Cost of Capital: Advanced Topics
READING 17
COST OF CAPITAL: ADVANCED TOPICS
EXAM FOCUS
This reading focuses on estimation of companies' cost of capital. Understand the qualitative factors that influence the risk premiums on debt and equity, and how the equity risk premium (ERP) is calculated based on historical data or on forward-looking estimates. Finally, understand the complications involved in estimating the cost of capital for privately held and international companies.
WARM-UP: WEIGHTED AVERAGE COST OF CAPITAL
The weighted average cost of capital (WACC) for a company is calculated as:
WACC = wD × rD × (1 - Tc) + wE × rE
where wD and wE are the weights of debt and equity in the firm's target capital structure, rD is the pre-tax cost of debt, Tc is the marginal tax rate (so rD × (1 - Tc) is the after-tax cost of debt), and rE is the required return on equity.
We consider the after-tax cost of debt if the interest expense is tax-deductible (use the company's marginal tax rate).
Professor's note: The weights in the equation above should be the company's target weights. Unless told otherwise, assume that current market value-based weights reflect the company's target capital structure.
MODULE 17.1: FACTORS AFFECTING THE COST OF CAPITAL AND THE COST OF DEBT
LOS 17.a: Explain top-down and bottom-up factors that impact the cost of capital.
Top-down (i.e., external or macro) factors include:
- Capital availability. Economies with plentiful capital availability will have lower costs of capital. Developed economies with established, liquid capital markets tend to have more stable currency values and better investor protections (rule of law), and accordingly greater capital availability compared with developing economies. In some less-developed countries that lack corporate debt markets, businesses must rely on bank lending or a shadow banking system of unregulated, non-bank sources.
- Market conditions. Factors include inflation, interest rates, and the state of the economy. Lower expected inflation leads to lower nominal risk-free rates. Risk premiums on both debt and equity shrink during economic expansions and rise during contractions. Transparent and predictable monetary policies in developed economies reduce risk premiums and interest rates. Countries with higher currency volatility must offer higher risk premiums to risk-averse investors.
- Legal and regulatory considerations; country risk. Common law jurisdictions tend to offer stronger investor protections, leading to lower risk premiums than civil law jurisdictions.
- Tax jurisdiction. Tax codes affect the deductibility of interest. All else equal, higher marginal tax rates increase the tax benefit of using debt in capital structure.
Bottom-up (i.e., company-specific) factors include:
- Business or operating risk. Volatility in revenues, earnings, and cash flows measures business risk. Businesses with stable revenues (utilities, subscription services) are less risky than cyclical businesses. Customer concentration raises risk. Use of debt increases financial leverage and the volatility of earnings and cash flows. Poor corporate governance and high ESG risks increase required risk premiums.
- Asset nature and liquidity. Company assets are collateral for debt servicing in liquidation. Tangible, non-specialized, liquid assets increase expected recovery rates and lower risk premiums. Specialized assets and intangibles (goodwill, patents, proprietary processes) lack liquid markets and lower recovery rates. Designating assets as collateral reduces cost of secured debt but may raise cost of subordinated unsecured debt because their claims become inferior.
- Financial strength and profitability. Higher profitability, stronger cash generation, and lower leverage reduce default probability and lower risk premiums. Analysts use leverage ratios such as debt-to-equity or debt-to-EBITDA.
- Security features. Embedded options affect cost: a callable bond increases the issuer's borrowing cost because it is less desirable to investors; a put option or conversion feature reduces the current borrowing cost. Cumulative preferred stock (accumulates missed dividends) has lower risk premium than noncumulative preferred stock. Classes of common equity with superior rights have lower cost than classes with inferior rights.
LOS 17.b: Compare methods used to estimate the cost of debt.
LOS 17.e: Estimate the cost of debt or required return on equity for a public company and a private company.
Estimated cost of debt is affected by whether debt is publicly traded, credit rated, and the currency of issuance.
Publicly Traded Debt
If the company's debt is publicly traded, the yield to maturity (YTM) on the longest-maturity straight debt outstanding generally provides the best estimate of the cost of debt. If the longest maturity security is thinly traded and a shorter-maturity security has reliable market prices, use the more liquid maturity instead.
