Money-Weighted Rate of Return (MWRR)

The discount rate that equates a project’s present value cash flows to its initial investment

What is the Money-Weighted Rate of Return (MWRR)?

The money-weighted rate of return (MWRR) refers to the discount rate that equates a project’s present value cash flows to its initial investment. It is used to determine the profitability of a project or investment and is used interchangeably with the internal rate of return (IRR).

Summary

• The money-weighted rate of return (MWRR) is the discount rate that equates a project’s present value cash flows to its initial investment.
• It represents the expected compounded annual rate of return on the project/investment.
• MWRR is used to determine the profitability of a project or investment and is used interchangeably with the internal rate of return (IRR).

Understanding Money-Weighted Rate of Return

In finance, the time value of money is an important concept which states that the same amount of money today is more valuable than it is in the future because money today can be invested to grow in value. Therefore, any cash flows in the future must be discounted to the present value for an accurate comparison.

As the discount rate that equates the net present value (NPV) to zero, the money-weighted rate of return represents the expected compounded annual rate of return on the project/investment. The NPV is the sum of the present value of cash inflows and outflows of the project.

The higher the money-weighted rate of return, the more valuable the project is, likewise with the net present value. Any projects with a negative MWRR or NPV should not be undertaken because they will incur a loss. When making a decision whether or not to pursue a certain project, the MWRR is often compared to a company’s cost of capital or hurdle rate.

The cost of capital refers to the weighted average cost of capital (WACC) to finance the project, and the hurdle rate is the minimum rate of return set for the project – usually the cost of capital with risk-adjusted considerations. If the MWRR is greater than these comparables, the project will increase a company’s value.

Benefits and Disadvantages of Money-Weighted Rate of Return

While both the NPV and MWRR are common tools used in comparing the profitability of potential projects, the benefit of MWRR to NPV is its ability to compare across projects of different sizes. The NPV returns a nominal value based on the magnitude of the project, while the MWRR returns a percentage that is better suited for comparisons.

The major downside to MWRR is its inherent assumption that all positive cash flows are reinvested at the same rate. It can overinflate the expected profitability of the project, so it should be taken with a grain of salt.

Another downside is the multiple solutions problem. Typically, project finance follows conventional cash flows, which involve negative cash flows at the onset (initial investment), followed exclusively by positive cash flows.

In cases of non-conventional cash flow, where cash flows bounce between negative and positive, the formula will result in multiple MWRR solutions. As such, the best option is to stick with using the NPV metric or adopting the MIRR (Modified Internal Rate of Return) formula.

Money-Weighted Rate of Return Example

The money-weighted rate of return is difficult to calculate by hand as it requires a lot of trial-and-error plugging; thankfully, there are many programs that can solve it easily, such as the =IRR() function on Microsoft Excel or Google Sheets.

An investor comes across an investment opportunity with expected cash flows, as shown above. To finance the initial investment of \$500,000, the investor can borrow at 6% interest. Should she invest?

By inputting the cash flows into Excel or Sheets and using =IRR(), we arrive at an MWRR of 30%. Since her MWRR is greater than her cost of capital (6%), the project is quite profitable and should be pursued (with consideration of other factors).

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