Final answer:
The present value of the cash flow stream Ryan Campbell will receive for the next 11 years, given a discount rate of 10%, is $46,774.22. To calculate the present value, the present value of an annuity formula is used with the specifics of Ryan's investment.
Step-by-step explanation:
The question posed is to calculate the present value of a series of future cash flows that Ryan Campbell will receive from an investment. In this case, Ryan will receive $7,942 each year for the next 11 years, with an opportunity cost (or discount rate) of 10%. To determine the present value of this annuity, we use the present value of an annuity formula:
PV = Pmt × [(1 - (1 + r)-n) / r]
Where:
- PV = Present Value of the annuity
- Pmt = Annual payment ($7,942)
- r = Annual discount rate (10% or 0.10)
- n = Number of periods (11 years)
Plugging in the values, we get:
PV = $7,942 × [(1 - (1 + 0.10)-11) / 0.10]
Using a calculator or financial software, we find that the present value (rounded to the nearest two decimals) is:
PV = $7,942 × 5.889
PV = $46774.22
This calculation suggests that receiving $7,942 per year for 11 years, discounted at a rate of 10%, is equivalent to receiving $46,774.22 today.