Lindon Company is the exclusive distributor for an automotive product that sells

Question

Lindon Company is the exclusive distributor for an automotive product that sells for $37.50 per unit and has a CM ratio of 30%. The company's fixed expenses are $236,250 per year. The company plans to sell 8,000 units this year. Required 1. What are the variable expenses per unit? (Round your answer to 2 decimal places.) Variable expenses per unit 2. Use the equation method: a. What is the break-even point in unit sales and in dollar sales? Break-even point in unit sales Break-even point in dollar sales b. What amount of unit sales and dollar sales is required to earn an annual profit of $56,250? Sales level in units

Explanation / Answer

2)-a)-Using equation method:-

px = vx + FC + Profit

Where,

p= price per unit,
x = number of units,
v= variable cost per unit

FC = Total fixed cost.

At break-even point the profit is zero therefore the CVP formula is simplified to:

px = vx + FC

Solving the above equation for x which equals break-even point in sales units:-

Break-even Sales units=x=FC/p-v

Break-even Sales units=x =$236250/$37.50 per unit-$26.25 per unit

                                             =$236250/$11.25 per unit =21000 units

Break-even Sales in dollars=Price per unit* Break-even Sales units

                                               =$37.50 per unit*21000 units =$787500

b)- SpQ = VeQ + Fe + Tp

Where:-

Sp = Sales price per unit.
Q = Number (quantity) of units to be manufactured and sold during the period.
Ve = Variable expenses to manufacture and sell a single unit of product.
Fe = Total fixed expenses for the period.
Tp = Target profit for the period

$37.50Q=$26.25Q+$236250+$56250

$37.50Q-$26.25Q=$236250+$56250

$11.25Q=$292500

Q =$292500/$11.25 =26000 units

Sales level in dollars=26000 units*$37.50 per unit =$975000

c)- New variable cost per unit (v) =$26.25-$3.75 per unit =$22.50 per unit

Break-even Sales units=x=FC/p-v

                                        X= $236250/$37.50 per unit-$22.50 per unit

                                             =15750 units

Break-even Sales in dollars =15750 units*$37.50 per unit

                                                =$590625

3) Using formula method:-

a)- Break-even point in unit sales = Fixed cost/Contribution per unit

                                                            =$236250/$11.25 per unit =21000 units

Break even point sales in dollars = Fixed cost/Contribution margin ratio

                                                         =$236250/30% =$787500

b)-Sales level in units to earn target profit =Fixed cost+ Target profit/ Contribution per unit

                                                                            =$236250+$56250/$11.25 per unit

                                                                              =$292500/$11.25 per unit =26000 units

Sales level in units to earn target profit =Fixed cost+ Target profit/ Contribution margin ratio

                                                                            =$236250+$56250/30%

                                                                              =$292500/30% =$975000

c)-New variable cost per unit =$26.25 per unit - $3.75 per unit =$22.50 per unit

    New contribution margin per unit =$37.50 per unit-$22.50 per unit =$15 per unit

New contribution margin ratio =$15 per unit/$37.50 per unit*100 =40%

Break-even point in unit sales = Fixed cost/New Contribution per unit

                                                            =$236250/$15 per unit =15750 units

Break even point sales in dollars = Fixed cost/ New Contribution margin ratio

                                                         =$236250/40% =$590625

px = vx + FC + Profit

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