In this article, I will show you how to calculate and interpret the build-up method. This method is essential for determining the discount rate (aka required rate of return or capitalization rate) in absolute valuation models, such as the discounted cash flow (DCF) model. The discussion will also cover the advantages and limitations of using the build-up method for stock valuation.
Despite not being widely discussed, understanding the build-up method can be helpful for more accurate stock valuations. It allows for a more thorough and personalized risk assessment than potentially flawed approaches like the Weighted Average Cost of Capital (WACC), which is frequently employed to estimate the discount rate in stock valuations.
The Build-Up Method's Five Core Components
The build-up method is predicated on the notion that different investments carry different levels of risk, and thus, investors require a return that compensates for this risk.
The build-up method starts with a risk-free rate and sequentially adds various risk premiums to arrive at a discount rate that reflects the expected rate of return given the risk profile of the investment. The formula for the build-up method is shown below:
Build-Up Method Discount Rate = Rf = ERP + SRP + IRP + CSRP
where:
- Rf = risk-free rate
- ERP = equity risk premium
- SRP = size risk premium
- IRP = industry risk premium
- CSRP = company-specific risk premium
These five discount rate inputs to the build-up method are described further below.
Risk-Free Rate (Rf)
The risk-free rate (Rf) is the expected return on an investment that carries no risk, establishing the base level for what investors would want to earn over time. It sets the starting point for the discount rate in the build-up method, providing a benchmark that all other investments (that are not considered risk-free) should aim to exceed.
At the 2020 Berkshire Hathaway Annual Shareholders Meeting, amidst the global COVID-19 pandemic, Warren Buffett shared his perspective on why the U.S. is unlikely to default on its debt:
“If you print bonds in your own currency, what happens to the currency will be the question,” said Buffett. “But you don’t default. The U.S. has been smart to issue its debt in its own currency.”
Warren Buffet
This principle is why U.S. Treasury bonds are seen as risk-free and are used in the build-up method to establish the risk-free rate for valuations.
For the build-up method, the 20-year U.S. Treasury bond is commonly selected as the benchmark for the risk-free rate. It matches well with the long-term outlook of stock investments, offers stability over time, and is considered free of default risk. The high liquidity of U.S. Treasury bonds also means their yields are a dependable measure of the time value of money.
For reference, a live chart of the 20-year U.S. Treasury bond is provided below:
Equity Risk Premium (ERP)
The equity risk premium (ERP), also known as the market risk premium, represents the extra return investors require to invest in the stock market over the risk-free rate. This forward-looking premium is a compensation for the inherent volatility and uncertainty of the stock market.
Historically, the equity risk premium has been observed by comparing the long-term performance of stock indices, such as the S&P 500 Index, to the returns of risk-free securities. The historical average of this premium is often used as a benchmark, although it should be adjusted based on current market conditions and future expectations.
The formula to estimate the the equity risk premium would be:
ERP = Rm - Rf
where:
- ERP = Equity Risk Premium
- Rm = Expected Market Returns
- Rf = Risk-Free Rate
The chart below delineates the disparity between the S&P 500's annualized returns and the year-end rates for the 20-year U.S. Treasury over the last ~20 years:
Drawing from this dataset, the S&P 500 Index's average annualized return is 9.32%, while the 20-year U.S. Treasury's is 3.46%. The ensuing difference, 5.86% (9.32% - 3.46%), is the historical equity risk premium, signifying the additional return investors have historically required for the increased risks of stock market investment compared to risk-free government bonds.
It's critical to reiterate, however, that the expected market return (Rm) should consider future expectations, though it can be informed by historical averages. This involves adjustment in light of prevailing market conditions and future economic forecasts. Similarly, the risk-free rate (Rf) hinges on the current yield of long-term government bonds.
Adjusting the forward-looking equity risk premium entails considering current economic conditions, investor sentiment, economic indicators, company earnings predictions, and historical market performance under comparable scenarios. Additionally, potential economic or policy shifts likely to influence future markets are factored in. For example, if an economic downturn is expected to lower the S&P 500's projected returns to 8%, the equity risk premium would accordingly be adjusted to 4.54% (8% - 3.46%). This rate reflects the adjusted risk level investors associate with equity investments.
