CFA Level IFinancial Statement AnalysisHard
A company reports net income of $1,000,000 and pays preferred dividends of $50,000. It has 500,000 common shares outstanding throughout the year. The company also has $500,000 par value of 6% convertible bonds outstanding, convertible into 50,000 common shares. The company's effective tax rate is 40%. What is diluted EPS?
- A$2.00
- B$1.94
- C$1.90
- D$1.76
Show answer & explanationAnswer & explanation
Correct answer: D. $1.76
Basic EPS = (NI − Preferred dividends)/Shares = ($1,000,000 − $50,000)/500,000 = $1.90. For diluted EPS, add back after-tax interest saved if bonds convert: $500,000 × 6% × (1−0.40) = $18,000. Diluted EPS = ($950,000 + $18,000)/(500,000 + 50,000) = $968,000/550,000 = $1.76. Since $1.76 < $1.90, the convertible bonds are dilutive and diluted EPS is used.
Why the other options are wrong
- A. This overstates EPS by not adding the extra convertible shares to the denominator.
- B. This results from using pre-tax rather than after-tax interest in the numerator.
- C. This is basic EPS, ignoring the dilutive effect of convertible bonds.
Diluted EPS (If-Converted Method)
Diluted EPS reflects the potential dilution from convertible securities using the if-converted method: adding back after-tax interest saved to net income and adding the as-if-converted shares to the denominator.
- Numerator adds back interest expense × (1 − tax rate)
- Denominator adds shares issuable upon conversion
- Security is dilutive only if it reduces EPS below basic EPS
Memory trick: If it converts, add back interest after tax and add the new shares.