March 02, 2015

"All values are anticipation of the future."

*Lincoln v. Commonwealth*, Justice Oliver Wendell Holmes

A basic tenet of corporate finance is the value of a business depends on investment and expected growth. Of the two factors, expected growth may be the most important since, conceptually, the expected return of an investment is equal to the sum of the cash flow yield of the investment *plus* the expected earnings growth rate.

The Gordon Growth Model is a generalized form of the Discounted Cash Flow Model, which assumes a business will grow and generate free cash flows at a constant rate. It is the basis for the Capitalization of Cash Flow Method and is generally used to calculate the terminal value when using the Discounted Future Cash Flow Method. The Gordon Growth Model determines value by multiplying the current year’s cash flows (in the case of the Capitalized Cash Flow Method) or the terminal year’s projected cash flows (in the case of the Discounted Future Cash Flow Method) by a capitalization factor, the formula of which is presented below:

**Capitalization Factor = (1+g )/(k-g )
**

The chart presents for different cost of capital ranging from 5 percent to 25 percent the change in the Capitalization Factor as the constant growth rate increases from -1.0 percent to 10.0 percent. As indicated in the chart, the Capitalization Factor is sensitive to changes in the constant growth rate, and such sensitivity is inversely related to the cost of capital.

The constant growth rate selected to value a business should reflect the company’s long-term sustainable growth rather than what is projected for the short term. Factors to consider when determining a firms’ constant growth rate include the following:

- the firm’s historical growth rate
- management’s growth expectations and goals
- the company’s ability to achieve growth
- the enterprise’s borrowing power
- the projected growth rate of the industry and the economy
- the economic environment

*The Long-Term Growth Rate of the Economy*

An economy’s long-term growth rate is comprised of two elements: expected inflation and expected real growth. The following presents several sources that are readily available and free that an appraiser may consider when estimating the forecasted long-term growth rate of the U.S. economy.

*Sources of Inflation and GDP Growth Forecasts*

*Surveys of Economic Forecasts*

*The Livingston Survey. The Livingston Survey *is the oldest continuous survey of economists’ expectations. Published twice a year, in June and December, the* Livingston Survey *summarizes the forecasts of economists from industry, government, banking, and academia.

In each issue, *Financial Valuation and Litigation Expert *presents the 10-year forecasts as reported in the *Livingston Survey *for inflation and real gross domestic product (GDP). In the December 2014 edition, the *Survey’s *panelists forecasted for the next 10 years that real GDP would grow 2.50 percent annually and that inflation as measured by the Consumer Price Index (CPI) would average 2.25 percent per year.

*Survey of Professional Forecasters . *The Philadelphia Fed also compiles the

*Government Agencies*

*Congressional Budget Office.* The Congressional Budget Office (CBO) is a federal agency within the legislative brand of the United States government that provides budget and economic information to Congress. The CBO’s mandate is to provide Congress with objective, nonpartisan, and timely analysis to aid in economic and budgetary decisions. Each year, the CBO issues *The Budget and Economic Outlook*, which is CBO’s outlook for the budget and the economy, and a midyear update. In* An Update to the Budget and Economic Outlook: 2014 to 2024*, the CBO projects that GDP will grow at 3.00 percent per year from 2015 to 2024, and that inflation, as represented by changes in the Consumer Price Index, will increase by 2.34 percent per year from 2014 to 2024.

*Office of Management and Budget.* Each year, the President submits to the Congress his budget for federal expenditures for the following fiscal year. The *Budget of the United States Government* contains the President’s budget message, information about his budget proposals, and other budgetary publications. The budget is based on five-year projections of key economic variables developed by the Office of Management and Budget (OMB). The Fiscal Year 2015 *Budget of the United States Government *was released March 4, 2014 and the Fiscal Year 2015 Mid-Session Review was delivered to Congress on July 11, 2014. The budget was based on economic assumptions available as of late-May 2014. The OMB forecasts that real GDP will grow from 2014 to 2024 at an annual rate of 2.6 percent and inflation, represented by the GDP chained price index, will increase at 2.0 percent per year.

*Social Security Administration.* Each year the Board of Trustees of the Old-Age Survivors and Disability Insurance program (OASDI or Social Security) are required by law to report on the financial status of these programs. The annual reports are released each year in the spring. The Trustees Report includes projections of annual revenues and expenditures based on assumptions regarding real GDP growth, inflation, and several other economic indicators that are developed by the Office of the Chief Actuary of OASDI. The Trustees Report includes three projected estimates to highlight the range of possible outcomes. These estimates are referred to as Intermediate or Best Guess estimates, High Cost, and Low Cost estimates. *The 2014 Annual Report of the Board of Trustees of the Federal Old-Age and Survivors Insurance and Federal Disability Insurance Trust Funds* was published July 28, 2014. The chief actuary’s intermediate forecast for real GDP is to grow by 2.7 percent per year from 2014 to 2024 and for the CPI to change over the 10-year period at an average rate of 2.13 percent per year.

