1.6 Capital Structure & Modigliani-Miller
Two economists, Modigliani and Miller, proved in 1958 that in a perfect world a company’s value does not depend on how it splits its funding between debt and equity. Cheaper debt is exactly canceled by owners demanding more return as the company gets riskier. It is like cutting a pizza: slicing it differently doesn’t make the pizza bigger. In the real world the split matters only through frictions. Debt interest saves tax, but too much debt raises the expected cost of going bust.
Why it matters: Any gain from borrowing must come from taxes, not from magic.
Summary: Modigliani and Miller proved in 1958 that, without taxes, distress costs or information gaps, how a company splits its financing between debt and equity cannot change its total value: cheaper debt is exactly offset by a rising cost of equity. Capital structure matters in practice only through those frictions, chiefly the interest tax shield and the expected cost of financial distress.
- Proposition II: rE = rA + (D/E) × (rA − rD); $400m of 6% debt on a $1,000m firm lifts the cost of equity from 10% to 12.67% and leaves WACC at 10%.
- With the 21% federal tax, permanent debt adds at most t × D: $84m on $400m of debt.
- IRC §163(j) caps deductible interest at 30% of adjusted taxable income, roughly EBITDA for tax years beginning after 2024.
- In the worked trade-off, value peaks at $897m with $600m of debt, where extra tax savings stop outrunning expected distress costs.
- Keeping the cost of equity fixed while adding debt overstated value by $126.5m (14.5%) in the example.
Capital structure is the mix of debt and equity a company chooses to finance itself. In 1958, economists Franco Modigliani and Merton Miller proved a deliberately provocative result: in a simplified world with no taxes, no bankruptcy costs, and perfect information, a company’s capital structure has no effect at all on its total value — the pie can be sliced between debt and equity in any proportion, but the size of the pie stays the same.
The proof is an arbitrage: if a levered firm traded above an identical unlevered one, investors would sell it, buy the cheaper firm and borrow personally (“homemade leverage“) until the values matched (Proposition I). It follows that the cost of equity rises in a straight line with leverage (Proposition II): rE = rA + (D/E) × (rA − rD), where rA is the assets’ required return and rD the cost of debt.
A firm with perpetual EBIT of $100 million and rA = 10%, with no taxes, is worth $100m ÷ 0.10 = $1,000 million. It borrows $400 million at 6% to buy back stock. Equity, now $600 million, receives $100m − $24m = $76 million: a return of 12.67%, exactly 10% + (400 ÷ 600) × (10% − 6%). WACC = 0.60 × 12.67% + 0.40 × 6% = 10.0%, unchanged. Cheaper debt is offset by costlier equity; hence analysts re-lever beta when leverage changes (1.5).
The theorem is famous less for being literally true — those assumptions never hold in the real world — than for clarifying exactly which real-world frictions do make capital structure matter: taxes (the debt tax shield introduced in 1.4 makes debt cheaper on an after-tax basis), the risk of financial distress and bankruptcy (too much debt raises the odds of default, which is costly and disruptive), and agency costs (debt can discipline management against wasteful spending, but too much of it can also push management toward excessive risk-taking).
Add the 21% federal corporate tax. Interest is deductible, so for permanent debt the present value of the interest tax shield is t × D (Modigliani and Miller’s 1963 correction): VL = VU + t × D. Unlevered, the firm is worth $100m × 0.79 ÷ 0.10 = $790 million; with $400 million of debt, $790m + 0.21 × $400m = $874 million. Two frictions cap it. IRC §163(j) limits deductible interest to 30% of adjusted taxable income, which for tax years beginning after December 31, 2024 is again roughly EBITDA: with EBITDA of $130 million, $39 million (carryforwards ignored). And financial distress costs (lost customers, fire sales, fees) are modeled as 20% of unlevered value, $158 million, times an assumed probability of distress.
| Debt ($m) | Interest at 6% | Deductible | PV of tax shield | Assumed distress probability | Expected distress cost | Firm value |
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0% | 0 | 790.0 |
| 200 | 12 | 12 | 42.0 | 1% | 1.6 | 830.4 |
| 400 | 24 | 24 | 84.0 | 4% | 6.3 | 867.7 |
| 600 | 36 | 36 | 126.0 | 12% | 19.0 | 897.0 |
| 800 | 48 | 39 | 136.5 | 30% | 47.4 | 879.1 |
PV of shield = 0.21 × deductible interest ÷ 0.06. Value peaks at $897.0 million with $600 million of debt (4.6× EBITDA); beyond it the cap stops the shield growing while distress costs accelerate. That is the trade-off theory: borrow until the marginal tax benefit equals the marginal expected distress cost.
