In this lesson, we'll explain the three different approaches to the modified rate of return. In addition, we'll compare the modified rate of return to the internal rate of return.
Modified Internal Rate of Return
The internal rate of return (IRR) is a performance metric in the form of an interest rate that is used in business to measure the attractiveness of a particular project or business investment. The higher a project's internal rate of return, the more attractive the project becomes for the business. Think of the IRR as a measure of the potential return on a project. However, the modified internal rate of return (MIRR) is a modified version of the internal rate of return and is also used to measure how appealing or lucrative an investment is to a potential investor.
When a company invests money in a project, the company usually makes an initial investment during the early phases of the project. This is negative cash flow. As the project progresses, the project will yield cash profits resulting in positive cash flow. When cash flows change from negative to positive throughout the project lifecycle, there can be several internal rates of return for each change (from positive to negative). The modified rate of return addresses the issue of multiple IRRs by accounting for the positive and negative cash flows separately.
For example, a company invests $10,000 into the creation of a new machine. Some other companies started hearing about the new machine and offered to invest as well, for a total of $10,000. During the project, the company had to invest another $15,000. The cash flow in this scenario is moving from negative to positive and back to negative again. The MIRR allows a company to determine the return on investment while accounting for these cash flow changes.
The MIRR is also useful because the conventional IRR assumes that profits are reinvested in the same project and will return the rate calculated in the IRR. This is often not realistic because maybe a project doesn't require any additional funds. The MIRR solves this problem by allowing profits to be reinvested at more realistic rates that reflect market conditions. It allows the user to set the reinvestment rate to get a more realistic result.
The MIRR solves for the limitations of the IRR and accounts for what the company does with positive cash flows when received such as reinvesting at a specific reinvestment interest rate. The MIRR also assumes a finance rate for any negative cash flows. The MIRR is used to compare projects with non-conventional cash flow methods, whereas the IRR is not useful to measure non-conventional cash flow.
The formula for the modified internal rate of return is:
FV = Future Value
PV = Present Value
n = number of periods
Calculating the MIRR
There are three different approaches to the modified internal rate of return that business analysts and investors use to review potential investment returns. The three approaches to calculating the modified rate of return are the discounting approach, reinvestment approach, and combination approach.
MIRR: Discounting Approach
Discounting cash flows of a project is the exact opposite of compounding interest on an investment. The MIRR discounting approach involves discounting all negative cash flows of a project back to the initial start of the project. The negative cash flows are discounted at an assumed finance rate.
For example, a project has an initial capital outlay of $1000 and a finance rate of 10%. The cash flow in year one is $2500, cash flow in year two at -$3000, and cash flow of $4000 in year three. We will use a reinvestment rate of 8%.
-1000 + -3000/((1.10)(1.10)) = $3479.34
$3479.34 is the sum of negative cash flow discounted to year of initial investment.
Now, for the numerator, we will calculate the future value of the positive cash flows. Since $2500 is received at the end of year one, we will find what it is worth at the end of year three at the reinvestment rate of 8%:
$2500 * 1.08 * 1.08 = $2,916
Then add the $4000 at the end of year three for a total positive return of:
$2916 + $4,000 = $6,916
Over 79,000 lessons in all major subjects
Get access risk-free for 30 days,
just create an account.
One of the disadvantages of the IRR is the method assumes cash flows are reinvested at the firm's cost of capital. However, when a project begins, the firm may not be able to find alternate investments with the same rate as the cost of capital rate. Interest rates may be higher or lower at the time cash flows are realized. With the reinvestment approach, the MIRR assumes a specific reinvestment rate and each year cash is reinvested at the same reinvestment rate.
For example, a two-year project with an initial capital outlay of $250 has a cost of capital of 14% with cash flows of $150 in year one and $200 in year two.
The reinvestment approach assumes cash flows are reinvested at the firm's cost of capital:
$150 (cash flow at year one) * 1.14 = $171 + $200 (cash flow at year two) = $371 $371 = future value of positive cash flow at the second year.
Based on the MIRR formula: MIRR = square root of ($371 / 250) - 1 = 0.2181
The MIRR equals 21.81%.
MIRR - Combination Approach
The combination approach discounts negative cash flow of a project back to the first day of the project while reinvesting positive cash flow. The combination approach is used when a project has capital outlays during the project lifecycle as well as positive cash flow at various stages of the project.
Assume a project with a capital outlay of -$2000 with a finance rate of 10% and cash flow in year one of -$3000, cash flow year two is $2300, and cash flow year three is $4000, and the reinvestment rate is 11%.
First, discount negative cash flow at the finance rate of 10%:
-2000+ -3000 / 1.10 = -$4727.27
Next, calculate future value of cash flow at the reinvestment rate of 11%:
2300 * (1.11) + 4000 = 6553
Now, calculate the MIRR using the formula:
((6553 / 4727.27) ^ 1/3) -1 = 0.115
The MIRR is 11.5%.
The modified internal rate of return provides a more realistic investment measurement. The MIRR takes into account non-conventional cash flows of a project. It is very possible for business projects to have both positive and negative cash flows over the course of the project. There are three approaches to calculate the MIRR: discounting, reinvesting, and the combination approach.
The MIRR calculations are more realistic and take into account potential changes in cash flow during a project. Each MIRR approach yields an accurate calculation based on various cash flow fluctuations. Many business leaders use the MIRR over the internal rate of return because of the accuracy and realistic outcome of each calculation.
The following exercise is designed to help students apply their knowledge on the modified rate of return.
You are the Chief Financial Officer of Yummy Feet, a company that makes gummy candies shaped like feet. The company is contemplating upgrading its manufacturing machine for candies since it came across an offer to buy a used machine that is old but can double the production levels of the company. This would allow Yummy Feet to mass produce its candies while not committing to a long-term solution. You decide to compute the Modified Rate of Return since you learned all about it in your lesson. Below are the details of the proposal:
$, %, or years
Number of years remaining
Cost of machine
Additional cash flow from extra sales, year 1
Additional cash flow from extra sales, year 2
Cost of Capital
1. Using the Discounting Approach, calculate the Modified Internal Rate of Return.
2. Using, the Reinvestment Approach, calculate the Modified Internal Rate of Return.
1. Present value of negative cash flows:
All negative cash flows are incurred in year 0, the finance rate is 12%. Therefore, the computation is:
= (50,000 + 10,000) * (1.12)^0
Future value of positive cash flows:
We need to multiply the year 1 cash flows by the reinvestment rate of 7%.
= 60,000 * 1.07 + 60,000
Calculation of MIRR:
MIRR = (124,200 / 60,000) - 1 = 3.5%
The answer is 3.5%.
2. Present value of negative cash flows:
All negative cash flows are incurred in year 0, the cost of capital is 10%. Therefore, the computation is:
= (50,000 + 10,000) * (1.10)^0
Future value of positive cash flows:
We need to multiply the year 1 cash flows by the cost of capital of 10%.
= 60,000 * 1.10 + 60,000
Calculation of MIRR:
MIRR = (124,200 / 60,000) - 1 = 5%
The answer is 5%.
Register to view this lesson
Are you a student or a teacher?
Unlock Your Education
See for yourself why 30 million people use Study.com
Did you know… We have over 200 college
courses that prepare you to earn
credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the
first two years of college and save thousands off your degree. Anyone can earn
credit-by-exam regardless of age or education level.