Size Risk Premium (SRP)
The size premium (SP) reflects the higher expected returns of smaller companies compared to larger ones, acknowledging their greater risk and typically lower liquidity. To establish a more comprehensive understanding and application of the size premium, we can reference the seminal work of Eugene F. Fama and Kenneth R. French, who are well-known for their multi-factor models that expand on the Capital Asset Pricing Model (CAPM).
Fama and French introduced a three-factor model that includes size as a key factor influencing stock returns. Their research indicates that, controlling for market risk (beta (β)), stocks of smaller firms have higher expected returns than those of larger firms. Specifically, Fama and French's paper titled "Common Risk Factors in the Returns on Stocks and Bonds" suggests that size and value factors capture a significant portion of the risks and returns in equities, over and beyond the market beta.
To derive a size premium, you'd start by examining historical data showing the performance differential between small-cap and large-cap stocks. A simplified expression on how one might calculate the size premium based on historical returns is shown below:
SP = Rsmall-cap - Rlarge-cap
where:
- SP = Size Premium
- Rsmall-cap = Average historical return of small-cap stocks
- Rlarge-cap = Average historical return of large-cap stocks
Comparing the annualized returns for the S&P 500 Index, commonly used as a benchmark for large-cap stocks, with the Russell 2000 Index, often used for small-cap stocks, provides a high-level overview of the size premium.
The chart below delineates this disparity over the last ~20 years:
We know the average annualized return of the S&P 500 Index is 9.32%. By subtracting this from the average annualized return of the Russell 2000 Index over the same period, which is 10.67%, we calculate a size premium of 1.35%. However, this is a preliminary estimate of the size premium and not a definitive measure.
While the concept of the size premium may seem straightforward, its practical application demands a more detailed approach than simply comparing the average historical returns between a large-cap and small-cap benchmark. Investors must analyze the specific market cap range corresponding to the firm’s decile to understand the premium's true impact. The size premium is dynamic, influenced by current market conditions and economic cycles, and must be evaluated with consideration to these factors.
Professional investors often turn to reliable databases to capture an accurate size premium that corresponds with current market conditions. For example, if the historical return for the smallest decile (10th decile) of stocks is 12%, while that for the largest decile (1st decile) is 7%, the size premium is the difference between these figures, which would be 5% (12% - 7%). This method ensures that the size premium used is grounded in the latest market realities.
For reference, two of these main databases are listed below:
- Duff & Phelps Valuation Handbook (formerly known as the SBBI Valuation Yearbook): This is one of the most widely recognized sources for size premium data. It includes a variety of charts and tables, including the size premium chart.
- Morningstar’s Ibbotson Reports: These reports often include historical size premium data and are used by professionals for valuation purposes.
Another important step is to tailor the size premium to the company's beta, ensuring it reflects the specific risk profile of the company. Beta measures how much a company's returns fluctuate relative to the overall market, offering a key metric of its systematic risk. By adjusting the size premium for beta, it aligns more closely with the company's unique risk characteristics.
Simply using the average return difference between small and large companies as the size premium can misrepresent the risk for companies that do not conform to the average small company profile. For instance, a small company with a lower beta is less risky, and using an average size premium could overestimate its risk, leading to an inflated discount rate and a potentially undervalued company.
By incorporating beta into the size premium, the premium becomes more representative of the company's unique volatility, avoiding over- or underestimation of its systematic risk. This beta-adjusted premium harmonizes with the CAPM, which correlates expected returns to beta, ensuring that valuations are more closely aligned with the company's actual market risk.
Now, here's a quick guide on interpreting beta (β):
- β < 1: Indicates the stock is less volatile than the market.
- β = 1: Implies the stock's price tends to move with the market.
- β > 1: Suggests the stock is more volatile than the market.
