6.3 Cost of Capital: Advanced Topics

6.3 Cost of Capital: Advanced Topics

Blueprint note: Cost of Capital: Advanced Topics is one of the four Corporate Issuers learning modules at Level II. Section 7.1 covers the equity-valuation mechanics of CAPM, beta unlevering, and multifactor models; this section covers the corporate-issuer perspective — what moves a company's cost of capital, how each component is estimated when data are scarce, and how the result is benchmarked.

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1. Top-Down and Bottom-Up Determinants

Top-down factors (affect all issuers in a market)

Bottom-up factors (differ across issuers)

The two lists interact: an issuer's bottom-up profile is expressed relative to the top-down base. A cyclical, highly levered small-cap in a high-country-risk market compounds both sets of effects, which is why cost-of-capital dispersion is far wider across emerging markets than within a single developed market.

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2. Estimating the Cost of Debt

When debt trades

Use the yield to maturity of the issuer's outstanding debt, matched to the expected maturity of the financing and to the currency. Two adjustments matter:

• Use the current market yield, not the coupon. The coupon reflects rates and credit at issuance, which may be years stale.
• Strip out embedded options. For callable debt, the appropriate measure is the option-adjusted yield rather than the yield to maturity, because the yield to maturity of a callable bond includes the value of the option written to the issuer.

When debt does not trade

1. Debt-rating (matrix pricing) approach. Identify the issuer's rating, then take the yield on an index or a set of comparable bonds with the same rating and maturity. The estimate is only as good as the rating's currency, and it fails when the issuer's credit has changed since the rating was affirmed.
2. Synthetic rating. Where no rating exists, map a coverage ratio — most commonly EBIT divided by interest expense — onto a rating scale, then apply the corresponding credit spread over the matched-maturity government yield. This is the standard route for private companies.
3. Recent borrowing cost. Use the rate on a recently negotiated bank facility, adjusted for any change in market spreads since it was agreed.

The after-tax cost of debt is $r_d (1 - t)$, and the marginal statutory rate is the appropriate rate unless the issuer cannot use the shield — a loss-making company with no carry-back capacity has an effective tax benefit of zero, so its after-tax cost of debt equals its pre-tax cost.

Cost of preferred equity

$r_p = \frac{D_p}{P_p}$

There is no tax adjustment, because preferred dividends are not deductible.

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3. Estimating the Equity Risk Premium

Historical approaches

Estimate the realised excess return of equities over a government bond or bill over a long sample. Four choices drive the answer, and vignettes vary them deliberately:

Forward-looking approaches

1. Gordon growth (implied) estimate. Rearranging the constant-growth model at the index level:

$ERP = \frac{D_1}{P_0} + g - r_f$

where $D_1/P_0$ is the forward dividend yield on the index (add net buyback yield where the market distributes heavily through repurchases) and $g$ is the expected long-run growth rate of dividends, anchored to nominal GDP growth.

1. Macroeconomic (supply-side) build-up. Decompose the expected equity return into expected inflation, expected real earnings growth, expected repricing (change in the P/E), and income return, then subtract the risk-free rate.

2. Survey estimates. Averages of forecasts from academics, practitioners, or chief financial officers. Simple, but prone to anchoring on recent returns.

Worked example. An index has a forward dividend yield of 1.9%, a net buyback yield of 1.3%, an expected long-run nominal growth rate of 4.2%, and the 10-year government yield is 4.0%.

• Total cash distribution yield: $1.9% + 1.3% = 3.2%$
• Expected equity return: $3.2% + 4.2% = 7.4%$
• Implied ERP: $7.4% - 4.0% = 3.4%$

Note how much lower this is than a long-run historical arithmetic estimate of 6% to 7%. Which one a vignette wants depends on whether it asks for a historical or a forward-looking premium — the two are not interchangeable, and using an arithmetic historical premium in a low-rate environment systematically overstates the cost of equity.