*Federal Reserve Bank of Cleveland. *Each month the Federal Reserve Bank of Cleveland releases its estimate of long-range inflation expectations. These estimates of long-range inflation are based on a model developed by economists at the Cleveland Fed, which combines information from a number of sources. On January 16, 2015, the Cleveland Fed reported its latest estimate of 10-year expected inflation to be 1.66 percent.

*Treasury **Securities*

In both the Capital Asset Pricing Model and the build-up method, the yield on Treasury bonds is often used as the proxy for the risk-free rate used to determine the cost of capital. The yield on Treasury bonds, also referred to as the nominal interest rate, is comprised of two elements: the expected real rate of interest and the expected inflation rate. The real rate of interest is the return an investor requires in order to forego current consumption for future consumption.

Economic theory holds that the nominal rate of interest should approach the expected overall growth rate for the economy. Therefore, the yield on Treasury bonds should represent the expected nominal growth rate of the economy over a comparable term. For the week ending October 10, 2014, the average yield on the 20-year Treasury bond was 2.82 percent.

The yields on Treasury Inflation-Protected Securities (TIPS) are a source for determining the real rate of interest. The U.S. government first issued TIPS in 1997. TIPS are securities whose principal is adjusted every six months for changes in the Consumer Price Index. The coupon rate on TIPS is constant, but generates a different amount of interest when multiplied by the inflation-adjusted principal.

Comparing the yields on TIPS to the yields on Treasury bonds with similar maturities should yield the expected inflation rate over the period. The term *breakeven inflation rate *(the BEI) refers to the expected rate of inflation based on the relationship between the yield on Treasury bonds and TIPS. A simple method to calculate the BEI is to subtract the yield on a TIPS from the yield of a Treasury bond with the same maturity. For the week ending October 17, 2014, the average yield on 20-year TIPS was 0.64 percent and the average yield on 20-year Treasury bonds was 2.67 percent, yielding a breakeven inflation rate of 2.03 percent.

Adjustments to TIPS for changes in the CPI incorporate a 2 ½ month lag. For example, adjustments to TIPS effective April 1 are based on CPI published for January. In periods where there are significant changes in the inflation expectations, this lag could affect the pricing of TIPS.

The breakeven inflation rate has two components: expected inflation and an inflation risk premium. The inflation risk premium is inherent in nominal Treasury bonds, since Treasury bondholders expect a premium to protect them from the risk that actual inflation may deviate from real inflation. According to the Federal Reserve Bank of San Francisco (FRBSF), the inflation risk premium causes the breakeven inflation rate to overstate inflation.

The FRBSF also found that the breakeven inflation rate understates inflation because TIPS yields include a liquidity premium. The market for TIPS is less than 10 years old and smaller than the market for nominal Treasury bonds. A study of breakeven inflation rates from 1998 to 2004 found the breakeven inflation rates had increased over the period. According to the FRBSF, the increase probably was due to artificially low breakeven rates when TIPS were first introduced. The FRBSF hypothesized the liquidity premium in TIPS had declined as the market for TIPS has grown yielding higher breakeven inflation rates. The FRBSF expects that as the market for TIPS matures, the inflation risk premium and the liquidity premium will become constant.

The Federal Reserve Bank of Kansas City (FRBKC) concurred, noting that if current trends continue, TIPS should become more liquid and the liquidity premium should gradually decline. As a result, the breakeven rate will more closely approximate market inflation expectations. However, the FRBKC cautions that breakeven inflation may never be a perfect measure of expected inflation because both the inflation risk premium and the liquidity premium may still vary over time. The FRBKC advises that to derive the best estimate market expectations of future inflation, one should combine the breakeven inflation rate with other information.

Yields on both Treasury bonds and TIPS are available from the Federal Reserve in the Federal Reserve Statistical Release H.15: Selected Interest Rates.

*Historical Rates.* Some appraisers consider historical rates of inflation and real GDP growth when estimating the economy’s long-term growth rates. For example, in the now defunct Ibbotson Cost of Capital Yearbook, the authors determined the long-term estimate of nominal growth by combining the historical real GDP growth rate with the BEI. The table below summarizes the findings described previously.

