Question

Newkirk, Inc., is an unlevered firm with expected annual earnings before taxes of $21.6 million in perpetuity. The current required return on the firm’s equity is 16 percent, and the firm distributes all of its earnings as dividends at the end of each year. The company has 1.36 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 $30.6 million of perpetual 9.6 percent debt and use the proceeds to buy back shares.

c-1. How many shares will be repurchased? (Enter your answer in dollars, not millions of dollars, e.g., 1,234,567. Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)

Shares repurchased

c-2. What is the price per share after the recapitalization and repurchase? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Price per share $

d. Use the flow to equity method to calculate the value of the company’s equity after the recapitalization. (Enter your answer in dollars, not millions of dollars, e.g., 1,234,567. Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)

Value of the equity $

Answer 1

Solution for C-1 :

a. Vu = EBIT(1-tc) / Ro

= 21,600,000(1-0.36) / 0.16

= $89,100,000

b. Since it is unlevered firm, its value of equity and value of the firm is equal.

Price per share = Value of equity / Number of outstanding shares

= 89,100,000 / 1,360,000

= 65.515

c. NPV of financing side effects is equal to the after-tax present value of cash flows resulting from the firm's debt.

NPV = Proceeds − After tax PV of interest payment

= 30,600,000 - (1-0.34)(0.096)(30,600,000) / 0.096

= $ 10,404,000

Using APV value of the company after the recapitalization is:

Value of the firm = 89,100,000 + 10,404,000

= $ 99,504,000

After the announcement, value of equity is still same as the value of the firm.

New price per share = 99,504,000 / 1,360,000

= $73.16

c. If the company uses the proceeds to buy back shares then number of shares repurchased will be:

C-1 Number of shares repurchased = 30,600,000 / 73.16

= 418,261

So, new number of shares outstanding = 1,360,000 - 418,261

= 941,739

The value of equity after the repurchase will be:

New value of equity = 99,504,000 - 30,600,000

= $ 68,904,000

C-2 So new price per share after the recapitalization and repurchase = 68,904,000 / 941,739

= $ 73.16

d. Rs = Ro + B/S(Ro - Rb(1 - tc)

Rs = 0.16+ 30,600,000/68,904,000(0.16 - 0.096(1-0.34)

= 0.2029

after recapitalization, the net income of the company will be:

EBIT	21,600,000
Interest	2,937,600
EBT	18,662,400
Tax	6,531,840
Net income	12,130,560

If the company provides all the net income to the shareholders, then the value of the equity is:

• S=Cash flow available to equity holders / Rs

Where,

• S = Value of equityholders
• S=12,130,560 / 0.2029
• = $ 59,780,763