Question

ZZZ Inc. has 10 million shares outstanding at $15 each and maintains a constant debt-to-value (D/V) ratio of 25%. ZZZ generates a constant stream of after-tax cash flows each year in perpetuity, all of which are paid out as interest to bondholders and dividends to stockholders. Suppose that the managers of ZZZ make an announcement that ZZZ will execute a recapitalization to increase its target D/V ratio. As a result of the recapitalization, the firm’s weighted average cost of capital (rWACC) will decrease by 2% (if, for example, rWACC were 20% before the recapitalization, rWACC would be .98 x 20% (= 19.6%) after the recapitalization). The corporate tax rate for ZZZ is 35%. What is the value of ZZZ (i.e. the sum of the market value of the debt and the market value of the equity) after the announcement?

Answer 1

• Total Shares outstanding = 100,00,000 shares
• Price per share is $15
• Total value of equity is $15,00,00,000
• D/V is 25% i.e. 0.25:1
• Value of debt = 15,00,00,000 * 0.25 = 3,75,00,000
• Total Value of ZZZ = $18,75,00,000
• Corporate Tax is 35%

Suppose value of WACC is X before recapitalization. So after recapitalization, value of WACC is 0.98X as there is reduction of 2%

So calculation of value X is as under

Value of ZZZZ	WACC
18,75,00,000	X
(?)	0.98X

So 0.98X * 18,75,00,000 / X = $18,37,50,000

So value of equite post recapitalization is $18,37,50,000