*Reasonable Ranges of a Constant Growth Rate*

For mature companies in mature industries, it is generally accepted that the constant growth rate will most likely fall between the expected rate of inflation and the expected rate of nominal growth of the underlying economy. The expected inflation rate is considered the floor as it is believed a mature company should be able to increase prices at the rate of inflation even if/when its unit sales are not growing. The economy’s nominal growth rate is considered the cap of the constant growth rate because a company that is growing in perpetuity at a rate greater than the economy will at some point be larger than the economy in which it operates.

Very few companies last forever, as assumed in the Gordon Growth Model. “Over the last 50 years, the average lifespan of S&P 500 companies has shrunk from around 60 years to closer to 18 years.”^{1} The assumption a company will grow at least at the rate of inflation is valid if the business is profitable and does not have a risk of insolvency^{2} or some other indicator of a limited life. Examples of businesses with limited lives include solo professional practices and “mom-and-pop” businesses which rely heavily on the owner of the business for generating revenue and most likely will cease upon the death of the owner.

For companies with an expected limited life or a risk of insolvency, the constant growth rate assuming perpetual life can be adjusted for the risk of such event. The formula to calculate the constant growth rate adjusted for the probability a company will default or cease operations is as follows:^{3}

^{}**g' = (1+g ) (1-p )-1
**

For a business with a known average expected life, the probability of the company ceasing operations is the inverse of the average expected life.

The constant growth rate can be negative. A negative constant growth rate implies that a firm is being liquidated over time or has a limited life. It may be the best choice when an industry is being phased out because of technological advances or structural changes in the economy. A negative constant growth rate will also be applicable for companies where the probability of ceasing operations in any given year is greater than the constant growth rate assuming a perpetual life.

Since the riskless rate should represent an economy’s expected nominal growth rate, some use the rule of thumb that the constant growth rate used should not exceed the riskless rate used in the valuation. However, some firms can be expected to achieve growth rates above the economy’s long-term nominal growth rate for a significant period of time. When valuing such a firm, it may be more effective to use a multi-stage discounted cash flow model.

If the temporary high-growth period is expected to extend into the constant growth period, a premium can be added to the economy’s forecasted long-term growth rate to reflect above-average growth in the initial years. However, the amount of premium that can be added is limited. Some commentators suggest that a firm’s perpetual growth rate cannot be more than 1 percent or 2 percent above the economy’s forecasted long-term growth rate because of the sensitivity of the Gordon Growth Model to the constant growth factor.

However, it is possible for a constant growth rate to be greater than the expected growth rate of the economy for several years, particularly with a business with limited competition. The impact of the terminal value, and inherently the constant growth rate, on the value of a business decreases (increases) as the cost of capital increases (decreases) and as the number of periods until the firm is assumed to achieve constant growth increases (decreases). The further out in time the constant growth period, the less impact the constant growth rate will have on the present value of the capital growth factor. In addition, the greater cost of capital, the less sensitive the indicated value is to the terminal value and the constant growth rate.

*Conclusion*

The economy’s expected long-term growth rate is one of the factors to consider when estimating a firm’s constant growth rate. Other factors to consider when selecting the constant growth rate include the underlying characteristics of the subject entity, its industry, and its future. The sources listed above are just a few of the resources available to estimate the expected inflation rate and expected real growth rate of the U.S. economy. Generally, the constant growth rate for most businesses will fall between the forecasted rate of inflation and the economy’s expected nominal growth rate. However, depending on the facts and circumstances, it may not be unreasonable for the selected constant growth rate to be outside the generally accepted range to reflect a certain period of higher growth.

This article was published in the March 2015 Issue of *Financial Valuation and Litigation Expert *Newsletter*.*

**Contact the author:**

Lindsey D. Lee, CPA/ABV*, CFA, ASA

ldleehou@outlook.com

^{1} Eric Knight, “The Art of Corporate Endurance,” April 2, 2014, https://hbr.org/2014/04/the-art-of-corporate-endurance.

^{2} See Global GT LP v. Golden Telecom, Inc., 993 A.2d 497, 522 (Del.Ch. 2010) citing Peter A. Hunt, Structuring Mergers & Acquisitions: A Guide to Creating Shareholder Value, (2009) and Shannon P. Pratt & Alina V. Niculita, Valuing a Business: The Analysis and Appraisal of Closely Held Companies (5th ed. 2008).

^{3} Gary Schurman, “Schurman FLPERP Model – Giving a Perpetuity a Finite Life,” July 2011, http://www.appliedbusinesseconomics.com/webmain.htm. Then click on The Classroom.