$3).$ Problem $4-32$ Changes in Cost Structure; Break$-$Even Analysis; Target Profit $[$LO$5,$ LO$6,$ LO$8]20$ marks

Alliance Enterprises is considering extensively modifying their manufacturing equipment. The modifications will result in less wastage of materials, which will reduce variable manufacturing costs and introduce changes to the production process that will improve product quality. This will allow Alliance to increase the selling price of the product. Annual fixed costs are expected to increase to $$750,000$ if the modifications are made. Expected fixed and variable costs as well as the selling prices are shown below:

Cost Item Existing Equipment Modified Equipment

Selling price per unit $ $36$ $ $40$

Variable cost per unit $2825$

Fixed costs $330,000750,000$

Required:

$1.$ Determine Alliance Enterprises$$ break$-$even point in units with the existing equipment and with the modified equipment. $4$ marks

$2.$ Determine the sales level in units at which the modified equipment will achieve a $25\%$ target profit$-$to$-$sales ratio $($ignore taxes$).4$ marks

$3.$ Determine the sales level in units at which the modified equipment will achieve $$63,000$ in after$-$tax operating income. Assume a tax rate of $30\%.4$ marks

$4.$ Determine the sales level at which profits will be the same for either the existing or modified equipment. $8$ marks