Final answer:
The value of the missing cash flow for year 2 is $2,184.97, calculated by first finding the present values of the known cash flows, subtracting this from the total present value, and adjusting for the end of the second year.
Step-by-step explanation:
The student is asking about the calculation of the present value of a cash flow stream and specifically the value of a missing cash flow in year 2 when the present value of the entire cash flow stream is $8,600, discounted at an annual rate of 9.4%. Using the present value formula, which considers both the amount of cash flows and the time at which they are received, we can calculate the missing value.
First, we need to calculate the present value of the cash flows that are known:
- $2,200 discounted at the end of the first year: $2,200 / (1 + 0.094) = $2,011.33
- $2,800 discounted at the end of the third year: $2,800 / (1 + 0.094)3 = $2,118.09
- $3,400 discounted at the end of the fourth year: $3,400 / (1 + 0.094)4 = $2,472.59
Next, we subtract the sum of these present values from the total present value of the cash flow stream:
$8,600 - $2,011.33 - $2,118.09 - $2,472.59 = $1,997.99
Finally, we adjust the found value for the end of the second year:
Year 2 cash flow = $1,997.99 * (1 + 0.094) = $2,184.97 (rounded to two decimal places)
Therefore, the value of the missing cash flow for year 2, when discounted at 9.4 percent annually, is $2,184.97.