Corey's comic book store has been up and running for 4 years. Corey feels that his store has been successful and is considering moving to a larger property to allow for greater inventory and customer opportunities in his business. He would like investors to cover the cost of his expansion.
The profits of Corey's comic book store for its first four years are outlined below. According to this information, what would be the best estimate for Corey to quote as expected profits in the next year in his new business plan?
| Year | Net Profits |
| ---- | ----------- |
| 1 | $14,250.00 |
| 2 | $15,390.00 |
| 3 | $16,621.20 |
| 4 | $17,950.90 |
| 5 | |
A. $20.550 .19
B. $19,090.90
Answer (1)
Calculate the percentage increase in profit from Year 1 to Year 2: approximately 0.08.
Calculate the percentage increase in profit from Year 2 to Year 3: approximately 0.08.
Calculate the percentage increase in profit from Year 3 to Year 4: approximately 0.08.
Calculate the average percentage increase: 0.08, and estimate Year 5 profit: $19 , 386.97 .
Explanation
Problem Analysis We are given the net profits for the first four years of Corey's comic book store and want to estimate the profit for the next year (Year 5). The profits are:
Year 1: $14,250.00 Year 2: $15,390.00 Year 3: $16,621.20 Year 4: $17,950.90
To estimate the profit for Year 5, we will calculate the percentage increase in profit from year to year, then find the average percentage increase, and apply that to Year 4's profit.
Year 2 Increase First, let's calculate the percentage increase from Year 1 to Year 2: 14250 15390 − 14250 = 14250 1140 = 0.08
Year 3 Increase Next, the percentage increase from Year 2 to Year 3: 15390 16621.20 − 15390 = 15390 1231.20 = 0.08
Year 4 Increase Then, the percentage increase from Year 3 to Year 4: 16621.20 17950.90 − 16621.20 = 16621.20 1329.70 ≈ 0.08
Average Increase Now, we calculate the average percentage increase: 3 0.08 + 0.08 + 0.08 = 0.08
Year 5 Estimate Finally, we apply the average percentage increase to Year 4's profit to estimate Year 5's profit: 17950.90 × ( 1 + 0.08 ) = 17950.90 × 1.08 = 19386.972
Conclusion Therefore, the best estimate for Corey to quote as expected profits in the next year is approximately $19,386.97.
Examples
Estimating future profits is crucial for securing investments and planning business expansions. For instance, if Corey wants to expand his comic book store, he needs to convince investors that his business is likely to grow. By analyzing past profit trends, Corey can project future earnings, demonstrating the potential return on investment. This projection helps investors assess the risk and make informed decisions, ensuring the expansion is financially viable and beneficial for all parties involved.
