Davy owns Davy Writing Supplies $($DWS$).$ DWS has two main divisions: Mechanical Pencils and Fountain Pens. During the previous year, the Mechanical Pencil line generated $$500,000$ in sales revenue and had total traceable costs of $$240,000,$ $$90,000$ of which were fixeci costs. The fountain pens generated a segment margin of $$150,000.$ Common fixed costs totaled $$350,000$ and were arbitrarily allocated across the segments as follows: Mechanical Pencils $-$$$160,000,$ and Fountain Pens $$190,000.$ Davy has shown concern that the Fountain Pen line should be discontinued because it has shown an operating loss for the past couple of years.

If the Fountain Pens are dropped, the company would take advantage of the freed$-$up capacity and would open a new division to replace it$.$ This new division would sell Wood Pencils and is expected to generate $$320,000$ in sales and have a variable cost percentage of $25\%.$ The Wood Pencil division's traceable fixed costs would total $$25,000.$ Additionally, as a side effect of opening the new division, sales in the Mechanical Pencil division are expected to increase by $5\%.$

Assuming each of the scenarios are independent from each other, which of the following statements is correct?

If the Fountain Pens division is dropped and replaced with the Wood Pencil division, the company's operating income would increase by $$45,000.$

The Mechanical Pencil division's contribution margin percentage increases by $5\%$ if the Fountain Pens are dropped and replaced with Wood Pencils.

When comparing the traditional income statement to the segmented contribution margin income statement for DWS$,$ the operating income amounts will differ by the amount of Common Fixed Costs.

DWS$\text{'}$s common fixed costs would decrease by $$190,000$ if the Fountain Pen division is dropped.

Total traceable costs for the Wood Pencil division total $$105,000.$Only one answer can be right