Question

Newkirk, Inc., is an unlevered firm with expected annual earnings before taxes of $22.4 million in perpetuity. The current required return on the firm’s equity is 20 percent, and the firm distributes all of its earnings as dividends at the end of each year. The company has 1.44 million shares of common stock outstanding and is subject to a corporate tax rate of 35 percent. The firm is planning a recapitalization under which it will issue $31.4 million of perpetual 10.4 percent debt and use the proceeds to buy back shares.

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

$

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.)

Answer 1

(c-1) For an unlevered firm with no growth, the Value of equity is given by:

V_e=D₁/K_e

Where,

V_e is the value of the equity

D₁ is the dividend paid next year

K_e is the cost of equity or the discount rate or the required rate of return

In the given case,

EBT=$22,400,000

Tax Rate=35%

PAT= EBT*(1-Tax rate) =$14,560,000

Since the entire earnings is paid back as dividend, dividend is same as PAT

Hence, Value of equity as per the above formula= $72,800,000.

Value of each share = 72,800,000 / 14,40,000 = $ 50.56

Hence, number of shares repurchased = 621099 shares

(c-2). After the recapitalisation, the company becomes a levered company. As per MM Hypothesis (with taxes), the value of a levered company is given by:

V_L= V_UL+ Tax Advantage of Perpetual Debt

Where,

V_L is the value of the levered company

V_UL is the value of the unlevered company

Tax Advantage of perpetual debt is given by: Value of Debt*Tax Rate

Hence, in the above case:

Tax advantage of debt= $31,400,000*0.35=$10,990,000

V_L=72,800,000+10,990,000=$83,790,000

After recapitalisation, Value of equity=Value of firm-Value of debt=$52,39,0000

Number of shares outstanding = 14,40,000 – 621099 = 818901

Hence, price per share = 52390000 / 818901 = $63.976

(c-d) Value of equity after recapitalisation (already calculated above) = $52390000