Question

In 2019, Ivanhoe Ltd. issued $52,000 of 7% bonds at par, with each $1,000 bond being convertible into 100 common shares. The company had revenues of $70,200 and expenses of $39,500 for 2020, not including interest and taxes (assume a tax rate of 20%). Throughout 2020, 1,000 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.)

Calculate diluted earnings per share for the year ended December 31, 2020

Assume that the 52 bonds were issued on October 1, 2020 (rather than in 2019), and that none have been converted or redeemed. Calculate diluted earnings per share for the year ended December 31, 2020

Assume the bonds were issued in 2019. Assume that 15 of the 52 bonds were converted on July 1, 2020. Calculate diluted earnings per share for the year ended December 31, 2020

Answer 1

Solution:

Part 1 – Diluted Earnings Per Share for for the year ended December 31, 2020

Diluted Earnings Per Share = Adjusted Income / (Weighted Average No of Common Shares outstanding + Potential Diluted Shares)

Adjusted Income = Earnings After Interest and Taxes – Preferred Dividend + Paid out to Dilutive Securities

Here,

Adjusted Income

	$$
Revenue	$70,200
Less: Expenses	-$39,500
Bond Interest ($52,000*7%)	-$3,640
Income before tax	$27,060
Income taxes @	-$5,412
Net Income	$21,648
Plus: Paid out to Dilutive Securities after tax ($3,640*(1-0.20)	$2,912
Adjusted Income	$24,560

Weighted Average Shares = 1,000 Shares + Potential 100*52 Shares = 6,200 Shares

Diluted Earnings Per Share = Adjusted Income / (Weighted Average No of Common Shares outstanding + Potential Diluted Shares)

= $24,560 / 6,200 Shares

= $3.96

Part 2 - Assume that the 52 bonds were issued on October 1, 2020 (rather than in 2019), and that none have been converted or redeemed. Calculate diluted earnings per share for the year ended December 31, 2020

Calculation of Adjusted Income

	$$
Revenue	$70,200
Less: Expenses	-$39,500
Bond Interest ($52,000*7%*3 months / 12)	-$910
Income before tax	$29,790
Income taxes @	-$5,958
Net Income	$23,832
Plus: Paid out to Dilutive Securities after tax ($910*(1-Tax Rate 0.20)	$728
Adjusted Income	$24,560

Weighted Average Shares = 1,000 Shares + Potential Shares (*52*100*3/12) = 2,300 Shares

Diluted Earnings Per Share = Adjusted Income / (Weighted Average No of Common Shares outstanding + Potential Diluted Shares)

= $24,560 / 2,300 Shares

= $10.68

Part 3 – Assume the bonds were issued in 2019. Assume that 15 of the 52 bonds were converted on July 1, 2020. Calculate diluted earnings per share for the year ended December 31, 2020

Calculation of Adjusted Income

	$$
Revenue	$70,200
Less: Expenses	-$39,500
Bond Interest
(52*$1,000*7%*6/12)	-$1,820
(37*$1,000*7%*6/12)	-$1,295
Income before tax	$27,585
Income taxes @ 20%	-$5,517
Net Income	$22,068
Plus: Paid out to Dilutive Securities after tax ($1,820+1295)*(1-Tax Rate 0.20)	$2,492
Adjusted Income	$24,560

Weighted Average Shares = 1,000 Shares + (1,500*1/2) + 3,700 + (1,500*1/2) Potential Shares = 6,200 Shares

Diluted Earnings Per Share = Adjusted Income / (Weighted Average No of Common Shares outstanding + Potential Diluted Shares)

= $24,560 / 6,200 Shares

= $3.96

Hope the above calculations, working and explanations are clear to you and help you in understanding the concept of question.... please rate my answer...in case any doubt, post a comment and I will try to resolve the doubt ASAP…thank you