What is the IRR of the following set of cash flows? Year Cash Flow0 –$9,503 1 4,300 2 5,500 3 3,900 Multiple Choice22.11%21.06%20.01%20.64%21.48%
Question
What is the IRR of the following set of cash flows? Year Cash Flow0 –$9,503 1 4,300 2 5,500 3 3,900 Multiple Choice22.11%21.06%20.01%20.64%21.48%
Solution 1
The Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) of a project zero. In other words, it is the expected compound annual rate of return that will be earned on a project or investment.
Here are the steps to calculate the IRR:
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Set the NPV equation. The general form of the NPV formula is: NPV = ∑ [Ct / (1+r)^t] - C0, where:
- Ct is the net cash inflow during the period t
- r is the discount rate
- t is the number of time periods
- C0 is the initial investment
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In your case, the equation would be: 0 = -9503 + 4300/(1+r) + 5500/(1+r)^2 + 3900/(1+r)^3
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Unfortunately, this equation cannot be solved algebraically for r. You will need to use either a financial calculator or software (like Excel) to find the IRR.
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In Excel, you can use the IRR function. Enter the cash flows in a single row or column, and then use the IRR function with the range of the cash flows as the argument.
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The IRR function in Excel will give you the rate of return that makes the NPV zero.
The correct answer will be one of the multiple choice options you provided. Without a financial calculator or Excel, it's not possible to solve for the exact IRR from the information given.
Solution 2
The Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) of a project zero. In other words, it is the expected compound annual rate of return that will be earned on a project or investment.
Here are the steps to calculate the IRR:
-
Set the NPV equation. The general form of the NPV formula is: NPV = ∑ [Cash inflow / (1 + r)^n] - Initial Investment, where r is the rate of return, n is the period number.
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In this case, the equation would be: 0 = -9503 + 4300/(1 + r) + 5500/(1 + r)^2 + 3900/(1 + r)^3
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Solve the equation for r. This is typically done through trial and error or using a financial calculator or software.
Unfortunately, I can't solve this equation directly because it's a cubic equation and requires numerical methods to solve. However, you can use Excel's IRR function to find the IRR.
In Excel, you would enter the cash flows into cells (for example, A1 to A4), with the initial investment as a negative number. Then in another cell, you would type the formula =IRR(A1:A4)*100 to get the IRR as a percentage.
The answer should match one of the multiple-choice options you provided.
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