Last year, Candle Corp had $250 of assets, $300 of sales, $20 of net income, and a liability-to-asset ratio of 40%. Now suppose the new CFO convinces the president to increase the liability-to-asset ratio to 50%. Sales and total assets will not be affected, but interest expenses would increase. However, the CFO believes that better cost controls would be sufficient to offset the higher interest expense and thus keep net income unchanged. By how much would the change in the capital structure improve the ROE

It is given that the liability-to-asset ratio is 40%. It means that the remaining 60% of the assets are financed through Equity. The worth of assets is $250. When we multiply it with the weightage of Equity, we will get $150. The figure for Net Income is given, simply put the values in ROE formula and you will get 13% (20/150).

Now to check the impact on ROE by changing capital structure, you have to change the denominator figure. To calculate it, multiply $250 which is the worth of assets with the new weightage of Equity which is 50%. The new Equity is 125. Since the denominator value has decreased from 150 to 125, the financial metric ROE will improve by 3%.

I hope I made it very much clear. If you have any further queries, feel free to ask. Thanks!