::
Ok, I think the answer is 0.75.
simply_complex, your DTL formula is slightly incorrect.
DTL is actually % change in EPS / % change in sales.
Prior to the transaction, we had EPS of $1.56 on 500,000 shares. Backing out earnings using these two figures give us earnings of $780,000.
The question states that after the transaction, net income (or earnings) increased by 10%. This means that earnings now are at $858,000. The number of outstanding shares have also decreased from 500,000 to 400,000. As such, EPS after transaction is $858,000 / 400,000 = 2.145.
% change in EPS = (2.145 – 1.56) / 1.56 = 37.5%
% change in sales = stated in question as 50%
Therefore, DTL = 0.375 / 0.5 = 0.75