Interpreting changes in earnings per share. Company A and Company B both start Year 1 with \(\$ 1\) million of shareholders' equity and 100,000 shares of common stock outstanding. During Year 1, both companies earn net income of \(\$ 100,000\), a rate of return of 10 percent on common shareholders' equity at the beginning of Year 1. Company A declares and pays \(\$ 100,000\) of dividends to common shareholders at the end of Year 1, whereas Company B retains all its earnings and declares no dividends. During Year 2, both companies earn net income equal to 10 percent of shareholders' equity at the beginning of Year 2.

a. Compute earnings per share for Company A and for Company B for Year 1 and for Year 2.

b. Compute the rate of growth in earnings per share for Company A and Company B, comparing earnings per share in Year 2 with earnings per share in Year 1.

c. Using the rate of growth in earnings per share as the criterion, which company's management appears to be doing a better job for its shareholders? Comment on this result.