Question

In 2023 Blossom Ltd issued $55000 of 8% at par with each $1000 bond being convertible into 100 common shares. the company had revenues of $79800 and expenses of $43300 for 2023 not including interest and tax. Assume a tax rate of 20% throughout 2023, 1800 common shares were outstanding, and none of the bonds were converted or redeemed. (For simplicity, assume that the convertible bonds equity element is not recorded.)

a. Calculate income available to common shareholders.

b. Calculate diluted earnings per share for the year ended December 31, 2023

c. Assume the 55 bonds were issued on October 1, 2022. (rather than in 2021), and that none have been converted or redeemed. Calculate diluted earnings per share for the year ended December 31, 2023.

Answer 1

The income available to common shareholders in 2023 for Blossom Ltd is $25,680, calculated after accounting for expenses, interest on bonds, and taxes. The diluted earnings per share (EPS) for the year is $3.52, considering the potential conversion of bonds into common shares. This calculation remains the same even if the bonds were issued in the previous year, October 1, 2022.

Step-by-step explanation:

Calculating Income Available to Common Shareholders

To calculate the income available to common shareholders, we begin with the total revenues of Blossom Ltd for the year 2023, which are $79,800, and subtract the expenses, amounting to $43,300. However, we must also include the interest paid on the bonds, which is 8% of $55,000. This gives us an interest expense of $4,400. The pre-tax income is thus $79,800 - $43,300 - $4,400 = $32,100. We then apply the tax rate of 20% to the pre-tax income, resulting in $6,420 in taxes. The income available to common shareholders after taxes is therefore $32,100 - $6,420 = $25,680.

Calculating Diluted Earnings Per Share for 2023

To calculate diluted earnings per share (diluted EPS), consider that each $1,000 bond is convertible into 100 common shares, so the 55 bonds could convert into 5,500 shares. Add this to the 1,800 existing common shares, the total potential shares would be 7,300. With income available to common shareholders of $25,680 and potentially 7,300 shares, the diluted EPS is $25,680 / 7,300 = $3.52.

Adjustment for Bonds Issued on October 1, 2022

If the bonds were issued on October 1, 2022, instead of 2023, we would need to adjust the interest expense for 2023. The interest expense would cover three months of 2022 and all of 2023, but since we're only interested in the 2023 fiscal year, we would maintain the $4,400 interest expense for the 12 months of 2023. Consequently, the diluted EPS calculation remains the same with $25,680 income available to common shareholders divided by the potential 7,300 shares, resulting in a diluted EPS of $3.52 for the year ended December 31, 2023.