IRR: Even Cash Flows
Williams and Park Accounting Practice is considering investing in a new computer system that costs $9,000 and would reduce processing costs by $2,000 a year for the next six years.
Required:
Calculate the internal rate of return, using the time value of money charts. Round your answer to the nearest whole number. Do not round your interim calculations. Do not enter the percent sign (%).
To calculate the internal rate of return (IRR) for the investment, you need to find the discount rate that will make the present value of the cash inflows equal to the initial investment of $9,000.
In this case, the cash flows are represented by the reduction in processing costs, which is $2,000 per year for six years.
To find the IRR using time value of money charts, you can follow these steps:
1. Calculate the present value of the cash inflows for each year using the discount rate.
- Year 1: $2,000 / (1 + r)^1
- Year 2: $2,000 / (1 + r)^2
- Year 3: $2,000 / (1 + r)^3
- Year 4: $2,000 / (1 + r)^4
- Year 5: $2,000 / (1 + r)^5
- Year 6: $2,000 / (1 + r)^6
2. Sum up the present values of the cash inflows.
- PV = Present Value
PV = ($2,000 / (1 + r)^1) + ($2,000 / (1 + r)^2) + ($2,000 / (1 + r)^3) + ($2,000 / (1 + r)^4) + ($2,000 / (1 + r)^5) + ($2,000 / (1 + r)^6)
3. Set up the equation to solve for the discount rate (IRR).
- PV = $9,000
- Solve for r.
($2,000 / (1 + r)^1) + ($2,000 / (1 + r)^2) + ($2,000 / (1 + r)^3) + ($2,000 / (1 + r)^4) + ($2,000 / (1 + r)^5) + ($2,000 / (1 + r)^6) = $9,000
4. Use a financial calculator, spreadsheet software, or trial and error to find the discount rate (IRR) that satisfies the equation in step 3.
Alternatively, you can use the IRR function in spreadsheet software like Microsoft Excel to calculate the IRR directly by providing the cash flows and solving for the rate.
Once you have determined the discount rate that satisfies the equation, round it to the nearest whole number, and that will be your internal rate of return (IRR) for the investment.