Heidelberg Cement, one of the world’s largest building materials companies is concerned about preserving the wealth of its stockholders during a cyclical downturn in the building and construction business. The company has a constant dividend payout of €2.5 tied to a target payout ratio of 30%. Heidelberg Cement’s management is preparing a share repurchase recommendation to present to the firm’s board of directors. The following data has been gathered from the last 2 years.

a. How many shares should the company have outstanding in 2018 if its earnings available for common stockholders in that year are €900,000,000 and it pays a dividend of €2.5 given a target payout ratio of 30%?

b. How many shares would the company have to repurchase to have the level of shares outstanding in part a?

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Earnings available to common stockholders Number of shares outstanding Earnings per share Market price per share Price/earnings ratio 2017 805,585,200 198,420,000 4.06 89.89 22.14 2018 900,000,000 198,420,000 4.54 90.00 19.82