Each musical note has two attributes: pitch and duration. The pace and duration are independent of each other. The pitch is indicated by the vertical position of the note on the staff, by the key indication and by “accidental” placed next to the note. The duration is indicated by the type of note used.

The clef indication on the left side of the staff tells the player which sharps and flats should sound automatically. “Accidental” – sharps, flats and naturals positioned to the left of a note – inform the player of intonation deviations from the “norm” in the key signature.

Note durations are generally mathematical. A whole note is an open oval. A half note adds a stem to the entire note and is half the length of a whole note. A quarter note adds a tail to the stem and is half the length of a quarter note. Additional tails are added to the stem to indicate shorter notes.

These are not the only durations. Intermediate-level compositions can have triplets (three notes for each quarter note). Other divisions are less common and generally found in more advanced music.

The sequence of pitches is an integral part of a musical composition. But the composition is not complete without the duration of the intonation. I consider multiple equity and the internal rate of return – two metrics used to evaluate real estate investments – as similarly correlated. This article discusses how these metrics are used in real estate investing and how potential investors should use them when deciding whether to invest.

**What is the equity multiple?**

The multiple of the net assets for an investment is the sum of all the cash flows the investor receives from the investment divided by the investor’s investment amount. The multiple of equity is usually reported as a ratio, e.g. 1.5, 2.0, etc.

Suppose an investor has invested $ 100,000 in a real estate fund. The fund pays the investor $ 5,000 annually for five years. This is a total of $ 25,000. At the end of the fifth year, the property is sold and the investor receives $ 175,000 from the proceeds of the sale. Thus, the sum of the investor’s cash flow from the investment is $ 25,000 plus $ 175,000, which equates to $ 200,000. To calculate the investor’s equity multiple, we divide the cash flow of $ 200,000 by the investor’s initial investment and get an equity multiple of 2.0.

On the other hand, suppose another investor has also invested $ 100,000 in a real estate fund. That investor hasn’t received anything from the investment for ten years. Then, at the end of the tenth year, the investment is sold and the investor gets $ 200,000. By dividing that investor’s $ 200,000 cash flow by that investor’s $ 100,000 investment, we get an equity multiple of 2.0, the same as our first example.

These examples show the shortcomings of using the equity multiple to value an investment. Both of these investors doubled their money on their investments. But one doubled his money in five years and the other doubled his money in ten years.

Even though the two investments have the same capital multiple, they are not equivalent. And the reason is that the equity multiple doesn’t take into account the time – how long the investment is held – when evaluating the investment. ** **

**What is the internal rate of return?**

Most people know that having $ 100 today is better than having $ 100 in five years. People know that with inflation, $ 100 today they can buy over $ 100 they will be able to buy in five years. Also, if they have $ 100 today, they can invest $ 100 and receive interest on it, so it will be worth more than $ 100 in five years.

Two notes of the same pitch will sound different if they have different lengths. Similarly, two investments that produce the same cash flow should be valued differently based on the duration of the investment. This concept is called “time value of money”.

The internal rate of return (IRR) is a method of calculating the return on an investment that considers the value of money over time. An internal rate of return is expressed as a percentage, which represents the actual percentage return on the investment on an annual basis.

Most people calculate the IRR using the XIRR function in Excel. This function evaluates the dates of all outflows (i.e. the initial investment) and the dates of all inflows that the investor pays / receives. The XIRR function then returns the investor’s IRR as a percentage.

To see how this works, consider two $ 100,000 real estate investments. The first investment produces an annual cash flow of $ 2,000 (2% of the investment) and returns $ 110,000 (a 10% return) to the investor over a five-year waiting period. The second investment produces an annual cash flow of $ 1,000 (1% of the investment) and returns $ 114,000 (a 14% return) to the investor over a five-year waiting period.

One might think that the 14% return on the second investment is better than the 10% return on the first investment. However, the first investment has an IRR of 3.85%, compared to an IRR of 2.84% for the second investment.

**Which is better: stock multiple or IRR?**

Both the stock multiple and the IRR have their place in the valuation of real estate investments. The metrics an investor uses will depend in part on the investor’s investment goals.

Investors focused on wealth accumulation may be more interested in the actual amount of money they will receive from the investment (i.e. the multiple of the principal) than in the effective interest rate. Investors interested in tax benefits may be more interested in depreciation deductions.

A different investor in a high tax bracket may be more interested in how the money received will be treated. That investor will likely want any operating cash returns to be offset by the depreciation and will want the investment to be held long enough to make any long-term gains.

And neither the multiple of the capital nor the IRR assess the risk of a real estate investment. When assessing risk, an investor should consider both the inherent risk of investing in the real estate sector of a particular asset class in a specific market and the risk that the investor’s returns are not as expected. The first requires a deep understanding of real estate market conditions. The latter requires an understanding of the assumptions underlying the forecasts and general economic conditions, as well as an understanding of the local market.

**Conclusion**

Neither pitches nor note durations produce a complete musical composition. Likewise, neither the capital multiple nor the IRR provide a complete view of an investment. However, as these metrics are often presented side by side, investors should understand each metric and its strengths and weaknesses.

*This series draws on Elizabeth Whitman’s background and passion for classical music to illustrate creative solutions to the legal challenges faced by companies and real estate investors.*