3. What is the value in year 20 of a $1,000 cash flow made in year 8 if interest rates are 15 percent in years 6 through 13 and increase to 18 percent in the remaining years?
To find the value in year 20 of a $1,000 cash flow made in year 8 with changing interest rates, we need to calculate the present value of the cash flow at each interest rate and then calculate the future value of those present values.
Step 1: Calculate the present value of the cash flow at each interest rate.
- For years 8-13, the interest rate is 15 percent. We need to calculate the present value of the $1,000 cash flow in year 8 at a 15 percent discount rate.
- For years 14-20, the interest rate is 18 percent. We need to calculate the present value of the $1,000 cash flow in year 8 at an 18 percent discount rate.
To calculate the present value, we can use the formula: Present Value = Cash Flow / (1 + Discount Rate)^Number of Periods.
For years 8-13:
Discount Rate = 15%
Number of Periods = 13 - 8 + 1 = 6
Present Value = $1,000 / (1 + 0.15)^6
For years 14-20:
Discount Rate = 18%
Number of Periods = 20 - 13 = 7
Present Value = $1,000 / (1 + 0.18)^7
Step 2: Calculate the future value of the present values.
To calculate the future value of the present values, we can simply compound the present values forward to year 20 using the appropriate interest rate.
Future Value = Present Value * (1 + Discount Rate)^Number of Periods
Future Value = (Present Value for years 8-13) * (1 + 0.15)^7 + (Present Value for years 14-20) * (1 + 0.18)^7
By substituting the values into the formula and performing the calculations, you can find the value of the cash flow in year 20.