Question

You can purchase an optical scanner today for $550. the scanner provides benefits worth $90 a year. the expected life of the scanner is 10 years. scanners are expected to decrease in price by 25% per year. suppose the discount rate is 12%. when is the best time to purchase the scanner

Answer 1

The best time to purchase the optical scanner is in Year 3 as it has the highest NPV of -314.32.

Step-by-step explanation:

To determine the best time to purchase the optical scanner, we need to calculate the net present value (NPV) for each year and find the year with the highest NPV. The formula to calculate NPV is:

NPV = Benefits - Cost / (1 + discount rate)^year

Using this formula, we can calculate the NPV for each year:

1. Year 0: NPV = -550 / (1 + 0.12)⁰ = -550
2. Year 1: NPV = 90 - 550 / (1 + 0.12)¹ = -392.41
3. Year 2: NPV = 90 - 550 / (1 + 0.12)² = -349.52
4. Year 3: NPV = 90 - 550 / (1 + 0.12)³ = -314.32
5. Year 4: NPV = 90 - 550 / (1 + 0.12)⁴ = -285.32
6. Year 5: NPV = 90 - 550 / (1 + 0.12)⁵ = -261.29
7. Year 6: NPV = 90 - 550 / (1 + 0.12)⁶ = -241.32
8. Year 7: NPV = 90 - 550 / (1 + 0.12)⁷ = -224.71
9. Year 8: NPV = 90 - 550 / (1 + 0.12)⁸ = -210.91
10. Year 9: NPV = 90 - 550 / (1 + 0.12)⁹ = -199.54
11. Year 10: NPV = 90 - 550 / (1 + 0.12)¹⁰ = -190.37

Based on these calculations, the best time to purchase the scanner is in Year 3, as it has the highest NPV of -314.32.