4. Required Return on Equity: Public versus Private Issuers

Public company

The standard route is the CAPM, $r_e = r_f + \beta (ERP)$, using a beta estimated by regression on an index, adjusted toward 1.0 for mean reversion, or a bottom-up beta constructed from comparable companies. Multifactor extensions such as the Fama–French three-factor and Pastor–Stambaugh four-factor models add size, value, and liquidity premiums and are developed in section 7.1.

Private company: the build-up approach

Private companies have no traded price, so no regression beta. The build-up method sums premiums:

$r_e = r_f + ERP + \text{Size premium} + \text{Industry premium} + \text{Company-specific premium}$

• The size premium compensates for the empirically higher returns and higher failure rates of small companies.
• The industry premium adjusts for the risk of the sector relative to the market.
• The company-specific premium captures key-person dependence, customer concentration, thin management depth, and limited access to capital.
• The expanded CAPM is the intermediate form: $r_f + \beta(ERP) + \text{size} + \text{company-specific}$, using an industry beta in place of a regression beta.

Worked example. Risk-free rate 4.0%, equity risk premium 5.0%, size premium 3.5%, industry premium 1.0%, company-specific premium 2.5%.

$r_e = 4.0\% + 5.0\% + 3.5\% + 1.0\% + 2.5\% = \textbf{16.0\%}$

Applying a listed-company cost of equity of, say, 9% to the same cash flows would overstate the private company's value by a wide margin — the gap between 9% and 16% is precisely what the discounts covered in section 7.5 are not meant to double-count. Use a private-company discount rate or a marketability discount applied to a public-comparable valuation, not both for the same risk.

Country risk premium

For an issuer with material operations in an emerging market, the standard adjustment adds a country risk premium (CRP) to the equity return:

$CRP = \text{Sovereign yield spread} \times \frac{\sigma_{\text{local equity index}}}{\sigma_{\text{local sovereign bond}}}$

The sovereign yield spread is the emerging market government's yield on a bond denominated in a developed-market currency, less the yield on the developed-market government bond of the same maturity. Scaling by the volatility ratio converts a bond-market risk measure into an equity-market one.

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5. Benchmarking Cost of Capital and Capital Structure Against Peers

The final learning outcome asks candidates to evaluate a company's capital structure and cost of capital relative to peers. The discipline is to hold constant what drives dispersion:

1. Match the industry. Operating leverage and asset intensity differ enough between sectors that a cross-sector comparison is meaningless.
2. Match the geography and currency. A cost of debt in a high-inflation currency is not comparable to one in a low-inflation currency; compare real or spread-over-government terms.
3. Match the point in the cycle. Cost of capital estimated at the trough of a credit cycle differs materially from the same company's cost a year later.
4. Compare leverage on consistent definitions. Use net debt to EBITDA and debt to total capital at market value, with off-balance-sheet obligations capitalized for every company in the set — the discipline from section 5.6.
5. Explain, don't just rank. A higher WACC than peers is a finding only once you can attribute it: more cyclical revenue, higher operating leverage, a weaker credit rating, a smaller size, or a higher country risk exposure.

Illustration. Three issuers in the same industry:

Issuers A and B have nearly identical WACC despite very different capital structures — the classic pattern showing that the tax shield gained on the way from 25% to 40% leverage roughly offsets the higher cost of both components. Issuer C's WACC is materially higher because its credit deterioration has raised the cost of debt faster than the tax shield can offset. The inflection point at which additional leverage stops lowering WACC is the practical question a vignette asks, and the answer is found by watching the cost of debt curve steepen as the rating falls through investment grade.

Level II traps in this module

1. Using the coupon rather than the current market yield as the cost of debt.
2. Applying the statutory tax rate to a company that cannot currently use the interest shield.
3. Mixing a historical arithmetic equity risk premium with a current low risk-free rate and calling the result forward-looking.
4. Applying a public-comparable cost of equity to a private company, then also applying a marketability discount for the same risk.
5. Comparing a company's WACC to a peer set drawn from a different industry, currency, or point in the credit cycle.