1.4 The Weighted Average Cost of Capital (WACC)
A company funds itself with a mix of borrowed money and owners’ money, and each has a price. WACC, the weighted average cost of capital, blends the two prices using how much of each the company uses. Borrowing is cheaper, partly because the interest saves tax, but owners demand a higher return for taking more risk. The borrowing cost should be what the company would pay today, never an old coupon. For Harbor Tools the blend comes to about 8.5%.
Why it matters: WACC is the bar a project must clear, and set too low it makes bad projects look good.
Summary: WACC blends the after-tax cost of debt and the cost of equity, weighted by target market values: for Harbor Tools, 0.70 × 10.13% + 0.30 × 6.2% × 0.75 = 8.48%, rounded to 8.5%. Rd is today’s borrowing cost, taken from a traded yield or a synthetic rating, never an old coupon.
- Harbor’s bonds yield 6.2%; a synthetic rating from 3.89x interest coverage gives A− and 6.09%.
- In the three-scenario comparison, WACC bottoms at 8.34% with 42% debt, then jumps as coverage falls below 2.5x and the IRC §163(j) cap bites.
- Using a 3% coupon from 2021 instead of today’s 6.2% yield overvalues Harbor by 20%.
- Weights must be market values, because book equity is an accounting residual.
A company is financed by a mix of debt and equity, and each source of capital demands its own return. Lenders want interest; shareholders want a return commensurate with the risk they are taking on. WACC blends these two costs, weighted by how much of each the company actually uses, into a single discount rate representing the minimum return the company’s overall capital must earn to satisfy everyone who funded it.
WACC = (E/V × Re) + (D/V × Rd × (1 − Tax Rate))
Where E is the market value of equity, D is the market value of debt, V is E + D, Re is the cost of equity (from CAPM, covered next), and Rd is the pre-tax cost of debt (the yield the company would pay to borrow today, not the coupon on debt it issued years ago). The debt component is multiplied by (1 − Tax Rate) because interest payments are tax-deductible — this is called the “tax shield,” and it is one reason debt is often a cheaper source of capital than equity, at least up to a point.
Harbor Tools (Section 1.3: Discounted Cash Flow (DCF) — Building the Model) targets 30% debt and 70% equity at market values, has a cost of equity of 10.13% (Section 1.5: CAPM — The Cost of Equity), a pre-tax cost of debt of 6.2% and a 25% tax rate. WACC = (0.70 × 0.1013) + (0.30 × 0.062 × 0.75) = 0.07089 + 0.01395 = 8.48%, rounded to the 8.5% used in the DCF in Section 1.3: Discounted Cash Flow (DCF) — Building the Model (the rounding moves value per share by $0.06, from $15.30 to $15.24).
Where does the 6.2% come from? When a company’s bonds trade, use their yield to maturity: Harbor’s illustrative 10-year bonds yield 6.2%, in line with the 6.19% effective yield on the ICE BofA BBB US Corporate Index on October 1, 2026. When they do not trade, build a synthetic rating from interest coverage, EBIT ÷ interest. Harbor pays a 6% coupon on $600 million of debt, so coverage = 140 ÷ 36 = 3.89x, which Damodaran’s January 2026 table for large non-financial firms maps to A3/A− with a 0.89% default spread: Rd = 5.2% + 0.89% = 6.09%. The estimates sit 0.11 points apart; the traded yield wins when it exists, because it is a price, not a mapping.
