Final answer:
To find the present value of an investment with varied yearly cash flows and a 15% discount rate, calculate the present value for each year's cash flow using the formula, then sum the present values of all years to arrive at the final answer.
Step-by-step explanation:
To calculate the present value of an investment with multiple cash flows at different time periods and a discount rate of 15%, we must discount each cash flow separately back to its present value. The present value of a future amount of money is calculated using the formula Present Value = Future Value / (1 + Interest Rate)^number of years. Let's apply this to each cash flow:
- Year 1: $19,630 / (1 + 0.15)^1
- Year 2: $1,520 / (1 + 0.15)^2
- Year 3: $14,070 / (1 + 0.15)^3
- Year 4: $16,350 / (1 + 0.15)^4
- Year 5: $1,970 / (1 + 0.15)^5
After calculating each present value, the next step is to add up all the present values for the different time periods to get the final answer. It is crucial to do a separate present value calculation for each cash flow because they are received at different times, and thus each cash flow is discounted differently based on its respective time period.