Invest 500000 today and get 900000 at the end of 3rd year. Compute internal rate of return :
To compute the internal rate of return (IRR), we need to use a financial calculator or software, as it involves solving for the discount rate that equates the present value of cash inflows (900,000) with the initial investment (-500,000) over the given time period (3 years).
Using a financial calculator or software, we can input the following cash flow information:
- Year 0: -500,000 (initial investment)
- Year 3: 900,000 (cash inflow)
Using this data, the IRR can be determined. Assuming a discount rate of 10%, the present value of the cash inflow (900,000) at the end of 3 years would be:
900,000 / (1 + 0.10)^3 = 900,000 / 1.331 = 674,591.72
To equate this value with the initial investment, we solve for the discount rate:
-500,000 + 674,591.72 = 0
By using trial and error or using financial software, we find that the discount rate that solves this equation is approximately 18.91%. Therefore, the internal rate of return (IRR) for this investment is approximately 18.91%.
To compute the internal rate of return (IRR), we need to calculate the discount rate at which the present value of the investment's cash inflows equals the initial investment.
In this case, we have an initial investment of $500,000 and a cash inflow of $900,000 at the end of the 3rd year.
To start, let's consider the formula for the present value of a future cash flow:
Present Value (PV) = Cash Inflow / (1 + Discount Rate)^n
Where:
- PV is the present value
- Cash Inflow is the future cash flow
- Discount Rate is the rate at which future cash flows are discounted
- n is the number of periods (years)
We need to find the discount rate that makes the present value equal to the initial investment:
$500,000 = $900,000 / (1 + Discount Rate)^3
Now, let's solve for the Discount Rate:
(1 + Discount Rate)^3 = $900,000 / $500,000
Taking the cube root on both sides:
1 + Discount Rate = (900,000 / 500,000)^(1/3)
1 + Discount Rate = 1.3874
Discount Rate = 1.3874 - 1
Discount Rate = 0.3874
Finally, to convert the discount rate to a percentage, multiply by 100:
Internal Rate of Return (IRR) = Discount Rate * 100
IRR = 0.3874 * 100
IRR = 38.74%
Therefore, the internal rate of return (IRR) for this investment is approximately 38.74%.
To compute the internal rate of return (IRR), we need to follow a trial and error process. The IRR is the rate at which the present value of cash inflows equals the present value of cash outflows. In this case, the cash inflow is $900,000, and the cash outflow is the initial investment of $500,000.
To begin, assume an arbitrary rate of return (let's say 10%) and calculate the present value of the cash inflow and outflow using the formula:
Present Value = Cash Flow / (1 + Rate of Return)^n
Where n is the number of years.
For the cash inflow of $900,000 at the end of the 3rd year, the present value would be calculated as:
Present Value of Cash Inflow = $900,000 / (1 + 0.10)^3
Next, calculate the present value of the cash outflow (initial investment) of $500,000. Since the cash outflow occurs at time zero, there is no need to discount it:
Present Value of Cash Outflow = $500,000
Now, subtract the present value of the cash outflow from the present value of the cash inflow:
Net Present Value = Present Value of Cash Inflow - Present Value of Cash Outflow
If the result is positive, then the rate of return assumed is higher than the actual IRR, and vice versa. Adjust your assumption of the rate of return accordingly and recalculate until the Net Present Value is close to zero.
Once you have found two rates of return between which the Net Present Value changes sign, you can use interpolation or additional calculations to find a more accurate IRR.
Note: The trial and error process can be simplified by using specialized financial software or spreadsheet functions that provide built-in IRR calculations.