Valuation Methodologies ABC, Inc., is an unlevered venture that reached its matu
ID: 2720670 • Letter: V
Question
Valuation Methodologies ABC, Inc., is an unlevered venture that reached its mature life-cycle stage. ABC is expecting earnings before taxes of $30 million in perpetuity. The required return of the firm’s unlevered equity (rU) is 18 percent, and the firm distributes all of its earnings as dividends at the end of each year. ABC has 1 million shares of common stock outstanding and is subject to a corporate tax rate of 34 percent. The firm is planning a recapitalization under which it will issue $50 million of perpetual 10 percent debt and use the proceeds to buy back shares. 1.Calculate the value of ABC before the recapitalization plan is announced. What is the value of ABC’s equity before the announcement? What is the price per share? 2.Use the APV method to calculate the value of ABC after the recapitalization period is announced. What is the value of ABC’s equity after the announcement? What is the price per share? 3.How many shares will be repurchased? What is ABC’s equity value after the repurchase has been complete? What is the price per share? 4.Use the flow-to-equity method to calculate the value of ABC’s equity after the recapitalization.Explanation / Answer
Answer:1 The value of the all-equity firm, before the recapitalization plan is announced, is
Vu=Annual earnings/ro
=$30*(1-0.34)/0.18=$110 million
The value of ABC equity is also $110 million, since there is no debt. The price per share before the recapitalization is therefore
Price=Value of Firm/Number of shares=110/1=$110 per share
Answer:2 Because there are no personal taxes or costs of financial distress, the value of the leverage (tax shield) is rCB=0.34*50=$17 million. The value of the firm after the recapitalization is therefore: 110 + 17 = $127 million. This implies a price of $127 per share.
Answer:3 At this price, the $50 million proceeds from the debt issue enables the firm to repurchase 50 million / 127=393,700 shares. Thus about 606,300 shares will remain outstanding.
Answer:4 To use the flow-to-equity method, we need to calculate the earnings per share (i.e. the annual cash flow paid to shareholders):
EPS=(Earnings-interest payments)/Number of shares outstanding
=30*(1-0.34)-0.1*(1-0.34)*50/606300
=$27.21
The required return on equity will be
=18%+(50/77)(1-0.34)(18%-10%)=21.43%
These values together verify the stock price by the FTE approach, since we have
Annual cash flow paid to shareholders (EPS)/rs=27.21/0.2143=$127
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