W11 EPS Excerise

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Problems for Chapter 17 Example 1: Calculation of weighted number of outstanding common shares Date Share Changes Shares Outstanding January 1 Beginning balance 90,000 April 1 30,000 shares issued 120,000 July 1 39,000 shares repurchased 81,000 November 1 60,000 shares issued 141,000 December 31 Year end balance 141,000 Share issuance/repurchase: Adjust for the portion of the year affected Stock dividends, stock splits: Assume that this occurred on the 1st day of the year Solution Dates Outstanding Shares Outstanding Fraction/Weighted Shares Portion of the year Outstanding Weighted Shares Jan. 1-April 1 90,000 3/12 22,500 April 1-July 1 120,000 3/12 30,000 July 1-Nov. 1 81,000 4/12 27,000 Nov. 1- Dec.31 141,000 2/12 23,500 Weighted Total 103,000
Example 2: the weighted number of common shares when stock dividend issued during the year Baiye Limited January 1: 100,000 shares outstanding March 1: Issued 20,000 shares June 1: 50% Stock dividend (60,000 additional shares issued) November 1: Issued 30,000 shares December 31: Ending Balance = 210,000 shares outstanding Stock splits and stock dividends require restatement of the weighted average number of shares outstanding from the beginning of the year. By restating the number, valid comparisons of earnings per share can be made between periods before and after the stock split or stock dividend Share issuance/repurchase: Adjust for the portion of the year affected Dates Outstanding Shares Outstanding Fraction/Weighted Shares Jan. 1-March 1 150,000 2/12 25,000 March 1-Nov. 1 180,000 8/12 120,000 Nov. 1 – Dec. 31 210,000 2/12 35,000 Total weighted shares 180,000
Example 3 Convertible Bonds and preferred shares (complex capital structure) On January 1, 2020, Sharif Limited issued $2 million of face value, 10-year, 6% bonds at par. Each $1,000 bond is convertible into 16 shares of common stock. Sharif’s net income in 2020 was $300,000 and its tax rate was 40%. The company had 100,000 common shares outstanding throughout 2020. None of the bonds were exercised in 2020. Required: a) Calculate diluted earnings per share for the year ended December 31, 2020. b) Calculate diluted earnings per share for 2020, assuming the same facts as above, except that $1 million of 6% convertible preferred shares was issued instead of the bonds. Each $100 preferred share is convertible into five common shares. Solution Basic EPS = 300,000/100,000=$3/per share a. If converted at the beginning of the year, the interest expense of 2,000,000*6% =120,000 can be saved. That means the net income after tax is increased by 120,000*60% = 72,000. The number of converted shares 2,000,000/1,000*165=32,000. Ratio is 72,000/30,000=2.6, which is smaller than 3 (it is dilutive) Diluted EPS = (300,000+72,000)/(100,000+32,000)=2.82 b. 1 million of 6% convertible preferred shares. Preferred Share Dividend is: 1,000,000*6% = 60,000 No of common shares could be converted: 1,000,000/100*5=50,000 Ratio 60,000/50,000=1.2 (dilutive) Basic EPS: (300,000-60,000)/100,000 = 2.4 (the preferred dividend should be deducted from income to common shares) Diluted EPS = (300,000-60,000+60,000)/(100,000+50,000)=2.0
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Example 4: EPS with Options (complex capital structure) Viens Corp.’s net income for 2019 is $90,000. The only potentially dilutive securities outstanding were 1,000 call options issued during 2018, with each option being exercisable for one share at $14. None has been exercised, and 50,000 common shares were outstanding during 2019. The average market price of the company’s shares during 2019 was $20. Required: a) Calculate diluted earnings per share for the year ended December 31, 2019. b) Assuming that the 1,000 call options were instead issued on October 1, 2019, calculated diluted EPS for the year ended Dec 31, 2019. The average market price during the last three months of 2019 was $20. c) How would you answers for (a) if, in addition to the information for part (a), the company issued 1,000 put options with an exercise price of 1) $10? 2) $25? Solution: NI: 90,000 Common Shares: 50,000 a. Basic EPS = 90,000/50,000=1.8 Potential number of shares call option: 1,000 The number of shares increase (purchased using the proceed) should be: 14*1000/20=700 (14 is the exercise price and the proceeds are 14*1000, purchase price is the market price: 20). Diluted EPS = 90,000/(50,000+300)=1.789 b. 300*3/12=75 (3/12 is the portion of the year the call option exists) Diluted EPS= 90,000/(50000+75)=1.7973 c. Sell at 10 (the option is not in money, no dilutive effect) Sell at 25. The total cash payout is 1000*25= 25,000
Need to issue N=25,000/20=1250 shares to raise the same amount of money. The net change of shares is 1250-1000=250. Diluted EPS = 90,000/(50,000+300+250)=1.78