Question 1
Multiple ChoiceThe following information is available for a company for the current year:
Net income: $1,200,000
Average number of common shares outstanding: 150,000
Convertible Preferred Shares Outstanding:
1,500 shares
$8 dividend per share
Each preferred share is convertible into 4 shares of common stock
Convertible Bonds Outstanding:
$100,000 total face value
6% annual coupon
Each $1,000 bond is convertible into 20 shares of common stock
Corporate tax rate: 30%
What is the company’s diluted earnings per share (EPS) for the year?
Explanation
Step 1: Calculate after-tax bond interest to add back to net income:
Interest = 6% of $100,000 = $6,000
After-tax interest = $6,000 × (1 – 0.30) = $4,200
Step 2: Remove preferred dividends (for basic EPS only)
Preferred dividends = 1,500 × $8 = $12,000
Basic EPS Numerator:
= $1,200,000 – $12,000 = $1,188,000
Diluted EPS Numerator (assume full conversion):
= $1,200,000 + $4,200 (add back bond interest, no preferred dividend deducted)
= $1,204,200
Step 3: Add potential new shares:
Preferred: 1,500 shares × 4 = 6,000 shares
Bonds: $100,000 ÷ $1,000 = 100 bonds × 20 = 2,000 shares
Total new shares = 6,000 + 2,000 = 8,000 shares
Diluted EPS Denominator:
= 150,000 + 8,000 = 158,000 shares
Step 4: Diluted EPS:
\frac{1,204,200}{158,000} = 7.62
Question 2
Multiple ChoiceA company has the following information available for the current year:
Net income: $6,000,000
Outstanding shares at beginning of year: 2,500,000
Stock options outstanding (exercise price: $10): 120,000
Shares issued on 1 March: 360,000
Shares repurchased on 1 October: 150,000
Average market price of common stock during the year: $30
What is the company’s diluted EPS for the year, rounded to the nearest cent?
Explanation
Step 1: Calculate incremental shares from options using the treasury stock method
Proceeds from option exercise = 120,000 × $10 = $1,200,000
Shares repurchased using proceeds = $1,200,000 / $30 = 40,000
Net incremental shares = 120,000 – 40,000 = 80,000
Step 2: Weighted average shares outstanding
Beginning shares: 2,500,000 × 12/12 = 2,500,000
Incremental shares (options): 80,000 × 12/12 = 80,000
Shares issued on 1 March: 360,000 × 10/12 = 300,000
Shares repurchased on 1 October: 150,000 × 3/12 = 37,500 (reduction)
Total weighted average = 2,500,000 + 80,000 + 300,000 – 37,500 = 2,842,500
Step 3: Diluted EPS
= $6,000,000 / 2,842,500 = $2.45
Question 3
Multiple ChoiceFor its fiscal year-end, Veriton Group reported net income of USD180 million and had a weighted average of 45,000,000 common shares outstanding. The company has 1,500,000 convertible preferred shares that pay an annual dividend of USD4 each. Each preferred share is convertible into three common shares. The diluted EPS is closest to:
Explanation
When calculating diluted EPS with convertible preferred shares, assume the preferred dividends are not paid and the conversion occurs at the beginning of the period.
Net income = $180,000,000
Additional shares from conversion = 1,500,000 × 3 = 4,500,000
Adjusted shares = 45,000,000 + 4,500,000 = 49,500,000
Diluted EPS = $180,000,000 / 49,500,000 = $3.64