Final answer:
To calculate the present value of a stream of cash flows expected to grow at a 10% rate per year for 5 years and then remain constant, you need to discount each cash flow to its present value using the given discount rate. By using the present value formulas for a growing perpetuity and a perpetuity, you can calculate the present value of the cash flows for the first 5 years and the present value of the cash flow at the end of the 30th year. Adding these two values will give you the final answer, which is the present value of the stream of cash flows.
Step-by-step explanation:
Present Value Calculation:
To calculate the present value of a stream of cash flows, we need to discount each cash flow to its present value using the given discount rate. In this case, the cash flows are expected to grow at a 10 percent rate per year for 5 years and then remain constant thereafter until the final payment in 30 years.
Step 1:
Calculate the present value of the cash flows for the first 5 years using the discount rate of 5.00 percent. The cash flows are expected to grow at a rate of 10 percent per year, so the payments in the first year would be $1,000 * (1 + 0.10) = $1,100 and in the second year would be $1,100 * (1 + 0.10) = $1,210, and so on. We can use the formula for the present value of a growing perpetuity to calculate the present value of the cash flows for the first 5 years.
Step 2:
Calculate the present value of the cash flow at the end of the 30th year using the discount rate of 5.00 percent. Since the cash flows are expected to remain constant after the 5th year, we can use the formula for the present value of a perpetuity to calculate the present value of the cash flow at the end of the 30th year.
Step 3:
Add up the present values of the cash flows for the first 5 years and the present value of the cash flow at the end of the 30th year to get the final answer.
In this case, the present value of the cash flows for the first 5 years is $5,790.82 and the present value of the cash flow at the end of the 30th year is $84.71. Adding these two values gives us the present value of the stream of cash flows, which is $5,875.53.