Final answer:
The future value of the specified cash flow stream, with a discount rate of 6%, is calculated for each cash flow and summed to give a total future value of $1,235.6184 at year 4.
Step-by-step explanation:
The question involves calculating the future value of a series of cash flows with different amounts occurring at different times. To determine the future value, we apply the formula Future Value = Cash Flow × (1 + interest rate)time for each cash flow and sum them up. The given discount rate is 6%, and the cash flows are CF0=0 at time 0, CF1=-100 at time 1, CF2=200 at time 2, CF3=500 at time 3, and CF4=600 at time 4. The future values for each of these cash flows need to be adjusted according to their respective times.
First, let's calculate the future value for each cash flow separately:
- CF1's future value (in year 4) = -100 × (1 + 0.06)3 = -100 × 1.191016 = -119.1016
- CF2's future value (in year 4) = 200 × (1 + 0.06)2 = 200 × 1.1236 = 224.72
- CF3's future value (in year 4) = 500 × (1 + 0.06)1 = 500 × 1.06 = 530
- CF4 already occurs at year 4, so its future value remains 600
Next, we sum these future values to determine the total future value of the cash flow stream at time 4:
Total Future Value = -119.1016 + 224.72 + 530 + 600 = 1235.6184
In this scenario, the future value of the cash flow stream discounted at 6% to time 4 is $1,235.6184. This demonstrates how discounting cash flows to a single point in time provides a means to assess the value of payments that occur at various times in the future.