Question

Corporations Alpha and Beta have identical assets that generate identical cash flows and as result both have market value of V. They differ only in their capital structure.  Alpha has debt equal to​ 20% of the value of the firm​ V, while Beta has debt equal to​ 10% of V. The debt of both corporations is​ risk-free with a​ risk-free interest rate of r. There are no taxes and capital markets are perfect.

If Mr Pi owns​ 10% of Corporation​ Beta’s stock, an alternative investment package that could produce identical cash flows for Mr Pi would​ be:

Answer 1

We consider both company has a value of 100, cost of debt is 10% and income earned during the year is 100.

Company Beta has debt of 10 and equity of 90 whereas Alpha has debt of 20 and equity of 80

To have identical cash flow, we take 10% investment in equity of Alpha by paying 8 and invest in debt securities of Rs. 1

Now we calculate the cash flow in both the position.

Position in Beta

Cash Flow = (Income - Interest) * Stake Hold

= (100 - 1) * 10% = 9.9

Position in Alpha

Cash Flow =

Income from Company + Income from debt investment

= (Income - Interest) * Stake Hold + Debt * Int

= (100 - 2) * 10% + 10 * 10%

= 9.8 + 0.1 = 9.9

Hence return in both the company is same and the cash flow are replicated

We take 10% investment in equity of Alpha by paying 8 and invest in debt securities of Rs. 1