Non-Traded or Thinly Traded Debt
If debt is not traded or thinly traded, matrix pricing can be used: obtain yields on traded securities with similar maturity and credit rating, and infer the yield. If debt is not rated, use financial ratios (interest coverage, leverage) to infer a credit rating and then apply typical spreads for that rating. When using issuer ratings, recognise that a particular series of debt may have a different rating depending on seniority and security.
Example: Cost of debt using matrix pricing
Brevis Solutions is a technology provider for the healthcare sector. Sunil Tilak, CFA is estimating the cost of debt, which represents 30% of Brevis' capital structure. The 6-year, BB rated debt is thinly traded. Tilak collects data on similar BB rated securities that have liquid markets.
Estimate the cost of debt using the matrix method.
Answer:
First calculate the YTM of each of the four comparable securities.
Using a financial calculator for Listor:
PV = -114
N = 7
PMT = 8
FV = 100
CPT I/Y = 5.53%
We then construct a matrix of maturity and coupon rates and calculate average yields for each maturity to estimate yields for the target maturities.
Finally, use linear interpolation to determine the YTM for a 6-year bond as follows:
interpolated yield = yieldshort + [(yieldlong - yieldshort) / (maturitylong - maturityshort)] × (maturityinterpolated - maturityshort)
= 5.33% + [(5.39 - 5.33) / (7 - 4)] × (6 - 4)
= 5.33% + (0.02% × 2)
= 5.37%
In many countries, bank debt is the primary source of debt capital. Because we are interested in the marginal cost (the cost of a new bank loan), the rate on existing debt may not be a good estimate if firm characteristics or general interest rates have changed.
Leases
Finance (capital) leases can be used to estimate cost of borrowing. The rate implicit in the lease (RIIL) is the implied cost of capital and is the IRR that satisfies:
PV of lease payments + PV of residual value = Fair value of leased asset + Lessor's initial direct cost
If lease terms are disclosed, calculate RIIL directly. If not, the incremental borrowing rate (IBR) - the rate on a new secured loan of similar term - can be used.
Example: Capital lease
Company A has signed a 15-year lease on an asset, calling for annual payments of $10 million at year-end. The lease residual value is $30 million. The fair value of the asset is $120 million, and the lessor incurs a cost of $5 million at lease initiation.
Calculate the RIIL for this lease.
Answer:
Using a financial calculator:
Fair value of leased asset + lessor's initial direct cost = 120 + 5 = 125 → PV = -125
N = 15
PMT = 10
FV = 30
CPT I/Y = 4.28%
Thus, the rate implicit in the lease (RIIL) is 4.28%.
International Considerations for Debt
For foreign borrowers, include a country risk premium (CRP). A country risk rating reflects economic, political, exchange-rate, and capital market development risks. Country ratings can mirror debt ratings (AA, BBB, etc.) or be numerical. One practical measure of CRP is the median yield difference between sovereign debt of the country and a benchmark (benchmark country) government security. For example, if Country A is the benchmark (CRP = 0), and Country C's median interest rate is 6.80% vs benchmark 4.20%, then Country C's country risk premium is 6.80% - 4.20% = 2.60%.
Figure 17.1: Country Risk Premium
MODULE 17.2: ERP AND THE COST OF EQUITY
LOS 17.c: Explain historical and forward-looking approaches to estimating an equity risk premium.
Equity risk premium (ERP) is the extra return over the risk-free rate that an investor demands for investing in risky equity securities.
ESTIMATES OF THE EQUITY RISK PREMIUM
There are two broad approaches to estimating ERP: historical and forward-looking (ex-ante).
Historical estimates
A historical ERP is the difference between the historical mean return of a broad-based equity market index over some period and the risk-free rate over the same period. Strengths: objectivity and simplicity. Weaknesses: assumes stationarity (mean and variance constant), potential survivorship bias, sensitivity to sample choice.
Analysts must decide on four key issues when making a historical estimate:
- Index selection. Choose an equity market index that is a good proxy for average equity returns over time.
- Sample period. Longer periods cover multiple business cycles and reduce standard error, but older data may not reflect current conditions. Shorter samples can represent current conditions but may have higher forecast error.
