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FRM Exam Part II · Capital Structure in Banks

Optimal Capital Structure and Cost of Capital for Banks

Updated 11 October 2026 · Fact-checked

A bank's optimal capital structure balances cheap debt and deposits against the equity needed to absorb losses. Modigliani-Miller says funding mix does not change value without frictions. In banks, frictions such as deposit insurance, tax shields and regulation matter. You solve questions by finding which friction drives the answer.

Understand Optimal Capital Structure and Cost of Capital for Banks

Start with Modigliani-Miller (MM). In a world with no taxes, no bankruptcy costs, no subsidies and symmetric information, a firm's total value does not depend on how it is funded. More debt makes equity riskier, so the cost of equity rises exactly enough to keep the weighted average cost of capital (WACC) constant. Debt looks cheaper, but you pay for it through a higher required return on equity.

The key point for banks: this is a benchmark, not a description of reality. It shows that equity is not "expensive" in itself. Equity looks costly only when debt is cheaper for reasons other than risk transfer, such as tax deductibility of interest or subsidies.

For banks, the main friction is the safety net. Deposit insurance and implicit government support (too-big-to-fail) make deposit and debt funding cheaper than the bank's risk would justify. Depositors have little reason to charge for risk, so the bank can raise leverage without paying a matching rise in funding cost. This subsidy pushes banks toward high leverage and also creates moral hazard: shareholders gain from upside, while insurers and taxpayers bear part of the downside. Risk-based deposit premiums and capital regulation try to offset this.

The costs of leverage also exist. Higher leverage raises the probability of distress, the cost of failure and the risk of runs on short-term funding. Debt overhang can discourage lending, because new profits go first to creditors. Banks also gain from tax shields on interest. The trade-off view says the optimum is where the marginal benefit of cheap funding equals the marginal cost of distress.

Regulators set minimum capital because private choices ignore the cost of failure to others (systemic externalities). Banks argue that higher capital raises their funding cost and cuts lending. The MM-based reply is that the higher equity cost is partly offset by lower risk of debt, so the rise in WACC is smaller than the simple comparison suggests. Only the part tied to subsidies and taxes is a real cost to the bank, and it is not necessarily a social cost.

Key formulas to remember

MM Proposition I (no taxes)
V(levered) = V(unlevered)
Firm value is independent of the debt-equity mix, assuming no frictions.
MM Proposition II (no taxes)
Re = R0 + (R0 − Rd) × (D ÷ E)
Cost of equity rises linearly with debt-to-equity. R0 is the unlevered cost of capital; Rd is the cost of debt, assumed risk-free-like in this form.
WACC
WACC = (E ÷ V) × Re + (D ÷ V) × Rd × (1 − t)
V = D + E. Set t = 0 for the pure MM case. Under MM with no taxes, WACC equals R0 at any leverage.
Leverage ratio
Leverage = Assets ÷ Equity; Equity ratio = Equity ÷ Assets
Higher leverage amplifies ROE up and down.
Return on equity under leverage
ROE = ROA × (Assets ÷ Equity) − Cost of debt × (Debt ÷ Equity)
Useful when ROA is pre-interest return on assets. Check the question's definition of ROA.

How to solve Optimal Capital Structure and Cost of Capital for Banks questions

Use this approach for numeric and conceptual questions on bank funding and capital cost.

  1. 1Identify the setting: pure MM (no frictions) or one with taxes, deposit insurance or distress costs.
  2. 2List the givens: D, E, V, Re, Rd, tax rate t, unlevered cost R0.
  3. 3If asked for cost of equity or WACC, pick the right formula and check that weights use the same value base.
  4. 4Compute step by step and sanity check: Re must rise with leverage, and WACC must be constant under pure MM.
  5. 5If the question is conceptual, name the friction (tax shield, deposit insurance subsidy, moral hazard, distress cost) and its direction of effect.
  6. 6Separate private cost from social cost: a higher bank WACC from losing a subsidy is not a real economic cost.
  7. 7State the conclusion with the interpretation, then match it to the option.

Quickest way: Friction-first elimination

When to use it: Use for conceptual multiple-choice items where options mix MM claims with bank-specific claims.

  1. Ask: does the question assume no frictions? If yes, the answer is that funding mix does not change value or WACC.
  2. If deposit insurance or implicit guarantees appear, expect cheaper debt, higher leverage incentives and moral hazard.
  3. Reject options saying equity is simply more expensive than debt without a risk or subsidy reason.
  4. For numbers, use Re = R0 + (R0 − Rd) × D/E and check direction before computing.

