The postal service of St. Vincent, an island in the West Indies, obtains a significant portion of its revenues from sales of special souvenir sheets to stamp collectors. The postal service purchases the souvenir sheets from a supplier for $2.50 each.

The postal service of St. Vincent, an island in the West Indies, obtains a significant portion of its revenues from sales of special souvenir sheets to stamp collectors. The postal service purchases the souvenir sheets from a supplier for $2.50 each. St. Vincent has been selling the souvenir sheets for $14.00 each and ordinarily sells about 114,000 units. To test the market, the postal service recently priced a new souvenir sheet at $12.60 and sales increased to 129,960 units.

Required:

1. What total contribution margin did the postal service earn when it sold 114,000 sheets at a price of $14.00 each?

2. By what percentage did the St. Vincent post office decrease its selling price? By what percentage did unit sales increase?

3. What total contribution margin did the postal service earn when it sold 129,960 sheets at a price of $12.60 each?

4. What was the postal service’s increase (decrease) in total contribution margin going from the higher price of $14.00 to the lower price of $12.60?

5. How many sheets would the postal service have to sell at the lower price of $12.60 to equal the total contribution margin earned at the higher price of $14.00? (Round your answer to the nearest whole number.)

6. What percentage increase in the number of sheets sold at $12.60 must be achieved to equal the total contribution margin earned at the higher price of $14.00? (Round your intermediate calculations to the nearest whole number. Round final answer to 1 decimal place.)

 

Explanation

1.

The postal service’s contribution margin (CM) at a price of $14.00 is computed as follows:

CM	=	(P – V) × Q
CM	=	($14.00 − $2.50) × 114,000
CM	=	$11.50 × 114,000
CM	=	$1,311,000

2.

The percentage decrease in the selling price and the percentage increase in unit sales are computed as follows:

	Price				Volume
Revised price/volume	$	12.60			129,960
Original price/volume (a)		14.00			114,000
Change (b)	$	(1.40	)		15,960
Percentage (decrease)/increase (b) ÷ (a)		(10	)%		14	%

3.

The postal service’s contribution margin at a price of $12.60 is computed as follows:

CM	=	(P – V) × Q
CM	=	($12.60 − $2.50) × 129,960
CM	=	$10.10 × 129,960
CM	=	$1,312,596

4.

The increase in contribution margin is computed as follows:

Contribution margin at a price of $12.60	$	1,312,596
Contribution margin at a price of $14.00		1,311,000
Increase in contribution margin	$	1,596

5.

The postal service would have to sell 129,802 sheets computed as follows:

CM	=	(P – V) × Q
$1,311,000	=	($12.60 − $2.50) × Q
$1,311,000	=	$10.10 × Q
Q	=	129,802 sheets (rounded)

6.

The percentage increase is computed as follows:

(129,802 units – 114,000 units) ÷ 114,000 units = 13.9%

Thanks