At the beginning of January, Kesia Records paid $148,950 to acquire the exclusive rights to a new album. It costs them $1.13 to print a copy of this album, which they can sell for $9.75. The following chart shows the sales of that record, along with the overhead expenses of running a record studio, not counting production costs.
| Month | Albums Sold | Expenses |
|---|---|---|
| Jan. | 5,486 | $27,714 |
| Feb. | 8,191 | $21,689 |
| Mar. | 4,796 | $25,195 |
| Apr. | 7,490 | $28,766 |
| May | 6,272 | $24,604 |
| Jun. | 5,131 | $29,040 |
In which month did Kesia Records first break even?
A. January
B. March
C. April
D. May
Answer (2)
Kesia Records never broke even in any of the months from January to June. Their cumulative profits remained negative throughout this period. Therefore, the correct answer is that none of the listed months resulted in breaking even.
;
Calculate the profit per album: 9.75 - 1.13 = $8.62 .
Calculate the monthly revenue: Albums Sold × $8.62.
Calculate the total cost for each month: $148 , 950 + E x p e n ses + ( A l b u m s S o l d \times$ $1.13).
Calculate the cumulative profit for each month and determine when it becomes non-negative. Since the cumulative profit is negative for all given months, the record company did not break even in any of the months.
The record company did not break even in any of the listed months.
Explanation
Problem Analysis Let's analyze the financial performance of Kesia Records to determine when they broke even. We need to calculate the profit per album, the total revenue for each month, the total costs (including the initial cost for exclusive rights), and the cumulative profit to see when it becomes non-negative.
Calculate Profit Per Album First, calculate the profit per album: \text{Profit per album} = \text{Selling price} - \text{Printing cost} = $9.75 - $1.13 = $8.62 So, each album sold generates a profit of $8.62.
Calculate Monthly Revenue, Cost and Cumulative Profit Next, we calculate the total revenue, total cost, and cumulative profit for each month. The total cost includes the initial cost of $148 , 950 , the printing costs ($\text{Albums Sold} \times 1.13 ), and the monthly expenses.
January:
Albums Sold: 5,486
Expenses: $27 , 714
Revenue: $5486 \times 8.62 = $47,289.32$
Printing Cost: $5486 \times 1.13 = $6,208.18$
Total Cost: $$148,950 + $27,714 + 6 , 208.18 = $182,872.18$
Profit: $$47,289.32 - ($27,714 + 6 , 208.18 ) = $13,367.14$
Cumulative Profit: $$47,289.32 - 182 , 872.18 = − $135 , 582.86
February:
Albums Sold: 8,191
Expenses: $21 , 689
Revenue: $8191 \times 8.62 = $70,606.42$
Printing Cost: $8191 \times 1.13 = $9,255.83$
Total Cost: $$148,950 + $21,689 + 9 , 255.83 = $179,894.83$
Profit: $$70,606.42 - ($21,689 + 9 , 255.83 ) = $39,661.59$
Cumulative Profit: − $135 , 582.86 + $39,661.59 = -$95,921.27$
March:
Albums Sold: 4,796
Expenses: $25 , 195
Revenue: $4796 \times 8.62 = $41,341.52$
Printing Cost: $4796 \times 1.13 = $5,419.48$
Total Cost: $$148,950 + $25,195 + 5 , 419.48 = $179,564.48$
Profit: $$41,341.52 - ($25,195 + 5 , 419.48 ) = $10,727.04$
Cumulative Profit: − $95 , 921.27 + $10,727.04 = -$85,194.23$
April:
Albums Sold: 7,490
Expenses: $28 , 766
Revenue: $7490 \times 8.62 = $64,563.80$
Printing Cost: $7490 \times 1.13 = $8,463.70$
Total Cost: $$148,950 + $28,766 + 8 , 463.70 = $186,179.70$
Profit: $$64,563.80 - ($28,766 + 8 , 463.70 ) = $27,334.10$
Cumulative Profit: − $85 , 194.23 + $27,334.10 = -$57,860.13$
May:
Albums Sold: 6,272
Expenses: $24 , 604
Revenue: $6272 \times 8.62 = $54,064.64$
Printing Cost: $6272 \times 1.13 = $7,087.36$
Total Cost: $$148,950 + $24,604 + 7 , 087.36 = $180,641.36$
Profit: $$54,064.64 - ($24,604 + 7 , 087.36 ) = $22,373.28$
Cumulative Profit: − $57 , 860.13 + $22,373.28 = -$35,486.85$
June:
Albums Sold: 5,131
Expenses: $29 , 040
Revenue: $5131 \times 8.62 = $44,229.22$
Printing Cost: $5131 \times 1.13 = $5,807.03$
Total Cost: $$148,950 + $29,040 + 5 , 807.03 = $183,797.03$
Profit: $$44,229.22 - ($29,040 + 5 , 807.03 ) = $9,382.19$
Cumulative Profit: − $35 , 486.85 + $9,382.19 = -$26,104.66$
Determine Break-Even Month From the calculations above, we can see that the cumulative profit remains negative throughout the first six months. Therefore, Kesia Records did not break even in any of these months.
Final Answer Based on the provided data, Kesia Records did not break even in January, March, April, or May.
Examples
Understanding break-even points is crucial for businesses. For example, a bakery can use this concept to determine how many cakes they need to sell each month to cover their costs, including rent, ingredients, and labor. By calculating the break-even point, the bakery can set realistic sales targets and make informed decisions about pricing and production.
