Modified Internal Rate of Return
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Modified Internal Rate of Return
GLOSSARY Modified Internal Rate of Return: A calculation method that calculates an expected rate of return on an investment by taking the present value of the cash outflows and the future value of the cash inflows.
Calculation of the MIRR Assume that we are evaluating a project that has a cost of $30,000, after-tax cash inflows of $10,000 per year for four years, and a hurdle rate of 10%. Since the cash inflows are assumed to be received at the end of each year, the cash inflows would be reinvested as shown below. Notice that the 1st year's cash inflow is assumed to be reinvested for 3 years, so we multiply it times the future value factor for 10% and year 3 (i.e., 1.331). The 2nd year's cash inflow is assumed to be reinvested for 2 years, so we multiply it time the future value factor for 10% and year 2 (i.e., 1.210). Year 3's cash inflow is invested for 1 year and year 4's cash inflow is received at the end of the 4th year, so it is not available for reinvestment since it coincides with the end of the project's life.
Years Reinvested 3 2 Cash Inflow $10,000 $10,000 Future Value Factor (at 10%) 1.331 1.210 Future Value $13,310 $12,100
Year 1 2
3 4 Total
1 0
$10,000 $10,000
1.100 1.000
$11,000 $10,000 $46,410
Now, the only question remaining is: If I invest $30,000 in an account today and receive the equivalent of $46,410 in four years, what rate would be earned on the investment? We can find the MIRR in one of two ways: 1. The trial-and-error technique that was used earlier to find the IRR. Using any discount rate, like 10%, take the present value of the $46,410 received four years from now. (This is $31,699.) Since the present value of the benefits ($31,699) is larger than the present value of the cost ($30,000), we need to use a higher discount rate, like 12%. At 12%, the present value is $29,494. Since the PVB is now less than the PVC, the MIRR is less than 12%. We now have our range: the MIRR is between 10% and 12%. We are searching for the discount rate that will cause the PVB to equal the PVC. Here is what we know so far:
Percentage Tested 10% MIRR 12% PVB $31,699 $30,000 $29,494
On the middle row, the MIRR is the discount rate that will give us a PVB equal to the PVC of $30,000. Let's call the distance between 10% and the MIRR (above) a distance of x. The ratio of this distance to the distance between the outside two numbers (i.e., 10% and 12%) should be the same for both columns. In other words,
x / 2% = x= x= x= $1,699 / $2,205 $1,699 / $2,205 * 2% 0.7705 * 2% 1.54%
If x is 1.54%, then the MIRR is 1.54% away from 10% and is larger than 10% (since we know that the MIRR is between 10% and 12%); therefore, the MIRR must be 11.54%.
2. As an easier alternate method, we can solve for the geometric mean return. a. Divide the future value of the cash inflows by the present value of the cash outflows (i.e., $46,410/$30,000) to get a value of 1.547. Notice that this is the value that $1.00 would grow to in 4 years if you invested money to earn the hurdle rate of 10%. b. Set the result to the 1/n power (where n = 4 years). If you have a y-to-the-x key on your calculator, simply enter 1.547 as the yvalue and 0.25 (i.e., 1/4) as the x-value, and solve. The result is 1.1153. c. Subtract 1.0 from the answer and place the answer (0.1153) in percentage form. The answer is the MIRR of 11.53%.
Related Topics Present Value Table (MS Word format) Future Value Table (MS Word format)
GLOSSARY Modified Internal Rate of Return: A calculation method that calculates an expected rate of return on an investment by taking the present value of the cash outflows and the future value of the cash inflows.
Calculation of the MIRR Assume that we are evaluating a project that has a cost of $30,000, after-tax cash inflows of $10,000 per year for four years, and a hurdle rate of 10%. Since the cash inflows are assumed to be received at the end of each year, the cash inflows would be reinvested as shown below. Notice that the 1st year's cash inflow is assumed to be reinvested for 3 years, so we multiply it times the future value factor for 10% and year 3 (i.e., 1.331). The 2nd year's cash inflow is assumed to be reinvested for 2 years, so we multiply it time the future value factor for 10% and year 2 (i.e., 1.210). Year 3's cash inflow is invested for 1 year and year 4's cash inflow is received at the end of the 4th year, so it is not available for reinvestment since it coincides with the end of the project's life.
Years Reinvested 3 2 Cash Inflow $10,000 $10,000 Future Value Factor (at 10%) 1.331 1.210 Future Value $13,310 $12,100
Year 1 2
3 4 Total
1 0
$10,000 $10,000
1.100 1.000
$11,000 $10,000 $46,410
Now, the only question remaining is: If I invest $30,000 in an account today and receive the equivalent of $46,410 in four years, what rate would be earned on the investment? We can find the MIRR in one of two ways: 1. The trial-and-error technique that was used earlier to find the IRR. Using any discount rate, like 10%, take the present value of the $46,410 received four years from now. (This is $31,699.) Since the present value of the benefits ($31,699) is larger than the present value of the cost ($30,000), we need to use a higher discount rate, like 12%. At 12%, the present value is $29,494. Since the PVB is now less than the PVC, the MIRR is less than 12%. We now have our range: the MIRR is between 10% and 12%. We are searching for the discount rate that will cause the PVB to equal the PVC. Here is what we know so far:
Percentage Tested 10% MIRR 12% PVB $31,699 $30,000 $29,494
On the middle row, the MIRR is the discount rate that will give us a PVB equal to the PVC of $30,000. Let's call the distance between 10% and the MIRR (above) a distance of x. The ratio of this distance to the distance between the outside two numbers (i.e., 10% and 12%) should be the same for both columns. In other words,
x / 2% = x= x= x= $1,699 / $2,205 $1,699 / $2,205 * 2% 0.7705 * 2% 1.54%
If x is 1.54%, then the MIRR is 1.54% away from 10% and is larger than 10% (since we know that the MIRR is between 10% and 12%); therefore, the MIRR must be 11.54%.
2. As an easier alternate method, we can solve for the geometric mean return. a. Divide the future value of the cash inflows by the present value of the cash outflows (i.e., $46,410/$30,000) to get a value of 1.547. Notice that this is the value that $1.00 would grow to in 4 years if you invested money to earn the hurdle rate of 10%. b. Set the result to the 1/n power (where n = 4 years). If you have a y-to-the-x key on your calculator, simply enter 1.547 as the yvalue and 0.25 (i.e., 1/4) as the x-value, and solve. The result is 1.1153. c. Subtract 1.0 from the answer and place the answer (0.1153) in percentage form. The answer is the MIRR of 11.53%.
Related Topics Present Value Table (MS Word format) Future Value Table (MS Word format)
