what is the initial rate of return for the following project: An initial outlay of 9,500 resulting in a single cash flow of 16,281 in 7 years
To calculate the initial rate of return for a project, we need to use a formula called the net present value (NPV) formula. The initial rate of return, also known as the internal rate of return (IRR), is the discount rate that makes the present value of the expected cash inflows equal to the initial investment.
To find the initial rate of return for the given project, follow these steps:
Step 1: Determine the cash inflow for each year.
In this case, there is only one cash flow, which is $16,281 in 7 years.
Step 2: Calculate the present value of the cash inflow.
To calculate the present value, you need to discount the future cash flow to its present value using an appropriate discount rate. Let's assume a discount rate of 10% for this calculation.
PV = Cash Flow / (1 + r)^n
Where:
PV - Present Value
Cash Flow - Cash inflow
r - Discount rate
n - Number of periods
Using the values:
PV = 16,281 / (1 + 0.10)^7
PV = 16,281 / (1.10)^7
PV = 7,944.33 (rounded to two decimal places)
Step 3: Calculate the initial investment (outlay).
The initial investment, or outlay, is $9,500.
Step 4: Calculate the initial rate of return (IRR).
IRR is calculated by finding the discount rate that makes the NPV (Net Present Value) equal to zero.
NPV = PV - Initial Investment
0 = 7,944.33 - 9,500
To find the discount rate (IRR), you can use financial calculators or spreadsheet software, such as Microsoft Excel. You need to use the IRR function or trial-and-error method.
Using MS Excel:
- Input the cash flows in a column (cell A1 for the initial investment and A2 for the present value)
- Use the IRR function: =IRR(A1:A2)
- The IRR for this project is approximately 5.99%.
Therefore, the initial rate of return for this project is approximately 5.99%.