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How will dilutive securities affect earnings per share (EPS) when determining diluted earnings per share?

A) Increase EPS.

B) Decrease EPS.

C) Either decrease or increase EPS depending upon if the security is dilutive or antidilutive.

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Dilutive securities such as convertibles and options are found in a complex capital structure and always decrease EPS. Convertibles and options may also be antidilutive, which will increase EPS hence the name antidilutive. The only way to know if a security is dilutive or antidilutive is to compare the basic EPS to diluted EPS. If the diluted EPS is higher than the basic EPS then the security is antidilutive and should not be included when determining diluted EPS.

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In calculating the numerator for diluted Earnings Per Share, the interest on convertible debt is:

A) subtracted from earnings available to common shareholders after an adjustment for taxes.

B) added to earnings available to common shareholders.

C) added to earnings available to common shareholders after an adjustment for taxes.

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Formula = Diluted EPS = [(Net income − Preferred dividends) + Convertible preferred dividends + (Convertible debt interest)(1 − t)] / [(Weighted average shares) + (Shares from conversion of conv. pfd shares) + (Shares from conversion of conv. debt) + (Shares issuable from stock options)]

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In calculating the numerator for diluted earnings per share, the dividends on convertible preferred stock are:

A) added to earnings available to common shareholders with an adjustment for taxes.

B) added to earnings available to common shareholders without an adjustment for taxes.

C) subtracted from earnings available to common shareholders without an adjustment for taxes.

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Diluted EPS = [(Net income − Preferred dividends) + Convertible preferred dividends + (Convertible debt interest)(1 − t)] / [(Weighted average shares) + (Shares from conversion of conv. pfd shares) + (Shares from conversion of conv. debt) + (Shares issuable from stock options)]

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An analyst has gathered the following information about Barnstabur, Inc., for the year:

• Reported net income of $30,000.
• 5,000 shares of common stock and 2,000 shares of 8%, $90 par preferred stock outstanding during the whole year.
• During the year, Barnstabur issued at par, $60,000 of 6.0% convertible bonds, with each of the 60 bonds convertible into 110 shares of the Barnstabur common stock.

If Barnstabur’s effective tax rate is 40%, what will Barnstabur report for diluted earnings per share (EPS)?

A) $1.53.

B) $2.36.

C) $1.66.

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Diluted EPS = adjusted earnings after conversion (EAC) / weighted average plus potential common shares outstanding.
Step 1: Calculate Adjusted EAC

adjusted EAC:		net income - preferred dividends
	+	after-tax interest on convertible debt
	=	adjusted earnings available for common shares

preferred dividends = (0.08)(90)(2,000) = 14,400
convertible debt interest = (60,000)(0.06)(1 – 0.40) = 2,160
adjusted EAC = (30,000 – 14,400 + 2,160) = $17,760

Step 2: Calculate Weighted average plus potential common shares outstanding.

weighted average common shares			=	5,000
shares from conversion of convertible bonds	=	(60 × 110)	=	6,600
weighted ave. plus potential common shares outst.			=	11,600

Step 3: Calculate Diluted EPS

Diluted EPS = 17,760 / 11,600 = $1.53.

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Selected information from Baltimore Corp’s financial activities in the year 2004 is as follows:

• 
  Net income was $4,200,000 .
• 
  750,000 shares of common stock were outstanding on January 1.
• 
  The average market price per share was $50 in 2004.
• 
  Dividends were paid in 2004.

10,000 warrants, which allowed the holder to purchase 10 shares of common stock for each warrant held at a price of $40 per common share, were outstanding the entire year.  
Baltimore’s diluted earnings per share (Diluted EPS) for 2004 is closest to:

A) $5.60.

B) $4.94.

C) $5.45.

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Baltimore’s basic earnings per share (EPS) (net income / weighted average shares outstanding) for 2004 was $4,200,000 / 750,000 = $5.60.  
To calculate diluted EPS, we use the treasury stock method to account for the warrants:

• Number of common shares created if options are exercised = 10,000 × 10 = 100,000
• Cash inflow if warrants are exercised = $40 × 100,000 = $4,000,000
• Shares purchased with these funds = $4,000,000 / 50 = 80,000
• Net increase in shares outstanding = 100,000 – 80,000 = 20,000

Diluted EPS = $4,200,000 / (750,000 + 20,000) = $5.45.

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The Allen Corporation had 100,000 shares of common stock outstanding at the beginning of the year. Allen issued 30,000 shares of common May 1. On July 1, the company issued a 10% stock dividend. On September 1, Allen issued 1,000, 10% bonds convertible into 21 shares of stock each. What is the weighted average number of shares to be used in computing basic and diluted earnings per share (EPS), assuming the convertible bonds are dilutive?