- Mean type. Decide whether to use an arithmetic mean or geometric mean. The arithmetic mean estimates a one-period expected return well, but overestimates multiperiod returns; the geometric mean estimates multiperiod terminal wealth better. Both are used in practice.
- Risk-free rate proxy. Choose between short-term (T-bill) or long-term (government bond) rates. Short-term rates better proxy a "true" risk-free rate without coupon reinvestment risk, while long-term rates may better match the long duration of equities.
A weakness of historical approaches is non-stationarity; ERP appears countercyclical (lower in good times, higher in bad times). Survivorship bias (only surviving firms included) can bias historical ERP upward.
Forward-looking (ex-ante) estimates
Forward-looking estimates use current information and expectations. They avoid stationarity assumptions and survivorship bias. Three main categories are:
- Survey-based estimates. Consensus of experts; tend to give higher ERPs for developing markets; may be biased toward recent returns.
- Dividend Discount Model (DDM) estimates. Use dividend yields and expected growth to infer required returns.
- Macroeconomic models. Use economic variables and accounting relationships; an example is the Grinold-Kroner model.
Dividend Discount Models
The constant growth (Gordon Growth) model rearranged to isolate the required return is:
rE = D1 / P0 + g
The first term is the expected dividend yield on a broad index; the second term is the expected earnings/dividend growth rate (capital gains yield). Subtract the current risk-free rate to obtain an ERP estimate when required. If growth is not constant, multi-stage DDMs (two-stage, three-stage) may be necessary, and an analyst may need to allow for changes in market P/E.
Macroeconomic models - Grinold-Kroner (2001)
The Grinold-Kroner model decomposes the capital gains yield (g) in the DDM as:
g = ΔP/E + i + G - ΔS
where ΔP/E is the change in the market P/E, i is expected inflation, G is real earnings growth (approximated by real GDP growth or sustainable earnings growth), and ΔS is the net issuance of shares (shares buybacks reduce outstanding shares, raising per-share payouts; if ΔS is positive this is dilution and is subtracted).
Expressing expected market equity return using Grinold-Kroner:
Expected market return = DY + ΔP/E + i + G - ΔS
Then ERP = Expected market return - rf.
One approach to estimate expected inflation is to compare nominal Treasury yields with inflation-protected securities (TIPS): the difference approximates expected inflation.
Example: Macroeconomic model
Patrick McGill is estimating the ERP for the U.S. market using the S&P 500 as market proxy. McGill estimates:
- Dividend yield (DY) = 1.2%
- Real GDP growth (G) = 3%
- Market fairly valued (ΔP/E = 0)
- 10-year Treasury yield = 2.4%
- 10-year TIPS yield = 0.25%
- No net change in shares outstanding (ΔS = 0)
- Risk-free rate given as 0.50% (note: alternative practice is to use the nominal Treasury yield as rf).
Calculate the equity risk premium.
Answer:
Compute expected inflation using nominal Treasury and TIPS:
Expected inflation = (1 + nominal Treasury yield) / (1 + TIPS yield) - 1
Expected inflation = (1.024 / 1.0025) - 1 = 2.33%
Apply the Grinold-Kroner decomposition:
Expected market return = DY + ΔP/E + i + G - ΔS
Expected market return = 1.10% - 0.10% + 2.33% + 3% - 0 = 6.33%
If using a 10-year nominal Treasury yield as the risk-free rate (2.67% in the worked numbers):
ERP = Expected market return - rf = 6.33% - 2.67% = 3.66%
LOS 17.d: Compare methods used to estimate the required return on equity.
LOS 17.e: Estimate the cost of debt or required return on equity for a public company and a private company.
Common approaches to estimate the required rate of return on equity include:
- Dividend Discount Model (DDM) - required return equals dividend yield plus capital gains yield.
- Bond-yield-plus-risk-premium (BYPRM) - add an equity risk premium to the yield on the company's long-term debt.
- Build-up approaches - start at the risk-free rate and add ERP plus premiums for size, industry, and company-specific risks.
- Risk-based models (CAPM, multifactor, Fama-French) - use beta(s) and factor premia to compute required returns.