If our subject company has a beta of 1.2, suggesting it's 20% more volatile than the market, the size premium may be increased to reflect this greater risk. On the other hand, if the beta is 0.8, which indicates lower volatility, the size premium may be reduced.
The adjusted size premium is calculated by multiplying the historical size premium by the company's beta. If the historical size premium is 5.50% and the company's beta is 1.2, the adjusted size premium would be 6.60% (5.50% x 1.2). This adjustment ensures the valuation accurately captures the unique risk-return profile of the company, providing a more exact estimate of its value.
In conclusion, the size premium, as a critical firm-specific risk component in the build-up method, compensates for the additional risks associated with investing in smaller firms, such as higher volatility, lower market liquidity, and less diversified operations.
Industry Risk Premium (IRP)
The industry risk premium (IRP) quantifies the additional return that investors expect from investing in a particular industry over the general market. The premise is that different industries have varying levels of inherent risk due to unique characteristics and external factors influencing their operations and profitability.
Here’s a more detailed look at the IRP and what drives its estimation:
- Regulatory Environment: Industries subject to heavy regulation, like pharmaceuticals, utilities, or financial services, can have their profits and operations significantly impacted by changes in laws and regulations. These industries may warrant a higher IRP to account for the risk of regulatory changes.
- Market Volatility: Industries such as technology or biotechnology are subject to rapid innovation and product obsolescence, leading to higher market volatility. This can justify a higher IRP due to the unpredictability of returns.
- Economic Cycles: Some industries are more sensitive to economic cycles. For instance, luxury goods and construction tend to be more cyclical and may see a higher IRP during downturns.
- Competition: High levels of competition can reduce profitability and increase risk, which would be reflected in a higher IRP for such industries.
- Industry Beta: This is a measure of the volatility, or systematic risk, of an industry in relation to the market as a whole. An industry with a beta greater than one has historically been more volatile than the market, implying a higher IRP.
Professional investors often consult specialized databases, like the ones previously mentioned, to find data on industry risk premiums. They can then apply the relevant percentage directly to the industry of the target stock.
For retail investors, a more nuanced approach is recommended that involves adding a premium based on the assessed risk within an industry. For example, when evaluating a stock in a volatile sector such as energy, compared to a more stable one like utilities, you would typically assign a higher industry risk premium to the energy stock due to its greater inherent risks.
If you want to take a more sophisticated approach, you can attempt to derive an industry risk premium from beta, as described below.
Using Beta to Derive Industry Risk Premium
Beta, while a measure of volatility compared to the overall market, does not inherently quantify the additional return investors demand. Instead, it indicates the relative risk or volatility of an industry or stock. To translate beta into an expected return, and subsequently infer an industry risk premium, the Capital Asset Pricing Model (CAPM) can be utilized.
The CAPM formula is shown below:
E(Ri) = Rf + βi(E(Rm) - Rf)
where:
- E(Ri) = capital asset expected return
- E(Rm) = expected market return
- Rf = risk-free rate of return
- βi = investment beta
In this model, the risk-free rate is usually the return on long-term government securities, such as the yield on 10-year Treasury bonds, and provides a baseline for an investment assumed to be without risk. The market risk premium, (E(Rm) - Rf), is the excess return that investing in the market provides over a risk-free rate.
Now, one can refer to the dataset provided by Professor Aswath Damodaran, which details the betas of various U.S. industries. This beta dataset is particularly useful for this type of assessment.
We can use the industry beta to estimate the expected return with the CAPM formula, as the industry risk premium (IRP) would simply be the difference between the expected return and the risk-rate rate:
IRP = Expected Industry Return - Rf
This approach presupposes market efficiency and that both beta and the market risk premium remain consistent over time. However, it's important to consider that these factors are subject to change due to economic shifts, changing investor sentiment, and specific industry risks.
