## Family Law Newsletter

### Family Law Newsletter Summer 2013: Understanding Discount Rates and Capitalization Rates When Using in the Income Approach

**By Stephen J. Bravo, Apogee Business Valuations, Inc.**

*The author wishes to thank Michael Mattson for his assistance and insights with this article.*

*What is the income approach?*

The income approach is widely used in valuing closely-held businesses. At its essence, the value of a business is the present value of future benefits – usually earnings, cash flows, or dividends – that accrue to the owner. These future benefits represent what remains after all expenses, working capital needs and other expected obligations have been taken into account, and what remains, can be distributed to the owner without negatively affecting the future operations of the business.

The income approach is defined as a general way of determining a value of a business by using one or more methods through which anticipated (future) benefits are converted into value.[1] This approach requires the appraiser to determine the “anticipated benefits” to be discounted or capitalized to provide the value indication. This approach also requires the appraiser to determine the appropriate discount rate or capitalization rate to be applied to each future benefit.

Capitalized future earnings methods apply a capitalization rate to the earnings (cash flows) expected in the next year. They are most useful when current operations are indicative of future operations and stable growth is expected in the future. Discounted future earnings (cash flows) methods apply a discount rate to earnings projections for a period of years/periods. They are most useful when future operations are expected to be substantially different from current operations and growth is not expected to be stable—as when high growth rates are expected in the near term and lower growth rates are expected in the long term.

*What is a capitalization rate? *

- A capitalization rate is used to arrive at an estimate of the business being valued.

- It is used when future cash flows are expected to be stable and sustainable.

- It is a divisor in the formula:

- It is the rate which equates an economic income stream with value.

- It is used with a single year’s economic income.

- It is not an interest rate.

- It is not a discount rate.

- It is a rate that must match the economic income stream being capitalized. For example:

- If “net income” is determined by the appraiser to be the appropriate income stream then the capitalization rate must be computed using a discount rate that represents only net income rates of return and a growth rate that only represents expected growth in net income

- If “EBITDA” (earnings before interest, taxes, depreciation and amortization) is determined to be the appropriate income stream then the capitalization rate must be computed using a discount rate that represents only EBITDA rates of return and a growth rate that only represents expected EBITDA growth.[2]

- Example of determining a value using a single year’s economic income and a capitalization rate:

Company X’s most recent year’s cash flow is $100,000. This contains a one-time extraordinary gain on a sale of an asset of $10,000. Next year’s *sustainable* cash flow is expected to be 5% higher than this year’s. Company X’s capitalization rate is determined to be 12%. The value of Company X is computed as:

*How does the capitalization rate relate to a discount rate?*

- A capitalization rate is equal to the discount rate less a growth rate. The computation is:

*Discount Rate – Growth Rate = Cap Rate*

- It is only when the expected long-term growth is zero that the capitalization rate and discount rate equal one another.

*What is a discount rate?*

- It represents expectations about (future) investment rates.

- It is the rate of return investors require for investing in a particular asset – given its expected life and its risks.

- It incorporates the risk of the business being valued.

- It incorporates both cash income – i.e. dividends, interest payments and other forms of distributions – and capital gains and losses.

- It incorporates the time value of money (inflation and inflation uncertainty).

- It is used to reduce future earnings to their present value equivalent.

- Some other expressions commonly used to describe a discount rate are shown below.

- Expected rate of return
- Rate of return
- Cost of capital
- Return on capital (either “equity cost of capital” or “weighted average cost of capital, ” a.k.a. “WACC”)
- Investment rate

- A typical income approach model incorporating the discount rate (*r*) is:

Where:

CF_{i } is the expected cash flow for the i^{th} period;

r is the discount rate;

Cap Rate is the capitalization rate

g is the growth rate; and

n is the number of forecast periods.

Note: The last period (the “residual period”) is where the business is assumed to have stable, sustainable future cash flows and it is where the capitalization rate is used to value the business from that point into the future (into perpetuity).

- Example of determining a value using a multi-year discounted cash flow method:

Here, a discount rate is used to present value multi-year economic income and to present value the residual period. The residual period requires using a single-year capitalization of earnings and a capitalization rate:

Company Y’s most recent year’s cash flow is $100,000. This contains a one-time extraordinary gain on a sale of an asset of $10,000. Next year’s *sustainable* cash flow is expected to be 7% higher than this year’s, followed by 5% and 3% thereafter. Company Y’s discount rate is determined to be 15% (with a residual capitalization rate of 12% (15% less 3%)). The value of Company Y is computed as:

Note: this example assumes the cash flows are available throughout the year so the mid-year convention is used to determine the present value factor.

*What is a growth rate?*

- It is the average growth rate of future benefits into perpetuity (forever).

- It is used when the business being valued is expected to continue as a going concern with no expectation of being liquidated.

*Since the discount rate must be computed first, how is developed?*

- Expected rates of return cannot be directly observed in the market, so models are used to develop a discount rate.

- The models are, in large part, based on empirical data.

- Two models often used to develop an equity cost of capital are:

- Build-up
- Capital Asset Pricing Model (CAPM)

Note: The models described here are used to develop an *equity* discount rate which is the rate of return required to attract investors to fund an equity investment (like a business).[3]

- Build-up

- This model states that the cost of equity capital is a function of the current market risk-free rate of return (U.S. Treasury bonds), plus an equity risk premium, plus a size premium, plus a company-specific premium (if appropriate). The model is commonly expressed as:

* K _{e} = R_{f} + ERP + SS + *a

- CAPM

- This model states that the cost of equity capital is a function of the current market risk-free rate of return (U.S. Treasury bonds), plus an equity risk premium adjusted by the stock’s beta, plus a size premium, plus a company-specific premium (if appropriate).[4] The model is commonly expressed as:

* **K _{e} = R_{f} + *

*β*

*×ERP + SS +*a

*Where are these rates of return obtained from?*

- Two standard sources are Morningstar Inc.’s *Ibbotson* *SBBI Valuation Yearbook* and Duff and Phelps’s *Risk Premium Report*. There are other sources as well*.*

- Both sources use data obtained from the Center for Research in Security Prices (CRSP) at the University of Chicago, Booth School of Business.