Basic Shares

Diluted Shares

A) 132,000 139,000

B) 130,000 132,000

C) 132,000 146,000

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Calculating Basic Shares:
Jan 1 100,000 shares outstanding
May 1 30,000 shares issued
July 1 10% stock dividend issued
The 10% stock dividend is retroactive therefore:
110,000 shares × 12 months = 1,320,000
33,000 shares × 8 months = 264,000
         Total share-month = 1,584,000
         Average shares = (1,584,000 / 12) = 132,000
Calculating diluted shares:
(1,000 bonds) × (21 shares each) × (4 months) = 84,000 total share-month
                                                 84,000 / 12 = 7,000 Average shares
Total diluted shares = 7,000 (from convertible bonds) + 132,000 (from stock) = 139,000

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Quad Associates, Inc.’s net income for 2005 was $892,000 with 400,000 shares outstanding. The tax rate was 40 percent. Quad had 2,000 six percent $1,000 par value convertible bonds that were issued in 2004. Each bond was convertible into 40 shares of common stock. Quad, Inc.’s diluted earnings per share (Diluted EPS) for 2005 was closest to:

A) $2.01.

B) $2.23.

C) $2.41.

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Quad’s basic EPS (net income / weighted average common shares outstanding) was $892,000 / 400,000 = $2.23.
Diluted EPS is calculated under the assumption that the convertible bonds are converted into common stock, the bond interest net of tax is restored to net income, and the additional common shares are added to the denominator of the equation. Quad’s diluted EPS was [$892,000 + (2,000 × $1,000 × 0.06)(1 − 0.40)] / [400,000 + (2,000 × 40)] = $2.01. Since diluted EPS is less than basic EPS, we know that the bonds are dilutive and should be considered in calculating diluted EPS.

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Kendall Company’s net income for 20X4 is $830,000 with 200,000 shares outstanding. Kendall has 1,000 6% convertible bonds (each bond $1,000 face value and convertible into 20 common shares) outstanding for the entire year. Kendall’s tax rate is 40%. What is Kendall Company’s diluted earnings per share for 20X4?

A) $4.15.

B) $3.94.

C) $3.77.

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Kendall’s basic EPS is $830,000 / 200,000 = $4.15. To compute diluted EPS, bond interest paid net of taxes is added to net income, and the number of shares that would be issued in the conversion is added to the denominator. Kendall’s diluted EPS = [$830,000 + (1,000 × $1,000 × 0.06) × (1 – 0.4)] / (200,000 + 20,000) = $3.94. Since diluted EPS is less than basic EPS, we know that the bonds are dilutive and should be considered in calculating diluted EPS.

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Selected information from Caledonia, Inc.’s financial activities in the year 20X6 is as follows:

• Net income = $460,000.
• 2,300,000 shares of common stock were outstanding on January 1.
• The average market price per share was $2 and the year-end stock price was $1.50.
• 1,000 shares of 8%, $1,000 par value preferred shares were outstanding on January 1. Preferred dividends were paid in 20X6.
• 10,000 warrants, each of which allows the holder to purchase 100 shares of common stock at an exercise price of $1.50 per common share, were outstanding the entire year.

Caledonia’s diluted earnings per share for 20X6 are closest to:

A) $0.165.

B) $0.180.

C) $0.15.

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Caledonia’s basic EPS = (net income − preferred stock dividends) / (weighted average common shares outstanding)
= [$460,000 − ($1,000 × 1,000 × 0.08)] / 2,300,000 = $0.17. Using the treasury stock method, if the warrants were exercised, cash inflow would be 10,000 × 100 × $1.50 = $1,500,000. The number of Caledonia shares that could be purchased with the inflow, using the average share price, is $1,500,000 / $2 = 750,000. The net increase in common shares outstanding would have been 1,000,000 − 750,000 = 250,000.
Diluted EPS = $380,000 / (2,300,000 + 250,000) = $0.15.

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Young Distributors, Inc. issued convertible bonds two years ago, and those bonds are the only potentially dilutive security Young has issued. In 20X5, Young’s basic earnings per share (EPS) and diluted EPS were identical, but in 20X4 they were different. Which of the following factors is least likely to explain the difference between basic and diluted EPS? The:

A) average market price of Young common stock increased in 20X5.

B) bonds were redeemed by Young Distributors at the beginning of 2005.

C) bonds were antidilutive in 2005 but not in 2004.

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Average stock price is not a factor in determining whether convertible bonds are dilutive or antidilutive.
If Young redeemed the bonds, they would have no potentially dilutive securities outstanding in 20X5 and diluted EPS, if the company reported it, would equal basic EPS. Basic and diluted EPS would also be equal in 20X5 if the bonds were antidilutive in that year.