Question

You are given this data for a company for two successive periods. Period 6 Period 7 Materials $300,000 $360,000 Labour $212,000 $247,000 Overheads $418,000 $453,000 10,000 units Production level 12,000 units All production is sold for $100 per unit. Estimate the fixed costs and break-even point. It is now proposed to introduce a machine whereby fixed costs will rise by $116,000 and variable costs will fall by $10 per unit. Estimate: (a) the new break-even point, and (b) the sales necessary to maintain profits at $140,000, using the new machine.

Please explain how this question is to be answered. Basic formula and working out with steps.

Answer 1

Answer:-

Calculation of Fix cost portion in labour

Let fix cost part be x in Labour Cost and Variable cost per unit be y

So,

(x + y * 10000) = 212000               from Period 6

and (x + y * 12000) = 247000        from Period 7

Comparing bothe equations we got:-

Fix Cost (x) = $ 280000

Variable cost Labour = $ 17.5 p. u.

Similarly we calculated Variable Overheads = $ 17.5 p.u.

Total Variable Cost = $ 35 p.u. + $ 30 p.u.(Material)

Contribution = Sales - VC

                     = 100 - 65

                     = 35

Calculation of BEP

Break Even = FC/ Contribution p.u.

                    = 280000/ 35

                    = 4307 Units

Answer to part a)

New Fix Cost = 280000+116000

                      = $ 396000

New Variable Cost = 65 - 10 = 55

BEP = Fix Cost / Contribution p.u.

        = 396000/55

        = 7200 Units

Answer to part b)

Sales to earn profit of $ 140000 = (Fix Cost + Desired Profit)/ PV Ratio

                                                   = (396000 + 140000)/ 0.45

                                                   = $ 1191111 or 11911 units

Working Note:-

PV Ratio = Contribution/ Sales

               = (100-55)/100

               = 45%