Calculate the diluted earnings per share (EPS) for Artcraft, Inc. given the following information: * Net income: $30,000 * Common stock: 5,000 shares * Convertible preferred stock... Calculate the diluted earnings per share (EPS) for Artcraft, Inc. given the following information: * Net income: $30,000 * Common stock: 5,000 shares * Convertible preferred stock: 500 shares, 8% dividend, $90 par, convertible to 4 shares of common stock each * Convertible bonds: $60,000 face value, 6% coupon, each bond convertible to 110 shares of common stock * Effective tax rate: 40% Read more

Steps to Solve

1. Calculate income available to common shareholders. Subtract preferred dividends from net income to find the income available to common shareholders. $ \text{Income available to common shareholders} = \text{Net income} - \text{Preferred dividends} $ $ \text{Income available to common shareholders} = $3,000,000 - $600,000 = $2,400,000 $

2. Calculate the weighted average number of common shares outstanding. The weighted average number of common shares outstanding is given as 1,000,000.

3. Determine the impact of convertible preferred stock. Calculate the per-share dividend of the preferred stock. $ \text{Preferred dividend per share} = \frac{\text{Total preferred dividends}}{\text{Number of preferred shares}} = \frac{$600,000}{60,000} = $10 $ Calculate the number of common shares each preferred share converts into. $ \text{Conversion ratio} = \frac{\text{Par value}}{\text{Conversion price}}= \frac{$100}{$20} = 5 $ If converted, the preferred stock would increase the number of common shares by $ 60,000 \times 5 = 300,000 $ shares. Assess the impact on diluted EPS. If the preferred stock is converted, the preferred dividends would not be subtracted from net income. We need to see if this conversion is dilutive.

4. Determine the impact of convertible bonds. Calculate the after-tax interest expense that would not be paid if the bonds were converted. $ \text{Interest expense} = \text{Bond par value} \times \text{Interest rate} = $1,000,000 \times 6% = $60,000 $ $ \text{After-tax interest expense} = \text{Interest expense} \times (1 - \text{Tax rate}) = $60,000 \times (1 - 30%) = $60,000 \times 0.7 = $42,000 $ Calculate the number of common shares the bonds convert into. $ \text{Number of shares from bonds} = \frac{\text{Bond par value}}{\text{Conversion price}} = \frac{$1,000,000}{$25} = 40,000 $

5. Calculate diluted EPS. First check preferred stock conversion: Calculate EPS if preferred stock is converted: $ \text{EPS with preferred conversion} = \frac{\text{Net Income}}{\text{Weighted average shares} + \text{Shares from preferred conversion}} = \frac{$3,000,000}{1,000,000 + 300,000} = \frac{$3,000,000}{1,300,000} = $2.31 $ Calculate Basic EPS (without considering bond conversion yet, but after subtracting preferred dividends). $ \text{Basic EPS} = \frac{\text{Net income} - \text{Preferred dividends}}{\text{Weighted average shares}} = \frac{$3,000,000 - $600,000}{1,000,000} = \frac{$2,400,000}{1,000,000} = $2.40 $ Since $2.31 < $2.40, the preferred stock conversion is dilutive.

Next, check bond conversion, we are examining the impact on the EPS after preferred stock conversion. $ \text{Diluted EPS} = \frac{\text{Net Income} + \text{After-tax interest}}{\text{Weighted average shares} + \text{Shares from preferred conversion} + \text{Shares from bond conversion}} $ $ \text{Diluted EPS} = \frac{$3,000,000 + $42,000}{1,000,000 + 300,000 + 40,000} = \frac{$3,042,000}{1,340,000} = $2.27 $ Because $2.27 < $2.31, this conversion is dilutive and should be included. So, the diluted EPS is $2.27.