Diluted EPS Calculation | CFA Level 1 Exam Preparation

Diluted EPS Calculation

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Question

New Gestalt, Inc., a software firm had a net income of 1.7 million last year. It has 200,000 common shares and 300,000 convertible bonds with face value of 100 outstanding. The convertible bonds carry a coupon of 4% and can be converted one-for-one. The average stock price last year was 39 and the maximum price was 57. The effective interest rate on the convertible debt is 8%. New Gestalt issued 100,000 preferred shares with face value 100 and a coupon of 5% on March

31st of last year. Assume the convertible bonds are dilutive and that New Gestalt faces a 30% tax rate. Given the above, the number of shares used in Diluted

EPS equals ________.

Answers

Explanations

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A. B. C. D.

B

With dilution, there are 300,000 additional shares from the convertible bonds. Preferred equity does not count. Therefore, the number of shares used in Diluted

EPS equals 200,000 + 300,000 = 500,000.

To calculate the diluted earnings per share (EPS) for New Gestalt, we need to consider the impact of convertible bonds and preferred shares. Let's break down the information provided and calculate the diluted EPS step by step:

  1. Calculate the impact of convertible bonds: The convertible bonds can be converted into common shares on a one-for-one basis. Since there are 300,000 convertible bonds outstanding, this means that there could be an additional 300,000 common shares issued if all the bonds are converted.

  2. Calculate the weighted average number of common shares outstanding: The common shares outstanding include the initial 200,000 shares plus any additional shares from the conversion of the convertible bonds. Therefore, the weighted average number of common shares is 200,000 + 300,000 = 500,000 shares.

  3. Calculate the impact of the preferred shares: The preferred shares do not directly impact the diluted EPS because they do not have the potential to be converted into common shares.

  4. Calculate the diluted EPS: Diluted EPS is calculated by dividing the net income (adjusted for preferred dividends) by the weighted average number of common shares outstanding. However, before calculating the diluted EPS, we need to adjust the net income for the impact of the convertible debt and the tax rate.

    i. Calculate the interest expense on the convertible debt: The convertible bonds have a face value of $100 and carry a coupon rate of 4%. Therefore, the annual interest expense on the convertible debt is $100,000 (300,000 bonds * $100 * 4%).

    ii. Calculate the tax benefit from the interest expense: The tax rate is given as 30%. Therefore, the tax benefit from the interest expense is $30,000 (30% * $100,000).

    iii. Adjust the net income for the interest expense and tax benefit: The net income of $1.7 million needs to be reduced by the interest expense of $100,000 and increased by the tax benefit of $30,000. Adjusted net income = $1.7 million - $100,000 + $30,000 = $1.53 million.

    iv. Calculate the diluted EPS: Diluted EPS = Adjusted net income / Weighted average number of common shares outstanding Diluted EPS = $1.53 million / 500,000 shares = $3.06 per share

Therefore, the correct answer is B. 500,000 shares.

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