Final answer:
Calculate the present value of each payment at a 15% discount rate to determine the maximum price you would be willing to pay for the cash flows, comprising $10 annually over 5 years and an additional $700 at the end of 5th year.
Step-by-step explanation:
To determine the maximum price you would be willing to pay for the given cash flows, we need to calculate the present value of these flows using the discount rate which is the interest rate of 15 percent per annum. Given that you receive $10 each year for five years and an additional one-time payment of $700 at the end of the fifth year, the present value of each of these payments must be calculated separately and then summed to find the total present value.
The formula for the present value of a future payment is PV = FV / (1 + r)^t, where PV is the present value, FV is the future value, r is the interest rate, and t is the number of years until payment. Therefore, for each $10 payment, we need to discount it back for each respective year, and similarly for the $700 payment in year 5.
Here's an example of how we discount the first $10 payment: PV = $10 / (1 + 0.15)^1. Repeat this for each of the five $10 payments and the $700 payment to get their respective present values. Summing these values will give you the maximum price you are willing to pay for these cash flows today.
The present value of cash flows considering compound interest is important as it reflects the time value of money, which acknowledges that a dollar today is worth more than a dollar in the future due to its potential earning capacity. Keeping this in mind, you can determine what price to pay for an investment based on its future cash flows discounted at a specific interest rate to account for risk and return preferences.