Question

Yerba Industries is an all-equity firm whose stock has a beta of 0.60 and an expected return of 13%. Suppose it issues new risk-free debt with a 4.5% yield and repurchase 20% of its stock. Assume perfect capital markets. a. What is the beta of Yerba stock after this transaction? b. What is the expected return of Yerba stock after this transaction? Suppose that prior to this transaction, Yerba expected earnings per share this coming year of $4.50, with a forward P/E ratio (that is, the share price divided by the expected earnings for the coming year) of 13. c. What is Yerba's expected earnings per share after this transaction? Does this change benefit the shareholder? Explain. d. What is Yerba's forward P/E ratio after this transaction? Is this change in the P/E ratio reasonable? Explain. a. What is the beta of Yerba stock after this transaction? The beta of Yerba stock after this transaction is (Round to two decimal places.) b. What is the expected return of Yerba stock after this transaction? The expected return of Yerba stock after this transaction is %. (Round to two decimal places.) Suppose that prior to this transaction, Yerba expected earnings per share this coming year of $4.50, with a forward P/E ratio (that is, the share price divided by the expected earnings for the coming year) of 13. c. What is Yerba's expected earnings per share after this transaction? Does this change benefit the shareholder? Explain. . (Round to the nearest cent.) If prior to the transaction, Yerba expected earnings per share this coming year of 54.50, with a forward Ple ratio of 13, Yerba's expected earnings per share after this transaction is $ Does this change benefit the shareholder? Explain. (Select the best choice below.) O A. It does not benefit shareholders because if you take into account the shares they lost to the repurchase, their cash flows are actually the same. O B. It does not benefit shareholders because the risk of holding equity has increased

Answer 1

Note :

Following calculations are made on the basis of best assumptions can be made as per the information provided in given problems. The answer might be different as answers provided by other expert on the basis of different assumptions taken by other expert.

Relevant information
Stock Beta (By)	= 0.60
Expected Return of Stock - E(R)	=13%
Risk Free Rate of Return (Rf)	=4.5%
Repurchase of stock (Buy back)	=20%

Ans (a)	Beta after transaction
	Existing Beta of stock	= 100*0.6/100
		=0.60 (as given)
	Note : Is is assuming that amount received from issued of risk free debt is equal to repurchase of stock then,
	Note 2 : as we know that beta of risk free security is 0
	Hence,
	Beta after transaction =	(100-20)*0.6+(20*0)/100
	=	0.48

Ans (b)	Expected Return of stock aster transaction
	Since expected return can be calculated as per CAPM (Capital assets pricing model) as follows :
	Expected return before repurchase-E( R)	=Rf + (Rm-Rf)B
	Where,
	B	= 0.60
	Rm , market risk premium	?
	Rf	=4.5%
	E( R)	=13%
	Hence,
	13%	=4.5% +(Rm-4.5%)0.60
	13%	=4.5% + 0.60 Rm -2.7%
	Rm	= 18.67%
	Hence, expected return on beta after above transaction as per CAPM shall be :
		=4.5% + (18.67-4.5)0.48
		=11.30%

Ans ( c)	Relevant Data
		Amount in "$"
	Expected Earnings per share	4.5
	P/E Ratio	13 times
	Let, Number of shares of the company	=100
	Let, Risk free debt issued	=20
	Hence, Expected earning before above repurchase transaction	=4.5*100
		=450
	Expected earning after repurchase	=450- (20*4.5%)
	(earning - coupon amount on risk free debt e.i. 20*4.5%)	=450- 0.9
		=449.1
	No. of shares after above repurchase transaction	=100-20
		=80
	Hence, Earning per share after repurchase transaction	=449.1/80
		=5.6138 per share

Explanation : since earning per share of company increase and shareholders will get more returns in form of earning and dividend, wealth of shareholders will get increased

Change in shareholders market price (assuming boot strap effect of P/E ratio i.e. taking P/E Ratio before the transaction for calculation of market price after above transaction)

share Price before above transaction	=4.5*13
	=58.5 per share
Share price after above transaction	=5.6138*13
	=72.78 per share

Explanation : since share price increased due to above transaction, the benefits of appreciation in share will benefit the shareholder in form of capital gain. Hence, it will benefit the shareholder when they will sell their shares.
Correct answer :
(D) You can not tell. It depends on the shareholder's risk preference. Cash flows are higher, but so is risk, some of the shareholder will be better off,some will be worse off.

Ans ( d)	Where share price is same as before the above transaction i.e. 13*4.5=58.5, then P/E ratio shall be
	P/E ratio after repurchase	=58.5/5.6138
	(market price/EPS)	=10.42 times
	Explanation: Since P/E Ratio get decreased, there is value loss for shareholders in the market.
	Correct answer :
	(B) it is not reasonable and reflect the value loss of the recapitalization.