Hold Harbor’s enterprise value at $2,025 million, EBIT at $140 million and EBITDA at $180 million, and change only the mix (USD millions). Each case relevers the 0.91 unlevered beta (Section 1.5: CAPM — The Cost of Equity), rates the debt by coverage on Damodaran’s table, and allows the tax shield only on interest within the IRC §163(j) cap, approximated as 0.30 × EBITDA = $54 million.
| All equity | Target | Aggressive | |
|---|---|---|---|
| Debt ÷ value (D/V) | 0% | 30% | 50% |
| Debt | 0.0 | 607.5 | 1,012.5 |
| Interest at the synthetic rate | — | 37.0 | 85.2 |
| Coverage, EBIT 140 ÷ interest | — | 3.78x | 1.64x |
| Synthetic rating / pre-tax Rd | — | A− / 6.09% | B / 8.41% |
| Effective tax rate on interest | 25% | 25% | 15.9% |
| Relevered beta / cost of equity | 0.91 / 8.93% | 1.20 / 10.13% | 1.67 / 12.07% |
| WACC | 8.93% | 8.46% | 9.57% |
The flip point. On a 1-point grid, WACC falls to its minimum of 8.34% at 42% debt: coverage is 140 ÷ 53.7 = 2.61x, still BBB, interest just under the cap. At 44%, coverage drops to 2.39x, the rating falls to BB+ (6.58% pre-tax), interest of 58.6 breaches the cap, the effective tax rate on interest falls to 23%, and WACC jumps to 8.49%. By 50% it is 9.57%, above the all-equity 8.93%. (The 30% case shows 8.46%, not 8.48%, because it uses the synthetic 6.09% cost of debt.) The model omits financial-distress costs, so the true optimum sits below 42%.
Section 1.6: Capital Structure & Modigliani-Miller explains which frictions beyond this tax-and-rating arithmetic make capital structure matter.
Weight debt and equity by target market values, not book values. Take Rd from the yield to maturity on the company’s long-term debt if it is investment grade and trades; otherwise use a synthetic rating (coverage, then spread, then risk-free rate plus spread). Tax-effect Rd at the marginal rate, and cut that rate where losses or the IRC §163(j) cap limit the deduction. Recompute WACC when the target mix moves by more than about 10 points of D/V (a working heuristic). For junk-rated debt, a yield to maturity is a promised return, so it overstates the expected cost of debt by roughly the expected default loss.
Using the coupon on old debt as the cost of debt. Suppose Harbor’s bonds had been issued in 2021 with a 3% coupon. Plugging 3% into the formula instead of today’s 6.2% yield gives WACC = 0.07089 + 0.30 × 0.03 × 0.75 = 7.76%, and the same DCF then values Harbor at $18.34 a share instead of $15.24: a 20% overvaluation from a number copied off the balance sheet. Avoid it by pricing debt from current yields or a synthetic rating, never from the interest-expense line.
Should WACC use book values or market values?
Market values, or a target mix in market values, because WACC is the return investors require on what their claims are worth today. Book equity is an accounting residual: a company that has bought back many shares can show negative book equity while its stock is worth billions.
Why is the cost of debt multiplied by (1 − tax rate)?
Because interest is tax-deductible, the government in effect pays part of it: at 25%, Harbor’s 6.2% costs 6.2% × 0.75 = 4.65% after tax. The adjustment works only while the deduction does; in loss years, or on interest above the IRC §163(j) cap, the current-year benefit is zero.
How do you estimate the cost of debt for a private company?
Build a synthetic rating: compute interest coverage (EBIT ÷ interest), map it to a default spread with a published table such as Damodaran’s, and add the spread to the risk-free rate. Harbor’s 3.89x maps to A− and a 6.09% pre-tax cost. Check the result against yields on similar rated bonds.
WACC weights the after-tax cost of debt and the cost of equity by target market values, giving Harbor 8.48%. The cost of debt comes from a current yield or a synthetic rating, and debt lowers WACC only until coverage, ratings and the interest-deduction cap turn against it.
Four questions on this chapter. Decide on your answer first, then click “Reveal Answer.”
1. A company targets 60% equity and 40% debt at market values, with an 11% cost of equity, a 7% pre-tax cost of debt and a 25% tax rate. What is its WACC?
