Imagine you have an ice cream stand and are considering investing in a new machine.
On the initial look, it seems like a great idea. Let’s be honest; everyone loves ice cream, so the new machine always seems like a great idea.
Although your accountant might have a different opinion and quickly kill your excitement if you don’t crunch some numbers to prove that the machine is worth it in business terms.
This is where MIRR helps you determine the value of this investment by considering the cash flows you expect from the machine, the cost of financing (like a loan), and the interest you could earn if you reinvest those cash flows.
The Modified Internal Rate of Return (MIRR) calculator is designed to simplify your investment’s rate of return.
Understanding Modified Internal Rate of Return
MIRR helps you evaluate the attractiveness of an investment by focusing on realistic assumptions about reinvestment and financing. Unlike IRR, which can give multiple values for complex cash flows, MIRR provides a unique result.
Comparing MIRR and IRR
IRR assumes cash flows are reinvested at the IRR itself, which is often an unrealistic assumption.
MIRR uses distinct rates for financing and reinvestment, offering a more accurate reflection of available opportunities. IRR can generate misleading results and multiple IRR problems in non-conventional cash flows.
MIRR addresses these issues, providing a single, clear rate of return on your investment.
Modified Internal Rate of Return Formula
To calculate MIRR, you’ll need to know the finance rate (cost of investment) and the reinvestment rate (rate at which cash flows are reinvested).
Here’s the formula:
MIRR (%) = (Future Value (Positive Cash Flow) / Present Value (Negative Cash Flow))(1 / Number Of Years) - 1Where:
- Future Value (Positive Cash Flow): the future value of the positive cash flows, compounded at the reinvestment rate.
- Present Value (Negative Cash Flow): the present value of the negative cash flows, discounted at the finance rate (borrowing rate).
- Number of Years: the number of years of investment.
To calculate future value, use the following formula:
Future Value ($) = ∑(Positive Cash Flowt × (1 + Reinvestment Rate)(n−t))Where:
- Positive Cash Flowt is the positive cash flow of the current period
- Reinvestment Rate is the rate of reinvestment
- n-t where n is the total number of periods minus the current period
To calculate the present value, we will use the following formula:
Present Value ($) = ∑(Negative Cash Flowt × (1 + Finance Rate)−t)Where:
- Negative Cash Flowt is the negative cash flow of the current period
- Finance Rate is the rate of borrowing
- t is the current period
Steps to calculate MIRR:
- Calculate the present value of cash outflows using the finance rate.
- Calculate the future value of cash inflows using the reinvestment rate.
- Apply the MIRR formula.
Example Calculation
Let’s walk through a real example calculation to see how it works.
Imagine you invest $10,000 in a project that generates cash inflows over three years: $4,000 in year one, $4,500 in year two, and $5,000 in year three.
Let’s say the reinvestment rate is 5%, and the finance rate is 8%.
So, our initial inputs are the following:
- Initial Investment: $10,000
- Year 1 Cash Inflow: $4,000
- Year 2 Cash Inflow: $4,500
- Year 3 Cash Inflow: $5,000
- Finance Rate: 8%
- Reinvestment Rate: 5%
Now, let’s calculate our future and present values:
Future Value = 4,000 × (1 + 0.05)2 + 4,500 × (1 + 0.05)1 + 5,000 × (1 + 0.05)0
Future Value = 4,000 × 1.1025 + 4,500 × 1.05 + 5,000
Future Value = $14,135Present Value = 10,000 × (1 + 0.08)-0
Present Value = $10,000Having all the data for our MIRR formula, we can now plug it in to calculate the final MIRR:
MIRR = (14,135 / 10,000)1/3 - 1
MIRR = 0.12227 = 12.23%The MIRR for our project is 12.23%.
This is a pretty long calculation, isn’t it?
Using our MIRR calculator saves all the time you would have spent otherwise calculating it.