### CFA Practice Question

A company has 20,000 convertible bonds outstanding for nine months of a fiscal year. The bonds carry an interest rate of 5.5% and have a face value of 1,000 each. Each bond can be converted into 50 common shares. The company is in the 37% tax bracket. If its basic EPS is 0.87, are the convertible bonds dilutive or antidilutive?
A. They are antidilutive.
B. They are dilutive.
C. Dilutive if the stock price is below 20 and antidilutive if the stock price is above 20.
Explanation: Interest savings if bonds are converted = 20,000 x 1,000 x 0.055 x (1 - 0.37) = 693,000
No. of additional shares upon conversion = 20,000 x 50 = 1,000,000
Marginal EPS = 693,000/1,000,000 = 0.69.
Since this is less than basic EPS, 0.87, convertible bonds are dilutive. Note: we have ignored the effect of partial year in this approach since it will affect both the numerator and denominator the same way.

### User Contributed Comments4

User Comment
george2006 The explanation is incorrect. It failed to account for the fact that those convertible bonds were only outstanding for 9months of a year.

Therefore, Marginal EPS = 0.69/(9/12) =0.924

So the correct answer should be A!
george2006 I was wrong. The interest expense adjustment also needs to account for by a factor 9/12, which will cancel out each other.

So the net effect of partial year oustanding of convertible bonds on marginal EPS is as if the convertible bonds had been oustanding the whole year.

The correct answer is still B.
steved333 It doesn't really matter. The only way for convertible bonds to not be dilutive or to be antidilutive is if the interest savings after tax is somehow the same or larger of a number than the new number of shares that would be outstanding upon conversion. That means that either the company is paying WAY too much in interest, or the convertible feature is not worth the interest because you won't get shit for shares if you do convert!
chamad Interest savings if bonds are converted = 20,000 x 1,000 x 0.055 x 9/12 x (1 - 0.37) = 519,750
No. of additional shares upon conversion = 20,000 x 50 x 9/12= 750,000
Marginal EPS = 519,750/750,000 = 0.69 less than basic EPSthus dilutive
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