*The Build-up and CAPM models look to be very similar. Why is it that some risk premium components are the same and others are different? *

- Both models require a risk-free rate of return which is generally obtained by using the yield on the long-term (20-year) U.S. Treasury bond as of the valuation date. Any risky investment should return at a minimum the “risk-free” rate associated with this government bond. The 20-year bond serves as a proxy for the going concern assumption that the business will continue into perpetuity.

- Both models require an equity risk premium (ERP), which is computed as the large company stock total return minus the long-term government bond income return. Here, the CAPM modifies the ERP by taking into account expected movement of the value of the business compared to how the overall stock market is performing. The Build-up does not explicitly apply this “beta” but, rather attempts to capture price movement in other ways.

- Both models require a size premium, but it would be a mistake to use the same size premium for the Build-up and CAPM. Using the *Ibbotson SBBI Valuation Yearbook*, the build-up size premium should be computed as the arithmetic mean return of the 10^{th} (smallest) decile less the average return on the S&P 500 (representing the largest companies).[5] Using this “small in excess of large” return is a good assumption because it captures the entire small stock portfolio. This should be the typical starting point because most companies being valued are at least as small as many of the publicly traded companies included in the 10th decile. The appraiser can then decide to “build up” any more risk, if appropriate. The *Duff and Phelps* data does this too (although not identically). The CAPM size premium is explicitly provided for in the *SBBI Valuation Yearbook* and should only be used if employing the CAPM model. Often times we see the CAPM size premium applied when using the build-up model. This is a mistake because it does not capture the entire small stock size premium. Alternatively, when using the build-up model some appraisers will include an “industry risk premium” that became available with the *2001* *Ibbotson SBBI valuation Yearbook. * Care should be given before to applying this because often times there are very few companies used to calculate the risk premium (less than 10).

- The company specific risk (CSR) premium may also be added in both models to account for additional risk inherent in the business being valued that is not captured in any of the previous risk premiums. Some practitioners have developed quantitative methods for determining the CSR; however, the appropriateness of these methods is being vigorously debated in the appraisal industry. Most commonly, the CSR is entirely based on the opinion of the appraiser.

** **

** **

*After the discount rate is developed, how is the long-term growth rate determined?*

* *

- Generally, long-term growth expectations should consider the following:

- Industry analysts’ estimates for the first 3-5 years

- Longer-term industry forecasts

- Long-term economic forecasts

- Appraisers judgment based on all relevant information

* *

*If you had to sum it all up, what are the important conceptual underpinnings of an equity discount rate and capitalization rate?*

- Estimating the future expected rate of return is essential to valuing a business using the income approach.

- The rate of return is market driven and represents the return needed to attract investors to the investment rather than to an alternative investment. This rate of return is a function of the risks of the investment and not of the investor.

- Models used to estimate the discount rate can include both empirical and subjective premium components – the latter should be based on common sense, informed judgment and reasonableness (hall mark factors discussed in Revenue Ruling 59-60).

*Stephen J. Bravo is President and founder of Apogee Business Valuations, Inc. The firm performs business appraisals for purposes such as income taxes, estate & gift taxes, arbitration, shareholder litigation, divorce, mergers & acquisitions, and reviewing the quality of another appraisers work.*

*Mr. Bravo is an Accredited Senior Appraiser (ASA) of the American Society of Appraisers, Business Valuation. He is an Accredited Business Valuator (ABV) with the AICPA, and is a Certified Business Appraiser (CBV) with The Institute of Business Appraisers, Inc. Mr. Bravo is a Certified Public Accountant, a Certified Financial Planner (Institute of Certified Financial Planners), a Personal Financial Specialist (American Institute of Certified Public Accountants), and Notary Public. Mr. Bravo has a Master of Science in Taxation from Bentley College and his Bachelor of Science in Business Administration from Suffolk University. *

*Mr. Bravo is a technical editor of many business valuation books written entirely, or in part, by Dr. Shannon Pratt and Roger Grabowski, such as Valuing A Business, Cost of Capital, Business Valuation Body of Knowledge, Market Approach to Valuing Businesses, Business Valuation Discounts and Premiums, and Standards of Value: Theory and Applications. *

*He is on the editorial boards of Business Valuation Review published by the ASA, and Business Appraisal Practice published by the IBA, and is on the Panel of Experts published by Financial Valuation & Litigation Experts.*

[1] American Society of Appraisers, ASA Business valuation Standards, BVS-IV Income Approach to Business Valuation.

[2] Converting discount rates and growth rates based on different income streams is beyond the scope of this article.

[3] An invested capital discount rate using a weighted average cost of capital (WACC) can also be used to value a business. It requires a debt rate and an equity discount rate. A discussion of WACC and invested capital is beyond the scope of this article.

[4] Beta is the relationship between the rate of return on an individual stock and the rate of return on the entire stock market. The rate of return on the entire stock market is usually measured by a broad market index like the S&P 500 stock composite index.

[5]The Ibbotson SBBI Valuation Yearbook segregates stock returns into deciles by size, as measured by the market value of common equity. The NYSE/AMEX/NASDA index is a broad value-weighted index that measures the performance of New York Stock Exchange, American Stock Exchange companies in addition to those companies traded on the NASDAQ system.