Common mistakes in Optimal Capital Structure and Cost of Capital for Banks

  • Treating debt as cheaper so WACC must fall with leverage under MM.

    You compare Rd with Re and forget Re rises with leverage.

    Fix: Under no-friction MM, Re increases exactly to offset cheaper debt, so WACC stays at R0.

  • Using D ÷ V instead of D ÷ E in Proposition II.

    Both ratios appear in capital structure formulas.

    Fix: Proposition II uses debt-to-equity, D ÷ E. WACC weights use D ÷ V and E ÷ V.

  • Saying deposit insurance reduces bank risk-taking.

    Insurance sounds like protection.

    Fix: It protects depositors but weakens their monitoring, so it creates moral hazard and encourages leverage unless premiums are risk-based and capital is regulated.

  • Claiming MM proves higher capital requirements are costless to banks in reality.

    Overstating a benchmark.

    Fix: MM holds only without frictions. Taxes and subsidies make some private cost real. The point is that the cost is smaller than a naive comparison implies and is not a social cost.

  • Forgetting the tax factor (1 − t) on debt in WACC.

    You memorise the no-tax case.

    Fix: Apply (1 − t) to the cost of debt whenever a tax rate is given.

Worked examples

Example 1

An unlevered bank-like firm has a cost of capital R0 = 10%. Its debt costs Rd = 4%. Under MM with no taxes, what is the cost of equity if D ÷ E = 1.5, and what is the WACC?

Show the solution
  1. Use Re = R0 + (R0 − Rd) × (D ÷ E).
  2. R0 − Rd = 10% − 4% = 6%.
  3. 6% × 1.5 = 9%.
  4. Re = 10% + 9% = 19%.
  5. Weights: D ÷ E = 1.5 means D = 1.5E, so V = 2.5E. D ÷ V = 0.6, E ÷ V = 0.4.
  6. WACC = 0.4 × 19% + 0.6 × 4% = 7.6% + 2.4% = 10%.

Answer: Cost of equity = 19%; WACC = 10%, equal to R0, as MM predicts.

Example 2

A bank has assets of $100 billion, equity of $8 billion and debt (including deposits) of $92 billion costing 3% on average. Pre-interest ROA is 4%. Ignore tax. Compute ROE. Then, if assets earn 1% instead, compute ROE and explain what it shows.

Show the solution
  1. Leverage: Assets ÷ Equity = 100 ÷ 8 = 12.5.
  2. Debt ÷ Equity = 92 ÷ 8 = 11.5.
  3. ROE = 4% × 12.5 − 3% × 11.5 = 50% − 34.5% = 15.5%.
  4. Check in dollars: income = $4 billion; interest = $2.76 billion; profit = $1.24 billion; ÷ $8 billion = 15.5%.
  5. Second case: 1% × 12.5 = 12.5%; minus 34.5% = −22%.
  6. Check: income $1 billion − $2.76 billion = −$1.76 billion; ÷ 8 = −22%.

Answer: ROE is 15.5% in the first case and −22% in the second. High leverage amplifies returns in both directions, which is why equity absorbs losses and why leverage choice is a risk-return trade-off.

Exam tips

  • Read the first line for assumptions: no-friction means MM holds, any subsidy or tax means it does not.
  • Expect conceptual items on deposit insurance: the answer is usually cheaper funding, weaker market discipline and moral hazard.
  • When asked why banks resist higher capital, identify subsidies and tax shields as the true private cost, not equity being inherently dearer.
  • For numbers, check WACC equals R0 in the pure MM case as a quick verification.

Practice questions from Capital Structure in Banks

Optimal Capital Structure and Cost of Capital for Banks in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Optimal Capital Structure and Cost of Capital for Banks: frequently asked questions

How does deposit insurance affect bank leverage?

It lowers the funding cost of deposits below what the bank's risk would justify and weakens depositor monitoring. Banks therefore tend to hold more leverage. Risk-based premiums and capital rules aim to offset this moral hazard.

Does Modigliani-Miller apply to banks?

As a benchmark, yes. In a world without taxes, subsidies and distress costs, funding mix would not change bank value. In practice, deposit insurance, implicit guarantees and taxes break the assumptions, so MM is used to isolate what is a real cost.

Why does cost of equity rise when a bank adds debt?

Equity holders bear the residual risk, and more debt makes earnings to equity more volatile. They require a higher return. Under MM this rise exactly offsets the cheaper debt in the WACC.

What is the trade-off in choosing bank leverage?

Benefits include cheaper funding from the safety net and tax shields on interest. Costs include higher distress probability, run risk and debt overhang. Regulators add minimum capital because failure also harms others.