1. CCH, Inc. has no debt in its capital structure. There are 100 million shares
ID: 2792014 • Letter: 1
Question
1. CCH, Inc. has no debt in its capital structure. There are 100 million shares outstanding and the price per share is $30. The company is considering a debt-for-equity swap where they will issue $1 billion in debt at a 6% coupon rate (YTM = 6%) and use the proceeds to buy back stock (at $30 per share). Calculate the following:
A) If there are no taxes, what is the value of the firm without tax if after the debt-for-equity swap is completed? Show your calculation
B) If there are taxes that apply at a 35% rate, what is the value of the firm after the debt is issued? Show your calculation
C) If the firm issued more debt so that its debt/equity ratio was 10, what would be the value of the firm (including taxes but ignoring bankruptcy costs)? Show your calculation
Explanation / Answer
According to Modigliani-Miller theorem, the relation ship between a value of firm with debt and a firm without debt is as follows :
Value of debt with debt (Vd) = Value of firm without debt(Vn) + Tax Rate * Debt Amount
This increase is value is due to the follwing reason - in a country with taxes, interest paid is tax-deductibe (i.e, the firm can use expenses for interest payments to pay lower taxes). Since the debt is assumed to be perpetual, total value addition to the firm is tax rate*debt amount. This helps in increasing the value of the firm by the same amount
(A)
Tax rate = 0%
Value of firm (Vd) = Value of firm with no debt (Ve) = No of shares * share price = 100000000*30 = 3000000000
(B)
Tax Rate = 35%
Debt = 1000000000
Value of firm (Vd) = Ve + 1000000000*35% = 3350000000
(C)
Initial equity = 3000000000
New debt to equity ratio = 10:1
Debt = 10/(10+1) * Initial equity = 3000000000*10/(10+1) = 2727272727
Value of firm (Vd) = Ve+35%* 2727272727 = 3954545455
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