Every musical note has two attributes – pitch and duration. Height and duration are independent of each other. Pitch is indicated by the note’s vertical position on the staff, the key signature, and the “accidentals” placed next to the note. The duration is determined by the type of note used.

The key signature on the left side of the bow tells the musician what sharps and flats to play automatically. “Accidentals”—sharps, flats, and naturals placed to the left of a note—inform the musician of pitch deviations from the “norm” in the tonal signature.

The duration of banknotes is usually mathematical. The entire note is an open oval. A half note adds a root to a whole note and has half the duration of a whole note. A quarter note adds a tail to the stem and has half the duration of a half note. Additional tails are added to the stem to denote shorter notes.

These are not the only durations. Intermediate compositions may have triplets (three notes to every quarter note). Other divisions are less common and are usually found in more advanced music.

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

**What is Equity Multiple?**

The equity multiplier for an investment is the sum of all cash flows to the investor from the investment divided by the amount of the investor’s investment. The equity multiplier is usually reported as a ratio, such as 1.5, 2.0, etc.

Let’s say an investor has invested $100,000 in a real estate fund. The fund pays the investor $5,000 a year for five years. That’s a total of $25,000. At the end of the fifth year, the property is sold and the investor receives $175,000 of the sale proceeds. So the sum of the investor’s cash flow from the investment is $25,000 plus $175,000, which equals $200,000. To calculate the investor’s equity ratio, we divide the cash flow of $200,000 by the investor’s original investment and get an equity ratio capital of 2.0.

On the other hand, let’s assume that another investor also invested $100,000 in a real estate fund. This investor has received nothing from the investment for ten years. Then, at the end of the tenth year, the investment is sold and the investor receives $200,000. Dividing this investor’s $200,000 cash flow by the investor’s $100,000 investment gives us equity times 2.0—the same as in our first example.

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

Although the two investments have the same equity ratio, they are not equivalent. And the reason is that the equity ratio doesn’t take into account time—how long the investment is held—when it values the investment. ** **

**What is internal rate of return?**

Most people know that having $100 today is better than having $100 five years from now. People know that with inflation, $100 can buy more today than $100 will buy five years from now. Plus, if they have $100 today, they can invest the $100 and earn 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 durations. Likewise, two investments that produce the same cash flow should be valued differently based on how long the investment is held. This concept is called the “time value of money.”

The internal rate of return (IRR) is a method of calculating the return on an investment that takes into account the time value of money. The internal rate of return is expressed as a percentage that represents the effective rate of return on the investment on an annual basis.

Most people calculate IRR using the XIRR function in Excel. This function estimates the dates of all cash outflows (ie the initial investment) and the dates of all cash 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 real estate investments worth $100,000. The first investment produces annual cash flow equal to $2,000 (2% of the investment) and returns $110,000 (10% profit) to the investor over a five-year period of detention. The second investment produces annual cash flow equal to $1,000 (1% of the investment) and returns $114,000 (a 14% return) to the investor over a five-year holding period.

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

**Which is better – Equity Multiple or IRR?**

Both the equity ratio and the IRR have their place in evaluating real estate investments. Which metrics an investor uses will depend in part on the investor’s investment objectives.

Investors focused on accumulating wealth may care more about the actual amount of cash they will receive from the investment (ie, the capital ratio) than 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 most interested in how any cash received will be treated. This investor will likely want any operating cash gains to be offset by depreciation and will want the investment to hold long enough so that any gain is a long-term capital gain.

And neither the capital ratio nor the IRR assesses the risk of real estate investment. When assessing risk, an investor must consider both the inherent risk of investing in real estate of a particular asset class in a particular market and the risk that the investor’s returns will not be as expected. The former requires a thorough understanding of real estate market conditions. The latter requires an understanding of the assumptions underlying the forecasts and general economic conditions, in addition to an understanding of the local market.

**Conclusion**

Neither the pitch nor the duration of the notes create a complete musical composition. Likewise, neither the equity multiple nor the IRR provide a complete view of the investment. However, because 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 legal challenges facing businesses and real estate investors.*