Company X and Company Y have the same cost of capital and identical asset portfolios with a market value of 1000. Company X has zero debt. The expected return on equity for Company X is 15%. The firm value of Company Y is made up of 50% debt and 50% equity. The expected return on debt for Company Y is 9%. Assuming perfect capital market, what is the expected return on equity for Company Y

The expected return on equity for Company Y is:

= 0.21 or 21%

Explanation:

a) Data and Calculations:

                                       Company X    Company Y

Market value of assets     1,000              1,000

Equity                                1,000                500

Debt                                     0                    500

Expected return on equity  15%

Expected return on debt                           9%

Return on Company X = 150 (1,000 * 15%)

Return on Company Y debt = 500 * 9% = 45

Return on Company Y equity = (150 - 45)/500 = 0.21

b) Under perfect capital market conditions, the total return for Company Y will be equal to 150 as in Company X.  The rate of return will then be determined after subtracting the interest on debt (500 * 9%).  This will leave 105 as the return for equity.  This amount is then divided by the value of equity to derive the rate of return.

start by isolating the variable on one side by adding 43w^2 to both sides.   the equation will read:

25w^2+5=0

*subtract 5 from both sides*

25w^2=-5

*divide both sides by 25*

w^2=-1/5

*take the square root of both sides*

w=√(-1/5)

the square root of -1 is i.   the square root of 5 remains √5

the answer is i/√5.

hope this