will be the return on equity and return on asset (weighted average cost of capital) with the proposed change assuming that the company pays 25% tax? vii. If the proposed new capital structure induces agency costs and bankruptcy costs, what will the value of the after company? Given that the present value of the expected agency cost is $10,000 and the present value of the expected bankruptcy cost is $15,000. The tax rate is 25%

Answer 1

i) Market value of company = market value of equity (as it is all equity financed)

=No. of shares* Price per share

=108761 * $11 = $1,196,371

ii) Return on equity = Earnings per share/Price per share = $1.3/$11 = 11.82%

iii) As per Modigliani Miller, the change in capital structure does not lead to a change in value of company as the cost of equity rises proportionately (due to increase in leverage) to offset the cheaper debt

$299093 will be the new debt value and the new value of equity = $1196371 - $299093 = $897278

So, even after the proposed changes, the value of company = $1196371

iv) Return on Equity = Unlevered return on equity + (Unlevered return on equity-cost of debt)*D/E

=0.1182 + (0.1182-0.06)*299093/897278

=0.1376 or 13.76%

Return on Assets (WACC) = 299093/1196371*0.06 + 897278/1196371*0.1376 = 11.82%

v) If there is a tax of 25%

Value of company = Value of Unlevered company + Tax shield

= 1196371 + tax rate * Debt

=1196371+0.25*299093

=$1,271,144.25

The return on equity will remain the same at 13.76%

However, the new return on Assets = 299093/1196371*0.06* (1-0.25) + 897278/1196371*0.1376

=11.455%