Questions:
How do you determine if convertible bonds are dilutive?

The profit after interest and tax of PK in the year 2023 was $300 million (its tax rate was 40%). Moreover, it had common shares outstanding at the beginning of 2023 of 40 million. During the year 2023, it issued 10 million shares in May, 2 million in July and 5 million shares in August. At the end of the year, it has $200 million in convertible bonds which are convertible into 500,000 common shares. Their interest rate is 20%. 

Are the convertible bonds dilutive?

Reference answers:
To determine whether convertible bonds are dilutive, the Basic EPS and diluted EPS need to be compared. If the diluted EPS is greater than the basic EPS, it means that the convertible does not have a diluting effect on the earnings. You can compute the Basic and Diluted EPS as follows:

# Basic EPS: 

Basic EPS = Net income / weighted average number of shares

# Diluted EPS

Diluted EPS = (Net income + savings of interest) / (Weighted average number of shares + new shares that would be issued if the convertible bonds are converted to common shares)

To determine whether the convertible bonds are dilutive, the Basic EPS and diluted EPS need to be compared. If the diluted EPS is greater than the basic EPS, it means that the convertible does not have a diluting effect on the earnings.

# Basic EPS: 

Basic EPS = Net income / weighted average number of shares.

Net income = $300 million

Weighted average number of shares = 40 million + (10 million * 8/12) + (2 million * 6/12) + (5 million * 5/12) = 40+6.67+1+2.08 million = $49.75

Basic EPS = $300 million / $49.75 = $6.03  

# Diluted EPS

Diluted EPS = (Net income + savings of interest) / (Weighted average number of shares + new shares that would be issued if the convertible bonds are converted to common shares)

Net income = $300 million
After tax cost of convertible bonds = $200 million * 20% * (1-40%) = $24 million

Weighted average number of shares = 40 million + (10 million * 8/12) + (2 million * 6/12) + (5 million * 5/12) = 40+6.67+1+2.08 million = 49.75 million shares

New shares upon conversion = 0.5 million shares

Diluted EPS = ($300 million + $24 million) / (49.75 million + 0.5 million) = $6.45

# Result

Since the diluted EPS is greater than the basic EPS, it means that the convertible does not have a diluting effect on the earnings. EPS is diluted only if the diluted EPS is greater than the basic EPS which is not the case here.