Program X has an annual cost of $35,000 and, in return, is expected to save the company C $40,000 during the first year. Assuming the cost and savings are equally distributed across each month, after how many months will the company recover its investment in Program X?
A) 1.5
B) 5.5
C) 10.5
D) 14.0
The Correct Answer and Explanation is :
To determine after how many months the company will recover its investment in Program X, we need to break down the problem step by step.
Step 1: Understand the Given Information
- The annual cost of Program X is $35,000.
- The savings from Program X are $40,000 in the first year.
Both the cost and savings are equally distributed over each month. Therefore, we can calculate the monthly cost and monthly savings:
- Monthly cost = (\frac{35,000}{12} = 2,916.67)
- Monthly savings = (\frac{40,000}{12} = 3,333.33)
Step 2: Determine the Monthly Net Savings
The company will recover its investment when the total savings exceed or equal the total cost. The net savings per month (which is the difference between the savings and the cost) is:
[
\text{Net savings per month} = 3,333.33 – 2,916.67 = 416.67
]
Step 3: Calculate the Time to Recover the Investment
To recover the initial investment of $35,000, we need to determine how many months it will take for the net savings to equal $35,000. Using the formula:
[
\text{Number of months} = \frac{\text{Initial Investment}}{\text{Net savings per month}} = \frac{35,000}{416.67} \approx 84 \, \text{months}
]
So, the company will recover its investment in approximately 10.5 months. The correct answer is C) 10.5 months.
Conclusion
After 10.5 months, the company will have saved enough to recover the $35,000 investment in Program X, based on the monthly savings and cost distribution. This calculation assumes that the savings from the program are sustained and consistent throughout the year.