Question

A product at the jennings company enjoyed reasonable sales volume, but its contributions to profits were dissapointing. Last year, the 17,000 units were produced and sold. The selling price is $22 per unit, the variable cost is $18 per unit, and the fixed cost is $80,000.

A) what is the break even quantity for this product? Use both graphic and algebraic approach for your answer.

B) if sales were not expected to increase, by how much would jennings have to reduce their variable cost to break even?

C) Jennings believes that a $1 reduction in price will increase sales by 50 percent. is this enough for Jennings to break even? If not, by how much would sales have to increase?

D) Jennings is considering ways to either simulate sales volume or decrease variable cost. management believes that either sales can be increased by 30 or percent or that variable cost can be reduced by 85 percent of its current level. Which alternative leads to higher contributions to profits, assuming that each is equally costly to implement?  

E) What is the percent change per unit profit contribution generated by each alternative in part d?

Answer 1

(a)

Quantity = FC ÷ (P – VC) = $80000 ÷ ($22 - $18) = 20000 units for the break-even.

And then we can draw this chart below by using the break-even quantity and others data.

From the question we also can find two of these axis for total revenue and total cost:

Total revenue = PQ = 22Q;

Total cost = FC + VCQ = 80000 + 18Q; from the tradeoff calculating both of these two equal to $440000.

(b)

In this answer we need to use this formula as VC of break-even

= P – (FC ÷ Q)

= $22 - $80000/17000

= $22 – $4.71

= $17.29 for the break-even quantity.

So Jennings needs to reduce their variable cost from $18 to $17.29 per unit.

(c)

In this answer the selling price (P) is $21, using the same formula as Q = ;

The new Quantity = 80000/$21-$18 = 26667 units for the new break-even.

And we can find the new sales quantity = old sales + (old sales × 50%) = 17000 + 8500 = 25500;

so it is not enough for Jennings’s break-even, it needs to increase 26667 – 25500 =1167 units.

(d)

If sales increase by 30%, the new sales quantity = old sales + (old sales × 30%) = 17000 + 5100 = 22100 units; then we can calculate the total profit contribution, it equals to total revenue – total cost = $22×22100 – ($80000 + $18×22100) = $486,200 – $477,800 = $8,400.

As for variable cost decreases 85%, the new variable cost = old variable cost × 85% = $18 × 85% = $15.3; then we can calculate the total profit contribution under this case, it equals to total revenue – total cost = $22 × 17000 – (80000 + $15.3 × 17000) = $374,000 - $340,100 = $33,900

From these two cases above we can find the profit increased higher along with the variable cost reduced, so this alternative is the best.

(e)

In this answer we need to find the total profit contribution per unit first below:

Total profit contribution per unit = = ($22 * 17000 - ($80000 + $18*17000)) / 17000 = 374,000 - 386,000 / 17000 = -$0.71 per unit loss

Next we calculate the profit contribution per unit by increasing sales is = 8,400 / 22100 = $0.38. Similar can be obtained the profit contribution per unit by decreasing variable cost is $33900 ÷ 17000 = $1.994.

Then the percentage changing of the profit contribution per unit by sales increasing 30% is [$0.38 – (-$0.71)] ÷ $0.71 = $1.09 ÷ $0.71 = 1.5352 → 153.52%;

The percentage changing of the profit contribution per unit by variable cost decreasing 85% is [$1.99 – (-$0.71)] ÷ $0.71 = $2.7 ÷ $0.71 = 3.8028 → 380.28%.

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