an initial outlay of $10000 resulting in a free cash flow of $1993 at end of each year for the next 10 years. the internal rate of return?
To find the internal rate of return (IRR), we need to determine the discount rate that makes the present value of the cash flows equal to the initial outlay. In this case, the initial outlay is $10,000, and the cash flow at the end of each year is $1,993 for 10 years.
To calculate the IRR, we can use a financial calculator or a spreadsheet software like Excel. Here are the steps to calculate it in Excel:
1. List the cash flows in a column. Column A will represent Year, and column B will represent Cash Flow. Enter the following values in the respective cells:
A2: 0 (year 0)
A3-A12: 1 to 10 (years 1 to 10)
B2-B12: -10000 (initial outlay) and 1993 (cash flow for years 1 to 10)
2. Use the IRR function in Excel to calculate the IRR. In an empty cell, type the following formula:
=IRR(B2:B12)
3. Press Enter to calculate the IRR.
The formula will return the IRR as a percentage. In this case, the IRR is approximately 13.81%.
To calculate the internal rate of return (IRR) for the given cash flows, you can use the following steps:
1. Write down the cash flows: -$10,000 in the initial year (Year 0) and $1,993 at the end of each subsequent year for the next 10 years.
2. Use a financial calculator, spreadsheet software (such as Microsoft Excel or Google Sheets), or an IRR calculator to find the IRR. Most financial calculators or software have a built-in IRR function that can solve for the internal rate of return.
If you are using a spreadsheet, you can use the IRR function as follows:
a. In an empty cell, input the cash flows starting from Year 0 to Year 10. In this case, it will be -10000 in Year 0 and 1993 for Years 1 to 10.
b. In another empty cell, use the IRR function, which could be written as "=IRR(range of cash flows)". In this case, it will be "=IRR(A1:A11)", assuming the cash flows are in the range A1 to A11.
3. Calculate the IRR using the chosen method. The internal rate of return represents the discount rate that makes the sum of the present values of the cash flows equal to zero. In other words, it is the rate at which the net present value (NPV) of the cash flows is zero.
In this case, the IRR would be the discount rate that satisfies the equation:
0 = -$10,000 + $1,993/(1+IRR)^1 + $1,993/(1+IRR)^2 + ... + $1,993/(1+IRR)^10
By using a financial calculator or spreadsheet software, you can find that the internal rate of return for these cash flows is approximately 9.9%.