Answer:
a) return on equity (ROE) = net income / average shareholders' equity
average shareholders' equity = ($5,605 + $6,151) / 2 = $5,878
ROE for 2015 = $2,634.4 / $5,878 = 44.82%
b) 2. ROE usually increases since the repurchase of shares reduces the denominator (avg. stockholders' equity).
This is simple math, e.g. 1/2 > 1/3, if stockholders' equity decreases, while net income remains the same, ROE will increase.