Myers (1984) set the trade-off theory against the pecking order theory: because issuing equity signals that managers think the shares are overpriced, firms use internal cash first, then debt, then equity, and the debt ratio simply records past financing needs. The evidence splits. Graham (2000) put the tax benefit of debt at 9.7% of firm value and found the typical firm could double it by borrowing more, with large, profitable firms the most conservative, a puzzle for the trade-off theory. Of 392 CFOs surveyed by Graham and Harvey (2001), 19% had no target debt ratio and only 10% a strict one; 59% rated financial flexibility important, the top answer, against 21% for distress costs. Yet Frank and Goyal (2003), studying US firms over 1971 to 1998, found net equity issues tracked financing needs more closely than net debt issues, contrary to the pecking order. Working reading: trade-off sets a wide band; ratings, flexibility and timing pick the point inside it.
When leverage changes (a recapitalization, an LBO), never hold the cost of equity constant: apply Proposition II or re-lever beta, then recompute WACC. Credit permanent debt with at most t × D of value (21 cents per dollar federally), nothing on interest above 30% of EBITDA, and nothing if the company lacks taxable income. Stop borrowing when expected distress costs rise faster than the shield. Ignore this rule for banks and insurers, whose capital regulators set (Part 9: Regulation & Financial Law).
Adding “cheap” debt without repricing equity. With $400 million of debt the firm above is worth $874 million: equity of $474 million costs 10% + (400 ÷ 474) × 0.79 × 4% = 12.67%, so WACC = (474 ÷ 874) × 12.67% + (400 ÷ 874) × 6% × 0.79 = 9.04%, and $79m ÷ 0.0904 = $874 million. Leave equity at 10% and keep the no-tax example’s 60/40 weights, and WACC becomes 0.60 × 10% + 0.40 × 6% × 0.79 = 7.90%, giving $79m ÷ 0.0790 = $1,000.5 million. The $126.5 million (14.5%) overstatement exceeds the whole $84 million tax shield.
Is debt cheaper than equity?
Per dollar, yes: lenders are paid first and interest is deductible. But each extra dollar of debt makes the remaining equity riskier and raises its required return (Proposition II), so the firm’s only net saving is the interest tax shield, which shrinks as expected distress costs grow.
What is the optimal debt-to-equity ratio?
There is no universal number. It is where the next dollar of debt adds as much expected distress cost as it saves in tax, which depends on cash-flow stability, collateral, tax position and target rating. The worked example peaks near 4.6× EBITDA only under its assumed probabilities.
Why do some very profitable companies carry almost no debt?
They value flexibility above the tax saving. Graham (2000) found large, profitable firms the most conservative borrowers, and CFOs rank flexibility first. Spare capacity funds acquisitions or a downturn without issuing shares cheaply, an option the trade-off model ignores.
Modigliani and Miller showed that, without frictions, financing cannot change firm value because the cost of equity rises with leverage (Proposition II). With taxes, permanent debt adds at most t × D, capped by the §163(j) interest limit and offset by expected distress costs, so value peaks at a moderate debt level; whether firms target that peak or follow a pecking order remains contested.
Four questions on this chapter. Decide on your answer first, then click “Reveal Answer.”
1. With no taxes, a firm whose assets require a 10% return is worth $1,000 million. It borrows $400 million at 6% and buys back shares. What is its new cost of equity?
- 10.00%
- 14.00%
- 12.67%
- 11.60%
Reveal Answer
Answer: C. Proposition II: rE = 10% + (400 ÷ 600) × (10% − 6%) = 12.67%. Using D/V (0.4) instead of D/E gives 11.60%; WACC stays at 10%.
2. At a 21% tax rate, roughly what present value does $500 million of permanent debt add through the interest tax shield?
- $105 million
- $30 million
- $395 million
- $21 million
Reveal Answer
Answer: A. For permanent debt the shield’s present value is t × D = 0.21 × $500 million = $105 million, before any interest cap or distress costs.
3. In the trade-off example, why does firm value fall once debt rises from $600 million to $800 million?
- Proposition I lowers value once debt exceeds equity
- Expected distress costs outgrow the capped tax shield
- Interest stops being deductible above total EBITDA
- The cost of debt falls, so the tax shield shrinks
Reveal Answer
Answer: B. The §163(j) cap holds deductible interest at $39 million, so the shield grows only from $126.0m to $136.5m while expected distress costs jump from $19.0m to $47.4m.
