Question

An internet services provider is considering changing its capital structure. The firm's beta is 1.25, the current risk-free rate of return is 5.50%, and the market risk premium is 7.50%. Return on equity was 16.50% at its current capital structure. The company projects its cost of equity will be 12.65% at its optimal capital structure. The market value of the firm's equity is currently $4 billion.

A) What will be the expected net gain in firm value by moving to the optimal capital structure?

Select one:

A. $68.9 million

B. $76.3 million

C. $89.2 million

D. $93.9 million

B) What is the company's current equity return differential?

A. -2.54%

B. 1.63%

C. 3.13%

D. None of the above

Answer 1

A)

Question says company has reduced its cost of equity. which is wrong as for reducing cost of equity, beta need to be decreased putting risk free rate and market risk premium constant.

Here i believe cost of capital should be decreased to 12.65% rather than cost of equity.

Also Debt / Equity ratio i.e. Leverage is missing from the question as well as tax rate and interest.

I assumed D / E and tax rate to be 0 here.

So

Market value of firm's equity = $4 bn

i.e. from ROE formula

ROE = Net Income / Shareholder's Equity

0.165 = Net Income / 4

Net Income = $0.66 bn

If cost of capital changed to 12.65% than total value of company will be

= 0.66 / .1265

=$5.22 bn

If we have market value of debt as X

Than market value of equity will be = 5.22 - X

B)

Current equity return differential is

ROE - Expected return

= 16.5 - 5.5 - 1.25 * (7.5)

= 1.625%

Thank You!!