- 9.40%
- 7.55%
- 9.00%
- 8.70%
Reveal Answer
Answer: D. WACC = 0.60 × 11% + 0.40 × 7% × 0.75 = 6.6% + 2.1% = 8.70%. Skipping the tax shield gives 9.40%; swapping the weights gives 7.55%; a simple average gives 9.00%.
2. A private company has EBIT of $84 million and interest of $30 million. Damodaran’s January 2026 table maps 2.5–3.0x coverage to BBB with a 1.11% spread. With a 5.2% risk-free rate, what is its pre-tax cost of debt?
- 5.20%
- 6.09%
- 6.31%
- 6.58%
Reveal Answer
Answer: C. Coverage = 84 ÷ 30 = 2.8x, which maps to BBB; Rd = 5.2% + 1.11% = 6.31%. 6.09% and 6.58% use the A− and BB+ spreads; 5.20% omits the spread.
3. In Harbor’s scenario comparison, why does WACC rise when debt moves from 42% to 44% of value?
- Its rating falls and its interest deduction hits the cap
- The business’s unlevered beta rises with each dollar of debt
- The risk-free rate rises because the company borrows more money
- Shareholders demand a lower return as the debt load increases
Reveal Answer
Answer: A. At 44% debt coverage falls to 2.39x, the synthetic rating drops to BB+, and interest exceeds the $54 million §163(j) cap, so the cost of debt rises and its tax shield shrinks.
4. A company issued bonds in 2021 at a 3% coupon; similar bonds now yield 6.2%. Which pre-tax cost of debt belongs in today’s WACC?
- 0%, since the debt has already been raised
- 6.2%, what lenders demand for new money now
- 3%, the coupon written into the original bond terms
- 4.6%, the midpoint of the coupon and yield
Reveal Answer
Answer: B. WACC is a forward-looking opportunity cost, so Rd is today’s yield. In Harbor’s case, using the old 3% coupon overvalued the shares by about 20%.
1.5 CAPM — The Cost of Equity
The cost of equity is the return shareholders expect for owning a company’s stock. CAPM builds it in three steps. Start with the return on a safe investment, then add extra for the risk of the stock market as a whole, then scale that extra by beta, which measures how strongly this company’s stock swings compared with the market. A beta above one means bigger swings than the market. For Harbor Tools the answer is 10.13%.
Why it matters: The cost of equity feeds almost every valuation, so small errors here are magnified.
Summary: CAPM sets the cost of equity at the risk-free rate plus beta times the equity risk premium. For Harbor Tools: 5.2% + 1.20 × 4.1% = 10.13%, using the 10-year Treasury (5.24% on October 1, 2026) and Damodaran’s implied premium (4.14% on September 1, 2026).
- Beta measures only market-linked risk: a volatile stock that moves independently of the market can have a low beta.
- Take beta from peers: unlever at their leverage (1.08 → 0.91), then relever at the target’s (→ 1.20).
- Skipping the relevering step overvalued Harbor by 9.4%.
- Pair the risk-free rate and the equity risk premium from the same date and basis.
- CAPM is the standard starting point but weak empirically; Fama and French (1992) found a flat beta–return relation.
The Capital Asset Pricing Model (CAPM) is the standard method for estimating the cost of equity — the return shareholders require to compensate them for the risk of owning the stock rather than holding a risk-free asset. Its logic: a stock’s expected return should equal the risk-free rate, plus a premium for the stock’s own sensitivity to overall market swings.
Re = Rf + β × (Rm − Rf)
Rf is the risk-free rate (typically the yield on a long-term government bond — see Volume I’s Part 2 on the yield curve). Rm is the expected return of the overall stock market, so (Rm − Rf) is the equity risk premium (ERP). β (beta) measures how much the stock moves relative to the market — a beta of 1 moves with the market on average; a beta above 1 amplifies market moves; below 1, it dampens them. Beta captures only the market-linked part of a stock’s risk: a volatile stock whose swings are unrelated to the market can have a low beta.
