Question

Star, Inc., a prominent consumer products firm, is debating whether or not to convert its all-equity capital structure to one that is 40 percent debt. Currently, there are 2,000 shares outstanding and the price per share is $7. Its assets will be worth $21,500 in one year if the economy is strong, and $10,000 in one year if the economy is weak. Both events are equally likely. The interest rate on debt is 8 percent, and there are no taxes.

a. What is the expected return of Star stock without leverage?

b. If Star converts to the capital structure that consists 40 percent debt today and uses the proceeds from issuing debt to repurchase shares of existing stock, what will be the market value of its equity after the repurchase? How many shares of stock can Start repurchase?

c. What is the expected return of Star stock after the transaction in part (b)?

Answer 1

a) 12.46%

b) $8,400 , 1200 shares

c) 10,68%

Explanation :

Step 1: Calculate the expected return of Star stock without leverage as follows :

Total equity value = 2000 shares x $7 = $14,000

Value of Assets (strong economy). = $21,500

Value of Assets (weak economy) = $10,000

% gain in strong economy = ($21,500 - $14,000) / $14,000

= 53.57%

% loss in weak economy = ($10,000 - $14,000)/ $14,000

= (-28.57%)

Expected return of Star stock = 53.57% x 0.5 + (-28.57%) x 0.5

= 12.46%

Step 2: The market value of equity after repurchase is as follows :

Amount raised through debt = % of debt x total equity value

= 40% x  $14,000

  = $ 5,600

The above amount of $5,600 is used to buy back equity shares.

The number of shares repurchased = Total value of shares/ Price per share

= $5,600 divided by $7

= 800 shares

Number of shares remaining outstanding = Total numer of shares - shares repurchased

=. 2,000 - 800

=. 1,200 shares

Market Value of Equity after repurchase = $7 * 1200 = $ 8,400

Teh following shares of stock, Start can repurchase :

Step 3:

Expected Return of Stock at 40% debt in Capital structure:

= % of equity x return on equity (from step 1)  + % of debt x return on debt (given)

= 0.60 x 12.46% + 0.4 x  8%

= 7.48% + 3.2%

= 10.68%