- ABC Co. and XYZ Co. are identical firms in all respects except for their capital structure. ABC is all-equity financed with $600,000 in stock. XYZ uses both stock and perpetual debt; its stock is worth $300,000 and the interest rate on its debt is 10 percent. Both firms expect EBIT to be $73,000. Ignore taxes.
- Rico owns $30,000 worth of XYZ’s stock. What rate of return is she expecting?
- Show how Rico could generate exactly the same cash flows and rate of return by investing in ABC and using homemade leverage.
- What is the cost of equity for ABC? What is it for XYZ?
- The rate of return earned will be the dividend yield. The company has debt, so it must make an interest payment. The net income for the company is:
NI = $73,000 – .10($300,000)
NI = $43,000
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 = $43,000($30,000/$300,000)
Dividends received = $4,300
So the return the shareholder expects is:
R = $4,300/$30,000
R = .1433 or 14.33%
- 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 $30,000. The shareholder should then borrow $30,000. This will create an interest cash flow of:
Interest cash flow = .10($30,000)
Interest cash flow = –$3,000
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 = $73,000($60,000/$600,000)
Dividends received = $7,300
The total cash flow for the shareholder will be:
Total cash flow = $7,300 – 3,000
Total cash flow = $4,300
The shareholders return in this case will be:
R = $4,300/$30,000
R = .1433 or 14.33%
- ABC is an all equity company, so:
RE = RA = $73,000/$600,000
RE = .1217 or 12.17%
To find the cost of equity for XYZ we need to use M&M Proposition II, so:
RE = RA + (RA – RD)(D/E)(1 – tC)
RE = .1217 + (.1217 – .10)(1)(1)
RE = .1433 or 14.33%
- To find the WACC for each company we need to use the WACC equation:
WACC = (E/V)RE + (D/V)RD(1 – tC)
So, for ABC, the WACC is:
WACC = (1)(.1217) + (0)(.10)
WACC = .1217 or 12.17%
And for XYZ, the WACC is:
WACC = (1/2)(.1433) + (1/2)(.10)
WACC = .1217 or 12.17%
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.
