Question

# EPS with complex capital structure: The Rochester Corporation issued 10-year \$900,000 par 6% convertible bonds on...

EPS with complex capital structure: The Rochester Corporation issued 10-year \$900,000 par 6% convertible bonds on January 1, 2018 at 98. The bonds have a par value of \$1,000 with interest payable annually. Each bond is convertible into 10 shares of common stock; in two years this ratio will increase, meaning that each bond will be convertible into 30 shares of common stock. Assume Rochester uses straight-line amortization for its bonds and that its effective tax rate is 35%. Net income in 2018 is \$2,600,000 and the firm had 1,000,000 shares of common stock outstanding during the entire year.

Compute diluted EPS to the 4th decimal place

Solution:

Diluted Earning Per Share = (Net Income + Interest Expense Net of Tax) / (Common shares + Convertible Shares)

Here,

Net Income = \$2,600,000

Interest Expense = (Cash Interest on Bond) + (Amortization of Discount on Bond)

= (Total Bond Value * 6%) + [[Total Bond value * (100% - Issued %) * 1/Bond Period]]

= (\$900,000 * 6%) + [[\$900,000 * (1 - 0.98)] * 1/10]

= \$54,000 + \$1,800

= \$55,800

Interest Expense Net of Tax = Interest Expense * (1 - Tax Rate)

= \$55,800 * (1-35%)

= \$36,270

Common Shares = 1,000,000 Shares

Convertible Shares = (Total Bond Value / Par value per bond) * Highest Converstion Ratio

= (\$900,000 / \$1000) * 30

= 27,000 Shares

Now subsitituting all the figures into above Diluted EPS formula,

Diluted Earning Per share = (\$2,600,000 + \$36,270) / (1,000,000 + 27,000) shares

= \$2,636,270 / 1,027,000 shares

= \$2.5670 Per share

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