Let's explore a practical example. To evaluate a stock in the education sector, we would refer to Aswath Damodaran's industry-specific beta data, which indicates a beta of 1.10 for education in 2023. Assuming a market return (E(Rm)) of 10% and a risk-free rate (Rf) of 4% (in line with historical averages), the expected return according to the CAPM formula would be calculated as follows:
E(Ri) = 4% + 1.10 × (10% − 4%) --> 10.6%
The implied industry risk premium for the education industry would then be the expected industry return minus the risk-free rate:
IRP = 10.6% - 4% --> 6.6%
This 6.6% is the additional return investors might expect for the higher risk associated with the education industry relative to a risk-free investment. Remember that this figure is hypothetical and relies on the inputs being accurate and reflective of the current market conditions.
Company-Specific Risk Premium (CSRP)
The company-specific risk premium (CRSP) is the final adjustment made in the build-up approach when calculating the discount rate for a business valuation. This premium reflects the unique, non-systematic risks of the subject company that are not encapsulated by the market, size, or other risk premiums already accounted for. These risks are often idiosyncratic and could include the company's operational efficiency, the strength of its management team, or its customer and supplier relationships.
Determining the CSRP requires a deep understanding into the qualitative and quantitative aspects of the company. Factors that might influence the CSRP include, but are not limited to:
- Management Quality: The track record and expertise of the leadership team.
- Customer Concentration: Dependence on a limited number of customers.
- Supplier Dependence: Reliability and control over the supply chain.
- Operational Efficiency: Effectiveness of the company's operations.
- Financial Leverage: The extent and management of the company's debt.
The CSRP is inherently the most subjective component of the build-up method. Its accuracy is best informed by the investor's in-depth understanding of the target company and their personal judgment.
To illustrate how a CSRP might be applied, consider the following example in a table format:
CSRP Adjustment Example
By focusing on the distinct aspects of the company, the CSRP ensures that the discount rate reflects the specific risk profile of the business, separate from the general market, size, and industry risks. In this scenario, each risk factor is assessed, and a corresponding adjustment is added or subtracted from the CSRP. A negative adjustment is applied when the risk factor presents a lower risk compared to the norm, such as above-average operational efficiency. The total CSRP of +2.50% would then be added to the previous risk premiums to arrive at the total discount rate for the company.
It's important to note that this table is a simplified representation for illustration purposes. Novice investors are encouraged to enhance their understanding of risk assessment by studying a company's 10-K annual report, which can provide more precise insights into the application of appropriate risk factors.
How to Apply and Interpret the Build-Up Method Discount Rate in Stock Valuations
In absolute stock valuation methods, such as the discounted cash flow (DCF), the build-up method offers a way to estimate the appropriate discount rate for future cash flows. This rate signifies the rate of return that investors seek, aligned with the risk associated with the company being evaluated. By summing various risk premiums to a base risk-free rate, the build-up method incorporates the extra risks inherent in the investment.
After the discount rate is estimated using the build-up method, it's applied across absolute valuation models to determine the present value of expected future cash flows. This involves dividing each projected cash flow by one plus the discount rate to the power of the number of years until the cash flow will occur, repeated across the forecast horizon. The terminal value, representing all future cash flows after the forecast period, is also discounted back to the present using the same rate derived from the build-up method.
The accuracy of intrinsic value calculations in absolute valuation methods depends on the consistent application of this discount rate to all future cash flows.
For reference, the DCF intrinsic value formula is shown below:
DCF Intrinsic Value = [FCF1 / (1+r)1] + [FCF2 / (1+r)2] + .... + [FCFn / (1+r)n] + [FCFn * (1+g) / (r - g)]
where:
- FCF = free cash flow
- r = discount rate (required rate of return)
- g = growth rate
- n = time period
After applying the build-up method's discount rate, the present values of the forecasted cash flows and the terminal value are summed to determine the total intrinsic value of the company. This intrinsic value can then be compared to the company's current market valuation, and interpreted accordingly:
- Intrinsic Value < Market Value: Stock may be overvalued, which could be a sign for investors to exercise caution.
- Intrinsic Value = Market Value: Stock is likely fairly valued, indicating that the market price reflects the company's true worth as per the valuation model.
- Intrinsic Value > Market Value: Stock might be undervalued, suggesting a potential investment opportunity.
