Question

During the year, jones declared and paid dividends of $3.00 per share on its preferred stock. The preferred shares are convertible into 40,000 shares of common stock. The 8% bonds are convertible into 60,000 shares of common stock. Net income for the year is $1,615,000. Assume that the income tax rate is 25%. What is the diluted earnings per share (EPS) for the year?

a. $5.26
b. $4.88
c. $4.63
d. $4.20

Answer 1

To calculate the diluted earnings per share (EPS), first calculate the additional common shares from the convertible preferred stock and convertible bonds. Then calculate the diluted net income by adjusting the net income for the dividends on preferred stock and interest expense saved on the convertible bonds. Finally, divide the diluted net income by the total number of shares to get the diluted EPS.

Step-by-step explanation:

To calculate the diluted earnings per share (EPS), we need to consider the impact of the convertible preferred stock and convertible bonds. First, we calculate the additional common shares that would be issued if all the convertible preferred stock and convertible bonds were converted. The additional shares from the preferred stock are calculated by multiplying the number of preferred shares by the conversion ratio (40,000 shares). The additional shares from the convertible bonds are calculated by multiplying the number of convertible bonds by the conversion ratio (60,000 shares). Next, we calculate the diluted net income by subtracting the dividends paid on preferred stock from the net income and adding the interest expense saved by converting the convertible bonds. Finally, we divide the diluted net income by the total number of shares (original common shares + additional shares from preferred stock + additional shares from convertible bonds) to get the diluted earnings per share (EPS).

Let's perform the calculations:

1. Additional shares from preferred stock = Preferred shares * Conversion ratio = 40,000 shares * 1 = 40,000 shares
2. Additional shares from convertible bonds = Convertible bonds * Conversion ratio = 60,000 shares * 1 = 60,000 shares
3. Diluted net income = Net income - Dividends on preferred stock + Interest expense saved on convertible bonds
   = $1,615,000 - ($3.00 * Number of preferred shares) + (8% * Convertible bonds * Face value)
   = $1,615,000 - ($3.00 * 40,000) + (8% * 60,000 * $1,000)
   = $1,615,000 - $120,000 + $48,000
   = $1,543,000
4. Total number of shares = Original common shares + Additional shares from preferred stock + Additional shares from convertible bonds
   = 200 shares + 40,000 shares + 60,000 shares
   = 100,200 shares
5. Diluted EPS = Diluted net income / Total number of shares
   = $1,543,000 / 100,200 shares
   = $15.37

Therefore, the diluted earnings per share (EPS) for the year is $15.37.