Dividend Discount Model for a company
For an individual company,
rE = Dividend yield (DY) + Capital gains yield (CGY)
(Because rE is a required return, we do not subtract the risk-free rate when writing it this way.) If earnings growth is non-constant, use a two-stage or multi-stage model.
Example: Cost of equity using DDM
Cogenics, Inc. is expected to pay a dividend of $4 at the end of year 1. Dividends are expected to grow at a constant rate of 4% per year. The current Cogenics stock price is $100.
Betagenics, Inc. is expected to pay dividends of $1.50, $2.00, $2.50, and $3.00 at the end of each of the next four years, respectively. The current Betagenics stock price is $50, and the expected price at the end of four years is $60.
Compute the cost of equity for Cogenics and Betagenics.
Answer:
Cogenics:
Dividend yield = D1 / P0 = 4 / 100 = 4.00%
rE = DY + g = 4.00% + 4.00% = 8.00%
Betagenics (IRR computation):
Set up cash flows and compute IRR:
CF0 = -50
C01 = 1.50
C02 = 2.00
C03 = 2.50
C04 = 63.00 (This equals dividend in year 4 of 3.00 plus expected price 60)
CPT IRR = 8.78%
Thus rE (Betagenics) = 8.78%.
Bond-Yield-Plus-Risk-Premium (BYPRM) Method
BYPRM is a build-up method appropriate when the firm has publicly traded debt: add a required equity premium to the yield to maturity on the firm's long-term debt. The choice of which bond yield to use can be ambiguous if multiple issues exist.
Example: Applying BYPRM
Company LMN has bonds with 15 years to maturity, coupon 8.2%, price 101.70. An analyst estimates that equity holders require an additional 3.8% over the bond yield.
Answer:
Compute YTM using TVM keys:
PV = -101.70
N = 15
PMT = 8.2
FV = 100
CPT I/Y = 8.0%
Cost of equity = YTM + equity risk premium = 8.0% + 3.8% = 11.8%
Risk-Based Models
Capital Asset Pricing Model (CAPM)
CAPM estimates required return as:
required return on stock = risk-free rate + beta × equity risk premium
Example: CAPM
Expected risk-free rate = 4.0% and equity risk premium = 3.9%. For a stock with beta = 0.8, the required return is:
required return = 4.0% + (3.9% × 0.8)
= 4.0% + 3.12%
= 7.12%
CAPM beta is estimated by regressing historical stock returns against returns on a broad market index (returns may be excess over the risk-free rate or raw returns). For private companies, use a comparable public company's beta and adjust for differences in leverage.
Multifactor models
Multifactor models include multiple systematic factors. The general n-factor form is:
r = rf + Σ (βi × RPi)
where βi is sensitivity to factor i and RPi is the risk premium associated with factor i.
Fama-French models
The Fama-French three-factor model adds size (SMB) and value (HML) to the market factor (CAPM). The five-factor Fama-French model adds profitability (RMW) and investment (CMA).
Example: Fama-French Five-Factor Model
Suppose the current risk-free rate is 2.1%. Calculate the cost of equity for Fulton Corp. given the following information. Answer:
(The worked example and numeric inputs for this particular illustration were provided in source material; apply the five-factor formula with the provided betas and factor premia to compute rE.)
Cost of Equity for Private Companies
Private companies lack market price data, so CAPM and Fama-French cannot be applied directly. Illiquidity and lack of transparency increase risk. Typical additional risk premiums include:
- Size premium (SP)
- Industry risk premium (IP)
- Specific company risk premium (SCRP) - covers unique risks such as key-person risk, geographical concentration, customer/supplier concentration, lack of diversification, poor governance.
Factors affecting SCRP
Qualitative factors: industry characteristics, corporate governance, asset nature (tangible vs intangible), customer/supplier concentration, geographic concentration, competitive position, management quality. Lower governance quality, higher intangible composition, weak competitive standing, inexperienced management, or concentration increase SCRP.
Quantitative factors: operating and financial leverage, earnings and cash-flow volatility. Higher leverage and volatility increase SCRP.
