On January 2, 2017, Delila Inc.issued at par $10,000 6% bonds convertible into 1,000 of their common shares.No bonds were converted during 2017.Throughout 2017, Delila had 1,000 common shares outstanding (no preferred shares issued).Delila's 2017 net income was $6,000, and their income tax rate is 30%.No potentially dilutive securities other than the convertible bonds were outstanding during 2017.Delila diluted earnings per share for 2017 would be

Question

Quizplus · Accepted Answer

To calculate diluted earnings per share, we need to assume that the convertible bonds are converted into common shares. In this case, since each bond is convertible into 1,000 common shares, we would have 10,000,000 (10,000 bonds x 1,000 shares per bond) additional common shares outstanding if all bonds were converted.

To calculate diluted earnings per share, we need to divide the net income by the total number of outstanding shares (common shares plus potentially dilutive securities). In this case, the total number of outstanding shares would be 11,000,000 (1,000,000 common shares + 10,000,000 shares if all bonds were converted).

So, diluted earnings per share would be:

Diluted earnings per share = Net income / Total number of outstanding shares
Diluted earnings per share = $6,000 / 11,000,000
Diluted earnings per share = $0.000545

To convert diluted earnings per share back to a per-share basis, we need to multiply by the conversion factor, which is the ratio of the current number of shares to the new number of shares if all bonds were converted. In this case, the conversion factor is:

Conversion factor = Current number of shares / (Current number of shares + New shares from conversion of bonds)
Conversion factor = 1,000,000 / (1,000,000 + 10,000,000)
Conversion factor = 0.0909

So, diluted earnings per share (on a per-share basis) would be:

Diluted earnings per share = Diluted earnings per share x Conversion factor
Diluted earnings per share = $0.000545 x 0.0909
Diluted earnings per share = $0.0000496

To convert diluted earnings per share back to a per-bond basis, we need to multiply by the conversion ratio, which is the number of shares into which each bond is convertible. In this case, the conversion ratio is:

Conversion ratio = 1,000 shares per bond

So, diluted earnings per share (on a per-bond basis) would be:

Diluted earnings per share (per-bond basis) = Diluted earnings per share / Conversion ratio
Diluted earnings per share (per-bond basis) = $0.0000496 / 1,000
Diluted earnings per share (per-bond basis) = $0.0000000496

Finally, we need to multiply diluted earnings per share (per-bond basis) by 1,000 to get diluted earnings per share (per $1,000 bond). So, diluted earnings per share (per $1,000 bond) would be:

Diluted earnings per share (per $1,000 bond) = Diluted earnings per share (per-bond basis) x 1,000
Diluted earnings per share (per $1,000 bond) = $0.0000000496 x 1,000
Diluted earnings per share (per $1,000 bond) = $0.0000496

Finally, to convert diluted earnings per share (per $1,000 bond) to dollars per share, we need to divide by the bond's conversion price, which is $10,000 / 1,000 = $10. So:

Diluted earnings per share = Diluted earnings per share (per $1,000 bond) / Conversion price
Diluted earnings per share = $0.0000496 / $10
Diluted earnings per share = $0.00000496

Finally, we need to convert diluted earnings per share to a per-share basis by multiplying by the bond's conversion ratio:

Diluted earnings per share = Diluted earnings per share x Conversion ratio
Diluted earnings per share = $0.00000496 x 1,000
Diluted earnings per share = $0.00496

So, diluted earnings per share would be $0.00496, or $4.96 per share. Since the question asks for diluted earnings per share in dollars, we would choose option B).