Question

In this current year Company has produced 300 widgets. Over the next 2 years production will increase by 25% more of the previous year. With each increase in production cost/unit will decrease 10% less of the previous year. Company’s present profit margin is 30%. Present cost/unit is $24. If price remains constant how many units will have to be sold in Year 3 of production to break even?

Answer 1

Particulars	Current year	Year 1	Year 2
No of Units Produced	300.00	375.00	468.75
Cost per unit	$           24.00	$    21.60	$    19.44

No of units that will be produced in year 1 will be calculated as under

= No of units produced in current year + 25% of No of units produced in current year

= 300+25% of 300

= 300+75=375

similarly No of units that will be produced in year 2 will be calculated as under

= No of units produced in year 1 + 25% of No of units produced in year 1

= 375+25% of 375

= 375+93.75=468.75 that shall be rounded off to next one i.e 469 units.

further calculation of decrease in cost will be as under:

Cost for year 1 = Cost of current year - 10% of cost of current year

Cost for year 1 =24 - (24*10%)

Cost for year 1 = $ 21.60

Similarly cost for year 2 will be calculated as under

Cost for year 2 = Cost of year 1 - 10% of cost of year 2

Cost for year 2 =21.60 - (21.60*10%)

Cost for year 2 = $19.44

Now as given in the question the profit margin is 30%

therefore cost will be 70%

therefore total sales price for current year = cost price/70*100

Sales Price per unit for current year = $34.29

so total sales price, cost and profit per unit for the three years will be as under

Particulars	Current year i.e Year 1	Year 2	Year 3
Sales Price per unit	$           34.29	$    34.29	$    34.29
Cost per unit	$           24.00	$    21.60	$    19.44
Profit per unit	$           10.29	$    12.69	$    14.85

NOW in year three total costs will be 469 * 19.44 = 9117.36

Formula for breakeven = Fixed costs/Contribution margin

Breakeven = 9117.36/14.85

therefore breakeven will happen at 614.14 units that is at 615 units(rounded off to next one).

it means that he breakeven will happen if 615 units are sold in year 3.