Question

P = $100 VC = $60 TFC = $250,000 1.

Calculate the current break-even point in both units and dollars. A production manager is trying to control costs but is faced with the following trade-offs under four different situations:

a. Total fixed costs are reduced by 15%, but unit variable costs will rise by 5%.

b. Unit variable costs are reduced by 10%, but fixed costs will rise by 5%

c. Total fixed costs are reduced by 20%, but unit variable costs will rise by 10%.

d. Unit variable costs are reduced by 15%, but fixed costs will rise by 15%.

Determine the break-even in units and dollars for each different situation and then specify which situation (a, b, c or d) would you recommend she pursue?

Answer 1

1)

Break-even point = Total Fixed Cost / (Price-Variable Cost) = $250,000/($100 - $60)

= $250,000/$40 = 6,250 units

Break-even point in dollar value = no. of units * price per unit = 6250*$100 = $625,000

a.

Total fixed costs reduce by 15% and variable costs rise by 5%

new total fixed cost = original total fixed cost * (1-15%) = $250,000*0.85 = $212,500

new variable cost = original variable cost * (1+5%) = $60*1.05 = $63

new break-even point = $212,500/($100-$63) = $212,500/$37 = 5743.243 units

new break-even point in dollar value = no. of units * price per unit = 5743.243*$100 = $574,324.324

b.

Total fixed rise by 5% and variable costs reduce by 10%

new total fixed cost = original total fixed cost * (1+5%) = $250,000*1.05 = $262,500

new variable cost = original variable cost * (1-10%) = $60*0.9 = $54

new break-even point = $262,500/($100-$54) = $262,500/$46 = 5706.522 units

new break-even point in dollar value = no. of units * price per unit = 5706.522*$100 = $570,652.174

c.

Total fixed reduce by 20% and variable costs rise by 10%

new total fixed cost = original total fixed cost * (1-20%) = $250,000*0.8 = $200,000

new variable cost = original variable cost * (1+10%) = $60*1.1 = $66

new break-even point = $200,000/($100-$66) = $200,000/$34 = 5882.353 units

new break-even point in dollar value = no. of units * price per unit = 5882.353*$100 = $588,235.294

d.

Total fixed rise by 15% and variable costs reduce by 15%

new total fixed cost = original total fixed cost * (1+15%) = $250,000*1.15 = $287,500

new variable cost = original variable cost * (1-15%) = $60*0.85 = $51

new break-even point = $287,500/($100-$51) = $287,500/$49 = 5867.347​​​​​​​ units

new break-even point in dollar value = no. of units * price per unit = 5867.347*$100 = $586,734.694

I recommend that the production manager should pursue situation b as the break-even point is the lowest for that situation. This implies that the break-even can be achieved by the lowest number of units or cost.