For Harbor Tools (Section 1.3: Discounted Cash Flow (DCF) — Building the Model): the risk-free rate is 5.2% (the 10-year Treasury yielded 5.24% on October 1, 2026), the equity risk premium is 4.1% (Damodaran’s implied premium for the S&P 500 was 4.14% on September 1, 2026), and Harbor’s beta at its target financing mix is 1.20. Re = 0.052 + 1.2018 × 0.041 = 0.052 + 0.0493 = 10.13%, the cost of equity used in the WACC in Section 1.4: The Weighted Average Cost of Capital (WACC).
Note the basis gap: Damodaran computed the 4.14% premium against a 4.75% Treasury rate (FRED, August 31, 2026), 49 basis points below the 5.24% used here. The Decision Rule below pairs same-date inputs, so before using 10.13% in a live decision, replace both inputs with Damodaran’s first monthly estimate after October 1, 2026 and the Treasury rate it was computed against. The example keeps the September premium so that Sections 1.3 and 1.4 stay consistent.
One company’s regression beta is noisy, so practitioners start from peers. Step 1, adjust: Bloomberg’s default beta uses two years of weekly returns and reports an adjusted beta (Section 0.4: The Quant Toolkit) = 0.67 × raw beta + 0.33, which pulls estimates toward 1; a raw 1.12 becomes 1.08. Step 2, unlever: remove each peer’s financing with the relation published by Robert Hamada in 1972, βu = βL ÷ [1 + (1 − t) × D/E]. A peer median of 1.08 at D/E 0.25 gives 1.08 ÷ (1 + 0.75 × 0.25) = 0.91, the unlevered beta of the business alone. Step 3, relever at Harbor’s target D/E of 0.30 ÷ 0.70 = 0.43: βL = 0.9095 × (1 + 0.75 × 0.4286) = 1.20. Leverage raises equity beta because lenders are paid first, so the same business risk lands on a thinner slice of equity. The formula assumes debt carries no market risk, which overstates the relevered beta of heavily indebted companies.
Beta, the risk-free rate, and the market risk premium are all estimated, not observed directly — different data providers (Bloomberg, a company’s own investor relations team, an independent research house) will often quote slightly different betas for the same stock, depending on the time period and index used to calculate it. A large part of an analyst’s real job is defending which inputs they chose and why — the formula itself is the easy part.
With the cost of equity at 10.13%, the cost of debt at 6.2% and the target mix at 30% debt, every input to Harbor’s 8.5% WACC is now traceable to a market price, a published table or a stated assumption, which is the standard a reviewer will test the model against.
Use the yield on a Treasury whose maturity is close to the duration of the cash flows (the 10-year for most company DCFs), and pair it with an equity risk premium estimated on the same date against a comparable rate. Take beta from a peer median, unlevered at each peer’s own D/E and tax rate and relevered at the target’s, rather than from one regression on the company’s own shares. If peer betas span more than about 0.5, narrow the set to closer business matches before averaging (a working heuristic). Do not rely on CAPM alone where its single factor explains returns poorly; Section 5.8: Factor Investing — Fama-French and Beyond covers multifactor models.
Plugging in a peer’s levered beta without relevering. Harbor’s peers carry D/E of 0.25; Harbor targets 0.43. Use the peers’ 1.08 directly and Re = 0.052 + 1.08 × 0.041 = 9.63%, WACC = 0.70 × 0.0963 + 0.01395 = 8.13%, and the DCF gives $16.67 a share instead of $15.24: a 9.4% overvaluation from forgetting that Harbor’s shareholders carry more financial risk than the peers’ shareholders. Avoid it by always unlevering peers at their own leverage and relevering at the target’s.
What risk-free rate should I use in CAPM?