4. In Graham and Harvey’s 2001 CFO survey, which factor did the most respondents rate important for debt policy?
- Potential bankruptcy costs
- Industry peers’ debt levels
- The interest tax deduction
- Financial flexibility
Reveal Answer
Answer: D. 59% rated financial flexibility important or very important, ahead of credit ratings (57%), the tax advantage (45%) and distress costs (21%).
1.7 Comparable Company Analysis ("Comps")
Comparable company analysis values a business the way you might price a house: by looking at what similar ones sell for. You pick a group of similar listed companies, see what multiple of earnings the market pays for them, and apply that multiple to your target’s own earnings. Use the middle value and the typical range of the group, and measure every company’s earnings in the same way so you compare like with like.
Why it matters: It shows what the market pays today, not what the business is worth in theory.
Summary: Comparable company analysis values a business at the multiples the market currently pays for similar listed companies, applied to the target’s own earnings. Use the peer median and interquartile range of enterprise-value multiples, on consistently defined earnings.
- Ridgeline’s peers trade at 7.8× to 9.9× EBITDA; the median 8.85× on $150m of EBITDA gives $20.55 a share after $300m of net debt.
- EV multiples survive differences in leverage; P/E does not (12.7× versus 9.0× for the same business).
- Put every peer on the same period (LTM or NTM) and the same accounting; IFRS 16 lifts EBITDA relative to US GAAP.
- Applying peer multiples to a target’s adjusted EBITDA added $2.66 a share in the example, overstating value by 14.8%.
A DCF answers “what is this business intrinsically worth.” Comparable company analysis answers a different, more market-grounded question: “what is the market currently paying for businesses like this one.” The method: identify a set of publicly traded companies similar in industry, size, growth rate, and geography; calculate their valuation multiples (EV/EBITDA, P/E, EV/Revenue — introduced in Volume I’s Part 5); and apply the median or average multiple of that peer set to the target company’s own financial metrics.
The target is Ridgeline Instruments, an illustrative US maker of laboratory instruments and the consumables they use (the same company runs through 1.8, 1.10 and 1.12). Its LTM (last twelve months) EBITDA is $150 million, net debt $300 million, diluted shares 50 million, and the share price $19.00. Four listed peers trade at EV/LTM EBITDA of 8.5×, 9.2×, 7.8× and 9.9×.
| Peer statistic | EV/EBITDA | Implied EV ($m) | Less net debt ($m) | Equity value ($m) | Per share |
|---|---|---|---|---|---|
| 25th percentile | 8.33× | 1,248.75 | 300 | 948.75 | $18.98 |
| Median | 8.85× | 1,327.5 | 300 | 1,027.5 | $20.55 |
| 75th percentile | 9.38× | 1,406.25 | 300 | 1,106.25 | $22.13 |
Median = (8.5 + 9.2) ÷ 2 = 8.85×. EV = $150m × 8.85 = $1,327.5 million; equity = $1,327.5m − $300m = $1,027.5 million; per share = $1,027.5m ÷ 50m = $20.55. At $19.00 the market values Ridgeline at ($950m + $300m) ÷ $150m = 8.33×, the peers’ 25th percentile. The comps answer is the range, $18.98 to $22.13, and the question it raises is why Ridgeline sits at the bottom of it.
Comps are faster to build than a DCF and reflect real, current market sentiment rather than an analyst’s own projections — but they inherit the market’s own mood. If an entire sector is over-optimistic (as in the dot-com years) or unfairly punished (as many quality businesses were during broad market sell-offs), a comps-based valuation will faithfully reproduce that mispricing rather than correct for it. This is precisely why professionals build a DCF and comps side by side.
Two companies own identical businesses: EBIT $100 million, enterprise value $1,000 million, 21% tax. A has no debt; B has $500 million at 6%. Both trade at EV/EBIT 10.0×. A’s net income is $100m × 0.79 = $79.0 million, so its P/E is $1,000m ÷ $79.0m = 12.7×. B’s is ($100m − $30m) × 0.79 = $55.3 million on $500 million of equity, a P/E of 9.0×. The same business shows P/E multiples 3.6 turns apart purely because of financing; B’s riskier equity earns a lower multiple, which is Proposition II from 1.6 at work. So: use EV multiples (EV/EBITDA, EV/EBIT, EV/Revenue) when peers’ leverage differs, keep P/E for peers with similar leverage, and always pair EV with pre-interest earnings and equity value with post-interest earnings.
Before any multiple is applied, peers are made comparable: put every company on the same period (LTM or NTM, next twelve months, never mixed), strip one-off items the same way for every company, and watch accounting regimes. Under IFRS 16 nearly all lease costs move below EBITDA into depreciation and interest, while under US GAAP (ASC 842) operating lease cost stays inside operating expenses, so an IFRS peer’s EBITDA is flattered against a US peer’s. A rough guide is four to ten peers; with fewer, show every peer’s multiple rather than one statistic.
