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?
The correct answer and explanation is:
Correct Answer:
The company will recover its investment in 10.5 months.
Explanation:
To determine the time required for the company to recover its investment in Program X, we analyze the monthly cost and savings and calculate when the cumulative savings equal the total investment.
- Monthly Cost of Program X: The annual cost of $35,000 is distributed evenly across 12 months: Monthly Cost=Annual Cost12=35,00012=2,916.67 (rounded to 2 decimal places).\text{Monthly Cost} = \frac{\text{Annual Cost}}{12} = \frac{35,000}{12} = 2,916.67 \, \text{(rounded to 2 decimal places)}.
- Monthly Savings from Program X: The annual savings of $40,000 is also distributed evenly across 12 months: Monthly Savings=Annual Savings12=40,00012=3,333.33 (rounded to 2 decimal places).\text{Monthly Savings} = \frac{\text{Annual Savings}}{12} = \frac{40,000}{12} = 3,333.33 \, \text{(rounded to 2 decimal places)}.
- Monthly Net Savings: Each month, the savings exceed the cost by: Net Savings per Month=Monthly Savings−Monthly Cost=3,333.33−2,916.67=416.67.\text{Net Savings per Month} = \text{Monthly Savings} – \text{Monthly Cost} = 3,333.33 – 2,916.67 = 416.67.
- Time to Recover Investment: The total investment of $35,000 is recovered when the cumulative net savings equals $35,000: Months to Recover=Total InvestmentNet Savings per Month=35,000416.67≈10.5 months.\text{Months to Recover} = \frac{\text{Total Investment}}{\text{Net Savings per Month}} = \frac{35,000}{416.67} \approx 10.5 \, \text{months}.
Interpretation:
After 10 full months, the company will have saved $4,166.70, which still falls short of the $35,000 investment. In the 11th month, halfway through, the cumulative savings will reach exactly $35,000. Therefore, the company fully recovers its investment at the 10.5-month mark.
This calculation is crucial for decision-making, as it shows how quickly the program generates value relative to its cost. A recovery period of 10.5 months implies the program is cost-effective within its first year, making it a worthwhile investment.