Use the yield on a government bond in the same currency as the cash flows, with a maturity close to their duration: for a US company DCF, usually the 10-year Treasury (5.24% on October 1, 2026). A 3-month bill measures today’s short-term rate, not the long-run return investors give up, and it mismatches a valuation whose cash flows run for decades.
What is a reasonable equity risk premium?
Market-implied estimates for the US have recently been near 4%: Damodaran’s implied premium for the S&P 500 was 4.14% on September 1, 2026. Historical-average premiums depend heavily on the start date chosen, so state the period if you use one. Whichever source you pick, apply it consistently and pair it with the risk-free rate it was computed against.
What is the difference between levered and unlevered beta?
Levered (equity) beta is what you observe in a stock’s returns; it includes the extra risk that debt adds for shareholders. Unlevered (asset) beta strips that out to measure business risk alone. Harbor’s peers have a levered beta of 1.08 and an unlevered beta of 0.91; at Harbor’s heavier target debt, the relevered beta is 1.20.
Does CAPM actually work?
Partly. Its central idea, that only market-related risk earns a premium, remains the standard starting point for the cost of equity, but the evidence is weak: Fama and French (1992) found the relation between beta and average US stock returns flat over 1963–1990 once size was controlled for. Section 5.8: Factor Investing — Fama-French and Beyond covers the multifactor models that followed.
CAPM prices equity as the risk-free rate plus beta times the equity risk premium, giving Harbor 10.13%. Beta comes from peers, unlevered and relevered at the target’s financing mix, and every input should be dated and consistent.
Four questions on this chapter. Decide on your answer first, then click “Reveal Answer.”
1. The risk-free rate is 5.2%, the equity risk premium is 4.1% and a stock’s beta is 1.3. What is its CAPM cost of equity?
- 9.30%
- 5.33%
- 10.53%
- 12.09%
Reveal Answer
Answer: C. Re = 5.2% + 1.3 × 4.1% = 5.2% + 5.33% = 10.53%. Omitting Rf gives 5.33%, ignoring beta gives 9.30%, and multiplying beta by Rf + ERP gives 12.09%.
2. A peer has a levered beta of 1.10, a debt-to-equity ratio of 0.50 and a 25% tax rate. What is its unlevered beta under the Hamada formula?
- 0.73
- 0.98
- 1.51
- 0.80
Reveal Answer
Answer: D. βu = 1.10 ÷ [1 + 0.75 × 0.50] = 1.10 ÷ 1.375 = 0.80. Ignoring tax gives 0.73, using t instead of (1 − t) gives 0.98, and multiplying instead of dividing gives 1.51.
3. Using adjusted beta = 0.67 × raw beta + 0.33, what adjusted beta corresponds to a raw regression beta of 1.45?
- 1.30
- 1.45
- 1.15
- 0.97
Reveal Answer
Answer: A. 0.67 × 1.45 + 0.33 = 0.97 + 0.33 = 1.30. The adjustment pulls the estimate toward 1; swapping the weights gives 1.15.
4. A stock’s price swings wildly, but its returns are almost uncorrelated with the market. What does CAPM imply about its cost of equity?
- Well above the market return, because volatility is high
- Near the risk-free rate, because its beta is low
- Undefined, because CAPM needs a beta above 1
- Equal to the market return, because all stocks share a premium
Reveal Answer
Answer: B. CAPM prices only market-related risk; beta depends on correlation with the market, so a volatile but uncorrelated stock has a low beta and a cost of equity close to Rf.
- FRED, Market Yield on U.S. Treasury Securities at 10-Year Constant Maturity (DGS10) — 10-year Treasury 5.24% on October 1, 2026 (risk-free rate, 1.4 and 1.5)
- 26 U.S.C. §163, Interest (Cornell LII) — §163(j) 30% of adjusted taxable income cap, depreciation add-back, carryforward
- FRED, ICE BofA BBB US Corporate Index Effective Yield — 6.19% on October 1, 2026 (cost of debt cross-check, 1.4)