Use the peer median and the 25th-to-75th percentile range, not the mean, unless every peer is close to the median. If peers’ net debt to EBITDA differs by more than about one turn, value on EV multiples only. If the target’s growth or margin sits outside the peers’ range, do not apply the median: position the target inside the range by regressing peers’ multiples on growth or margin, or move to a DCF. Ignore comps entirely when the whole sector is being rerated (a bubble or a panic); they will reproduce the mispricing.
Applying peers’ multiples, computed on reported EBITDA, to the target’s “adjusted” EBITDA. Suppose Ridgeline’s $150 million includes $15 million of restructuring costs added back every year for three years. They recur, so they are costs. At 8.85×, the add-back inflates EV by $15m × 8.85 = $132.75 million, or $132.75m ÷ 50m = $2.66 a share: 12.9% on the $20.55 median value. Rebuild every company’s EBITDA, target included, from the same reported line, and treat add-backs that recur for two years running as recurring costs (Part 6: Accounting, Forensically covers non-GAAP adjustments).
Should I use the mean or the median peer multiple?
Use the median, and show the interquartile range. One peer trading at 25× because of a takeover rumor can drag the mean far from where most peers trade, while the median ignores it. Quote the mean only when the peer multiples cluster tightly, and then check that the two are close; if they differ by more than about half a turn, an outlier is driving the mean.
Should comps use trailing or forward multiples?
Either works if you are consistent. LTM multiples use reported numbers, so they are auditable; NTM multiples use analyst forecasts, so they reflect where the business is heading and are standard for fast-growing companies. What you must never do is mix them: applying peers’ LTM multiples to the target’s NTM earnings overstates value by roughly the target’s growth rate, about 10% for a company growing 10% a year.
What if there are no good listed peers?
Widen the definition carefully (similar end markets, business model, or margin structure rather than the same product) and say so, lean harder on precedent transactions (1.8) and the DCF (1.3), and widen the range you present. A comps set of two loosely related companies is an opinion dressed as market evidence.
Comps apply the median and interquartile range of peers’ enterprise-value multiples to the target’s consistently defined earnings, then bridge to equity by subtracting net debt. For Ridgeline that gives $18.98 to $22.13 a share; mismatched earnings definitions, periods or accounting regimes are the main source of error.
Four questions on this chapter. Decide on your answer first, then click “Reveal Answer.”
1. Peers trade at 8.0×, 9.0×, 10.0× and 11.0× EBITDA. The target has EBITDA of $200 million, net debt of $400 million and 100 million shares. What is the median-implied value per share?
- $14.00
- $19.00
- $16.00
- $15.00
Reveal Answer
Answer: D. Median = 9.5×; EV = $200m × 9.5 = $1,900m; equity = $1,900m − $400m = $1,500m; ÷ 100m = $15.00. $19.00 forgets net debt.
2. Why are EV multiples preferred over P/E when peers carry very different amounts of debt?
- EV multiples are unaffected by financing choices
- P/E cannot be used for profitable companies
- P/E ignores the company’s interest expense
- EV multiples exclude taxes, so they are cash-based
Reveal Answer
Answer: A. Enterprise value and EBITDA or EBIT belong to all capital providers, so leverage does not distort them; P/E falls as leverage rises even for an identical business.
3. A target’s EBITDA includes $10 million of restructuring add-backs that recur every year. At a 9.0× median and 40 million shares, by how much does using that adjusted EBITDA overstate value per share?
- $22.50
- $0.25
- $2.25
- $0.90
Reveal Answer
Answer: C. $10m × 9.0 = $90m of EV; $90m ÷ 40m shares = $2.25 a share.
4. What happens if you compare an IFRS 16 reporter’s EBITDA multiple with a US GAAP peer’s without adjustment?
- The US peer’s EBITDA looks higher, as its lease costs are capitalized
- The IFRS peer’s EBITDA is flattered; lease costs sit below it
- The IFRS peer’s EBITDA looks lower, as leases are fully expensed
- Nothing changes, as both standards treat leases the same way
Reveal Answer
Answer: B. IFRS 16 moves lease costs into depreciation and interest, while US GAAP keeps operating lease cost inside operating expenses, flattering the IFRS company’s EBITDA.
- 26 U.S.C. §11 (corporate tax rate) — 21% federal rate
- IRS, Questions and answers about the limitation on the deduction for business interest expense — §163(j) 30% cap and post-2024 ATI add-back