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Chartered Financial Analyst Level 1

Chartered Financial Analyst Level 1

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An analyst gathers the following information about a company for the fiscal year ended 31 December:

  • Net income: $1,200,000
  • Common shares outstanding on 1 January: 1,000,000
  • Common shares issued on 1 April: 100,000
  • Common shares outstanding on 31 December: 1,100,000
  • Face value of convertible bonds outstanding: $2,000,000
  • Coupon rate on convertible bonds: 8%
  • Tax rate: 30% If the bonds are convertible into 200,000 common shares and there are no other potentially dilutive securities outstanding, the company's diluted earnings per share (EPS) is closest to:

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Explanation:

Explanation

Basic EPS Calculation:

  • Net income: $1,200,000 (no preferred dividends).
  • Weighted average shares outstanding:
    • 1,000,000 shares for 3 months (January to March): 1,000,000 × (3/12) = 250,000.
    • 1,100,000 shares for 9 months (April to December): 1,100,000 × (9/12) = 825,000.
    • Total weighted average shares: 250,000 + 825,000 = 1,075,000.
  • Basic EPS: 1,200,000/1,075,000=1,200,000 / 1,075,000 = 1,200,000/1,075,000=1.12.

Diluted EPS Calculation:

  • After-tax interest on convertible bonds: 2,000,000×82,000,000 × 8% × (1 - 30%) = 2,000,000×8112,000.
  • Adjusted net income: 1,200,000+1,200,000 + 1,200,000+112,000 = $1,312,000.
  • Additional shares from conversion: 200,000.
  • Total diluted shares: 1,075,000 + 200,000 = 1,275,000.
  • Diluted EPS: 1,312,000/1,275,000=1,312,000 / 1,275,000 = 1,312,000/1,275,000=1.029, rounded to $1.03.

Why not A or C?

  • Option A incorrectly uses the period-end shares (1,100,000) plus conversion shares (200,000) without weighting, leading to an incorrect denominator.
  • Option C mistakenly adds the pre-tax interest ($160,000) to net income instead of the after-tax interest, resulting in an inflated numerator.
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