Question

A firm reported Net Income of $500,000. They have 100,000 shares of common stock with a price of $60 per share and 20,000 shares of preferred stock that pays a dividend of $6 per year. They have 2,000 convertible bonds with a face value of $1,000 and a 9% coupon rate. Each bond can be converted into 25 shares of stock. They have also issued 10,000 warrants that allows the owner to purchase stock for $50 per share. The tax rate is 25%. What is the difference between their Basic EPS and their fully diluted EPS (you have to solve for both).

a) $.23             b) $.55              c) $1.22            d) $1.83       

Answer 1

To answer the above question, We need to calculate Basic EPS and Diluted EPS to get the difference between the both.

Basic EPS = (Net Income - Preferred Dividend) / Weighted average number of Shares Outstanding

By Substituting the Values,

Basic EPS = [500000- (20000*6)] /100000 = 3.8

Now let us calculate Diluted EPS,

We have the details of convertible bonds where, Face value = $1000, No of Bonds = 2000, Coupon Rate = 9%

Total Interest Payable for the Bond = 1000*2000*9%*(1-25%) = 135000

Convertible No of Shares = 2000*25 = 5000

To find whether the bonds are dilutive or Anti Dilutive, we need to divide total Interest payable by convertible no of shares.

Hence, 135000/5000 = 2.7

Since 2.7 < Basic EPS 3.8, the bonds are dilutive. So no of shares from convertible bonds = 50000

Now, We have details of warrant where, no of Warrants = 10000 Since, The Exercise Price $50 < Market Price $60, The Warrants are Dilutive.

Proceeds from exercise of Warrants = 1000*50 = $50000

Shares Repurchased = Proceeds from exercise of warrants / Market Price of Shares = 50000/60 = 833

Shortfall / Shares Outstanding from Warrants = 10000-833 = 9167

So, Total number of shares = 100000+50000+9167=159167

Now, using the above number of shares, let us calculate the diluted EPS:

Diluted EPS = [(Net Income - Preference Dividend) + (Convertible Debt Interest)*(1 - Tax Rate)] / Weighted average dilutive number of shares

Diluted EPS = [(500000-(20000*6) + (1000*9%*2000*(1-25%)]/159167 = 3.23

Hence the Difference Between Basic EPS and Diluted EPS = 3.8-3.235 = 0.565

So the answer is option B