While this section provides a high-level overview of applying the discount rate in a DCF valuation, a complete example is detailed in my article 'How to Value a Company Using the Discounted Cash Flow Model.'
How to Interpret the Build-Up Method Discount Rate
In absolute valuation methods, the build-up method discount rate plays an important role by determining the present value of future cash flows and illustrating the associated investment risk.
When this rate exceeds the standard stock market return of ~10%, it suggests increased risk, mandating a correspondingly higher expected return. Conversely, a rate falling below the 20-year Treasury yield might indicate a diminished investment allure, mirroring returns similar to those of risk-free assets.
It's essential to measure each risk premium in this rate against prevailing market benchmarks to ensure a precise risk evaluation. Typically, a company with stability and a strong market stance might be attributed a lower rate. In contrast, those in volatile sectors or amidst uncertain economic conditions might see a higher rate.
Additionally, this rate should encompass facets like market benchmarks, past performance, investor outlooks, economic forecasts, inflation trends, prevailing interest rates, and the firm's fiscal standing. This comprehensive approach ensures a nuanced interpretation of the discount rate, which may help in providing a more informed and accurate valuation.
Pros and Cons of the Build-Up Method
The build-up method in stock valuation is a comprehensive approach that provides a structured way to consider the various risk components associated with an investment. However, its application to the stock market requires an understanding of its inherent strengths and weaknesses, as discussed in the sections below.
Pros of the Build-Up Method
- Customizable Risk Assessment: The method offers a detailed risk profile for individual stocks by separately identifying risk factors such as company size and specific business risks.
- Adaptable Framework: Unlike models that assume a homogeneous market, such as CAPM, the build-up method can be tailored to the distinctive aspects of the stock being analyzed.
- Transparent Calculation: It provides a clear breakdown of the discount rate, making the valuation process more transparent for analysts and investors.
- Versatile Application: While particularly useful for private companies, the build-up method can also be adapted for public companies, especially when analyzing small-cap stocks or industries with less market data.
Thus, the build-up method is particularly effective for evaluating stocks with unique risk profiles, such as small and medium-cap public companies that may not have ample market comparables. It's also beneficial in complex financial analyses where a detailed understanding of distinct risk components is required. This method shines when traditional market-based assessments fall short, providing a customized and transparent valuation process.
Cons of the Build-Up Method
- Subjectivity Risks: The inclusion of the company-specific risk premium introduces subjectivity and potential inconsistencies in valuations.
- Dependence on Past Performance: The method’s reliance on historical data may not capture future market shifts or industry changes.
- Analytical Complexity: The detailed nature of the method can result in a complex and time-consuming analytical process.
- Risk of Overestimation: There is a possibility of overstating the discount rate due to the risk of double-counting factors.
In summary, for stocks in highly efficient markets with extensive comparable data, the build-up method may be overly complex and unnecessary. It may also be less effective when the required data for accurately estimating risk premiums is not available. Additionally, for those preferring a straightforward valuation approach, the complexity and the time demand of the build-up method could be a significant drawback.
The Bottom Line
The build-up method is a nuanced approach in business valuation that incorporates distinct risk factors to determine an investment’s appropriate discount rate. It enhances the precision of valuation by considering the risk-free rate, equity risk premium, size premium, industry risk premium, and company-specific risk premium. This methodology excels in its detailed risk assessment, adaptability, and clarity in calculating the discount rate. However, challenges arise from the subjective nature of the company-specific risk premium, reliance on historical data, analytical complexity, and potential risk of overstating the discount rate.
In practice, the build-up method serves as a useful tool for value investors, particularly when valuing stocks with no direct market comparison or in fluctuating market conditions. It's also helpful in determining whether a stock is likely to outperform or underperform the historical market average annual return, which is approximately 10%, by breaking down and measuring individual risk factors. By integrating this approach with absolute valuation models, such as the discounted cash flow (DCF) model, investors can derive a valuation that thoroughly accounts for the various risks, supporting the identification of stocks that may be undervalued.