Question

ABC co. And XYZ co. are identical firms in all respects except for their capital structures. ABC is all-equity financed with $650,000 in stock. XYZ uses both stock and perpetual debt, it’s stock is worth $325,000 and the interest rate on its debt is 6.5 percent. Both firms expect EBIT to be $71,000. Ignore taxes

A.) Richards owns $39,000 worth of XYZ’s stock. What rate of return is he expecting?

B.) Suppose Richard invests in ABC co. and uses homemade leverage to match his cash flow in part A. Calculate his total cash flow and rate of return.

C.) What is the cost of equity for ABC and XYZ ?

D.) What is the WAAC for ABC and XYZ ?

Answer 1

A)

The rate of return earned will be the dividend yield = Annual dividend per share/ price per share.

The company has debt, so it must make an interest payment. The net income for the company is

Net Income = $ 71000 - (0.065* $325000)

Net Income = $49875

The investor will receive dividends in proportion to the percentage of the company’s shares they own.The total dividends received by the shareholder will be:

Dividends received = $49,875 * ($39,000/$325,000)

Dividends received = $5,985

So the return the shareholder expects is:

rS= $5,985/$39,000

rS= 0.1535 or 15.35%

B)

To generate exactly the same cash flows in the other company, the shareholder needs to match the capital structure of ABC. The shareholder should sell all shares in XYZ. This will net $39,000. The shareholder should then borrow $39,000. This will create an interest cash flow of:

Interest cash flow = 0.065(–$39,000)

Interest cash flow = –$2,535

The investor should then use the proceeds of the stock sale and the loan to buy shares in ABC. The investor will receive dividends in proportion to the percentage of the company’s share they own. The total dividends received by the shareholder will be:

Dividends received = $71,000 * ($78,000/$650,000)

Dividends received = $8,520

The total cash flow for the shareholder will be:

Total cash flow = $8,520 – 2,525

Total cash flow = $5,985

The shareholders return in this case will be:

rS= $5,985/$39,000

rS= 0.1535 or 15.35%

C)

ABC is an all equity company, so:

ROE / R(e) = EBIT/Equity

rS= r0 = 71,000 / 650,000

rS = 0.1092 or 10.92%

To find the cost of equity for XYZ,

rS= r0+ (r0–rB)(B/S)(1 – tC)

rS = 0.1092 + (0.1092 – 0.065) * (325/325)(1)

= 0.1534

D)

To find the WACC for each company, we need touse the WACC equation:

WACC = (S/V) rS+ (B/V) rB(1 – tC)

So, for ABC, the WACC is:

WACC = (1)*(0.1092) + (0)(0.065)

WACC = 0.1092 or 10.92%

And for XYZ, the WACC is:

WACC = (1/2)(0.1535) + (1/2)(0.065)

WACC = 0.1092 or 10.92%

When there are no corporate taxes, the cost of capital for the firm is unaffected by the capital structure; this is M&M Proposition I without taxes.