Question

The annual direct production cost for a plant operation at 70% capacity are $280000 while the sum of the annual fixed charges, overhead costs, and general expenses is $200000. What is the break-even pint in the unit of production per year if total annual sales are $560000 and the product sales at $40/unit? What were the annual gross earnings and the net profit for this plant at 100% capacity in year 1974 when corporate income tax required a 22% normal tax on the gross earnings plus a 26% surtax on gross earnings above $25000?

Answer 1

Now, let’s assume “x” be the total production and “$40” be the per unit price and total sales revenue is “$560,000”, => 40*x = $560,000, => x = $560,000/40 = 14,000 units. So, the total production is given by “x=14,000 units”.

Now, the production cost is “$280,000” and “w” be the per unit production cost, => the following relation must hold, => w*14,000 = 280,000, => w = $20 per unit. Now, let’s assume that “y unit” be the break even level of production, => here total revenue must be equal to “total cost”.

=> 40*y = FC + 20*y, => (40 – 20)*y = FC, => y = FC/20 = $200,000/20 = 10,000 units. So, the break even level of sales is given by “10,000 units”.

Now, with the 70% the total sales is given by “$560,000”, => at the 100% capacity the total sales is given by, “$560,000/0.7” and production cost is “$280,000/0.7” but the “fixed cost” will be same as before.

=> the gross earing is given by.

=> $560,000/0.7 - $200,000 - $280,000/0.7 = $800,000 - $200,000 - $400,000 = $200,000.

The Net profit is given by.

=> $200,000 – 0.22*$200,000 – 0.26*($200,000-$25,000)

=> $200,000 – $44,000 – $45,500 = $110,500, be the net profit after the tax.