Two approaches to estimate rE for a private company
Expanded CAPM: Start with CAPM using a comparable peer beta and add size, industry, and specific company risk premiums as appropriate:
rE = rf + β × ERP + SP + IP + SCRP
Build-up approach: Start at rf, add ERP (to obtain required return for an average large public company), then add SP, IP, SCRP for deviations from the average large public company:
required return = rf + ERP + SP + SCRP
International Considerations for Equity
Risks unique to emerging markets require additional premiums. Two ways to incorporate country risk are:
- Country-spread model. Estimate a country risk premium (CRP) using the sovereign yield spread relative to a benchmark developed-market government security and add CRP to required return.
- Country risk rating model. Use a country risk rating and corresponding spread or premium.
Sovereign yield spread is a convenient proxy but differences in legal and market environments complicate direct use. Aswath Damodaran recommends adjusting the sovereign yield spread by the ratio of the standard deviation of the country's equity market to the standard deviation of its bond market to scale the sovereign spread into an equity risk premium.
Extended CAPM
For globally operating companies, alternatives include:
- Global CAPM (GCAPM) - use a global market index to estimate ERP. Low correlation between developed and emerging markets may produce low or negative betas relative to a global index. A local market factor may be added to remedy very low global betas.
- International CAPM (ICAPM) - a two-factor model with (1) a global market index factor and (2) a foreign currency-denominated, wealth-weighted local market index. The first factor captures the firm's integration with the global economy; the second captures sensitivity to local currency movements.
For firms with exposure to developing markets, add a country risk premium if historical estimates are believed representative of future risk premia.
LOS 17.f: Evaluate a company's capital structure and cost of capital relative to peers.
This LOS uses a case-study approach to integrate prior concepts. Full case studies are time-consuming; exam questions are designed to be solvable in roughly three minutes each. Individual questions referencing the case material are appropriate for exam testing.
MODULE QUIZ 17.1, 17.2
Use the following information to answer Questions 1 through 6.
Daniel Hsu, CFA, follows the pharmaceutical industry for Applied Fundamentals LLC. Hsu has asked associate Rudolph Hsei to evaluate the cost of capital in two countries P and Q. Hsei collects the information shown in Exhibit 1.
Exhibit 1: Selected Information for Countries P and Q
Hsu is interested in estimating the cost of capital for two companies: Sizemore and Minicure. Sizemore is a large-cap company with a rich portfolio of successful drugs, while Minicure is a privately held company with a single drug, Mitra, which was approved by the FDA for treatment of early-stage dementia.
Exhibit 2 shows selected financial information relevant to Sizemore.
Exhibit 2: Sizemore, Selected Data ($ in millions)
Sizemore's tax rate is 34%.
After analyzing hundreds of rated securities, Hsu arrives at a matrix for interest coverage (IC) ratios and financial leverage (D/E) ratios by rating class and credit spread relative to the benchmark security (currently yielding 2.3%) as shown in Exhibit 3.
Exhibit 3: Rating Classes, Ratios and Spreads (truncated)
While discussing the computation of the equity risk premium, Hsei makes the following statements:
Hsu obtains estimates of economic data for use in the calculation of ERP as shown in Exhibit 4.
Exhibit 4: Selected Data: Wilshire 5000
Hsu then compiles consensus estimates of Sizemore's dividends and stock price. Sizemore is expected to pay a dividend of $1.00 per share in each of the next three years, and the stock price is expected to be $34 at the end of three years. Sizemore's current stock price is $25.
Hsei collects the following information and ponders how they might affect the SCRP for Minicure:
1. Based on the information in Exhibit 1, Hsei should conclude that relative to Country P, Country Q's cost of capital would be most likely be:
A. higher.
B. lower.
C. approximately the same.
2. Based on information provided in Exhibits 2 and 3 and elsewhere, the after-tax cost of debt for Sizemore should be closest to:
A. 2.31%.
B. 3.50%.
C. 4.05%.
3. Which statements made by Hsei regarding the equity risk premium are correct?
A. Statement 1 only.
B. Statement 2 only.
C. Neither statement is correct.
4. Using information in Exhibit 4, the estimate of equity risk premium (ERP) consistent with the Grinold-Kroner model is closest to:
A. 2.44%.
B. 3.44%.
C. 3.66%.
5. Based on DDM, Sizemore's cost of equity is closest to:
A. 11.39%.
B. 13.82%.
C. 14.42%.
6. How many of the factors considered by Hsei would support a higher specific company risk premium (SCRP) for Minicure?
A. Only one of the factors.
B. Two of the factors.
C. All three factors.
KEY CONCEPTS
LOS 17.a
Top-down (macro) factors: capital availability, market conditions, legal and regulatory considerations, tax jurisdiction.
