Imagine a bank with the assets below (with respective risk weights) and subject to a leverage ratio requirement. Banking regulation (leverage ratio requirement) requires the bank’s debt-to-asset ratio to be no larger than 94%.

List of Assets in the Bank’s Balance Sheet

Cash and Reserves, Value = $100M, Risk Weight = 0%.

Mortgage Loans 1, Value = $150M, Risk Weight = 20%.

Mortgage Loans 2, Value = $300M, Risk Weight = 60%.

C&I Loans, Value = $250M, Risk Weight = 100%.

Consumer Loans, Value = $200M, Risk Weight = 100%.

Calculate the minimum amount of equity capital (in dollars) that the bank needs to have to satisfy the capital requirement.

Question

Imagine a bank with the assets below (with respective risk weights) and subject to a leverage ratio requirement. Banking regulation (leverage ratio requirement) requires the bank’s debt-to-asset ratio to be no larger than 94%.

List of Assets in the Bank’s Balance Sheet

Cash and Reserves, Value = $100M, Risk Weight = 0%.

Mortgage Loans 1, Value = $150M, Risk Weight = 20%.

Mortgage Loans 2, Value = $300M, Risk Weight = 60%.

C&I Loans, Value = $250M, Risk Weight = 100%.

Consumer Loans, Value = $200M, Risk Weight = 100%.

Calculate the minimum amount of equity capital (in dollars) that the bank needs to have to satisfy the capital requirement.

BlackTom AI · Accepted Answer

Debt-to-asset ratio ≤ 94% implies equity/assets ≥ 1 − 0.94 = 0.06 (i.e., equity must be at least 6% of total assets).

1) Relevant knowledge points:
- Leverage (debt-to-asset) constraint uses raw (unweighted) balance-sheet amounts, not risk-weighted assets. 
- If D/A ≤ 0.94 and A = total assets, then equity E = A − D so E/A ≥ 0.06.
- Total assets = sum of all asset line items.

2) Compute total assets:
- Cash and reserves = $100M
- Mortgage Loans 1 = $150M
- Mortgage Loans 2 = $300M
- C&I Loans = $250M
- Consumer Loans = $200M
Total assets A = 100 + 150 + 300 + 250 + 200 = $1,000M

3) Solve for minimum equity:
- E/A ≥ 0.06 → E ≥ 0.06 × A
- E ≥ 0.06 × $1,000M = $60M
Thus minimum equity required is $60 million.

4) Why this is correct:
- The leverage requirement is stated in terms of debt-to-asset ratio, so the calculation uses raw assets. Using A = $1,000M, the smallest equity that keeps D/A ≤ 0.94 is 6% of assets, i.e., $60M. Any smaller equity would make debt exceed 94% of assets.

5) Why other choices are incorrect:
- $39.6M equals 6% of risk-weighted assets (RWA). If one computes RWA: 150×0.20 = 30; 300×0.60 = 180; 250×1.00 = 250; 200×1.00 = 200; cash = 0; total RWA = 660; 0.06×660 = 39.6. That is a risk-based capital number, not the leverage (debt/asset) requirement, so it’s not applicable here.
- $940M is 94% of total assets (allowed debt), not equity.
- $620.4M and $85.3M do not correspond to the leverage constraint minimum; they either exceed the minimum (so are unnecessarily large) or are derived from incorrect formulas.

Conclusion: The minimum equity required to satisfy the leverage (debt-to-asset ≤ 94%) rule is $60.0M, matching the provided answer.

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