Final answer:
The factory has a present value of $464,255.68, which is higher than its cost of $400,000, making it a good investment. The value is calculated using the present value formula and a discount rate of 12% for the forecasted cash inflows over three years.
Step-by-step explanation:
To calculate the value of the factory using the provided cash inflows and discount rate, we use the present value formula. The present value (PV) of each individual cash inflow is calculated by dividing the cash inflow by (1 + discount rate)^year. Therefore, for the factory:
- PV of Year 1 = $120,000 / (1 + 0.12)1 = $120,000 / 1.12 = $107,142.86
- PV of Year 2 = $180,000 / (1 + 0.12)2 = $180,000 / 1.2544 = $143,540.67
- PV of Year 3 = $300,000 / (1 + 0.12)3 = $300,000 / 1.4049 = $213,572.15
The total present value of the cash inflows is the sum of these values:
- Total PV = $107,142.86 + $143,540.67 + $213,572.15 = $464,255.68
Since the cost of the factory is $400,000, and the total present value of the cash inflows is $464,255.68, the factory appears to be a good investment because the total PV exceeds the cost. To round to two decimal places, the value of the factory is $464,255.68.
In conclusion, the answer to whether the factory is a good investment is Yes, based on the present value being higher than the cost of the factory.