Bottom-up (company-specific) factors: business/operating risk, asset nature and liquidity, financial strength and profitability, security features.
LOS 17.b
If a company's debt is publicly traded, the YTM for the firm's longest-maturity straight debt outstanding is the best estimate of cost of debt. If debt is not traded or thinly traded, use matrix pricing, comparing yields on traded securities with similar maturity and credit rating. If debt is unrated, use financial ratios (interest coverage, leverage) to infer rating. For finance leases, RIIL (the IRR that equates lease cash flows to fair value plus lessor costs) is the cost of debt. For foreign borrowers, add a country risk premium (e.g., sovereign yield spread relative to a benchmark government security).
LOS 17.c
Two types of ERP estimates: historical and forward-looking. Historical ERP equals the difference between historical mean market return and risk-free rate for a chosen sample period; concerns include survivorship bias and non-stationarity. Forward-looking estimates include surveys, DDM-based estimates, and macroeconomic models. The Grinold-Kroner formulation: ERP = [DY + ΔP/E + i + G - ΔS] - rf.
LOS 17.d, 17.e
Cost of equity via DDM: rE = dividend yield + capital gains yield.
Fama-French: required return = rf + β1 × ERP + β2 × SMB + β3 × HML. The five-factor model adds RMW and CMA.
Private company required return can be estimated with expanded CAPM (starting with CAPM and adding SP, IP, SCRP) or via build-up: required return = rf + ERP + SP + SCRP.
ANSWER KEY FOR MODULE QUIZZES
Module Quiz 17.1, 17.2
1.
A
Civil law countries afford fewer protections to investors compared with common law countries and hence investors in civil-law jurisdictions like Country Q may demand a higher risk premium. Countries with less-developed capital markets and highly volatile currencies would similarly call for a higher risk premium. (Module 17.1, LOS 17.a)
2.
A
Sizemore's interest coverage (IC) ratio = 3,421 / 814 = 4.20.
Sizemore's financial leverage (D/E) ratio = 8,671 / 17,342 = 0.50.
Both values fall within the range for a BBB classification; this indicates a 1.20% spread.
After-tax cost of debt = rD × (1 - T) = (2.30% + 1.20%) × (1 - 0.34)
= (3.50%) × 0.66
= 2.31% (Module 17.1, LOS 17.b)
3.
B
Statement 1 is incorrect. The arithmetic mean is a good estimate of a one-period expected return but a poor estimator for multiperiod terminal wealth. The geometric mean gives lower weight to outliers and better estimates terminal wealth. Statement 2 is correct: a weakness of the historical approach is the stationarity assumption; historical estimates may also suffer from survivorship bias. (Module 17.2, LOS 17.c)
4.
C
Expected inflation = (1 + nominal yieldTreasury) / (1 + yieldTIPS) - 1 = (1.0267 / 1.0033) - 1 = 2.33%.
ERP = [DY + ΔP/E + i + G - ΔS] - E(rf) = [1.10% - 0.10% + 2.33% + 3% - 0] - 2.67% = 3.66%.
Note: If a separate risk-free rate is provided, use that. Here the 10-year nominal Treasury yield is used as the risk-free rate in the worked numbers. (Module 17.2, LOS 17.e)
5.
C
Using CF function for Sizemore (DDM):
CF0 = -25
C01 = 1
C02 = 1
C03 = 1 + 34 = 35
CPT IRR = 14.42%
Thus Sizemore's cost of equity ≈ 14.42%. (Module 17.2, LOS 17.d)
6.
C
All three factors point to higher risk for Minicure:
- Management: strong R&D skills but possibly insufficient experience running a company.
- Assets: primarily specialized and illiquid rather than tangible and fungible.
- Supplier concentration: dependence on a limited supplier base reduces pricing power and increases operational risk.
Therefore all three factors support a higher SCRP for Minicure. (Module 17.2, LOS 17.d)
