Question

Consider Bank A, which currently has $195 worth of loans and $5 in cash as its assets, and $190 of demand deposits as its only source of debt. The interest rate on the loans is 5 percent and the bank pays 3 percent interest on the demand deposits.

a. Calculate any relevant measures of the bank’s profitability.
b. Now suppose regulators (1) require that the bank pay $1 per year in deposit insurance premiums and (2) impose a capital requirement of 10% of assets (the Bank will maintain the same assets, but change its capital structure). As a result of the regulation, Bank A’s cost of debt falls to 2%. Re-calculate the relevant measures of the bank’s profitability.
c. What is the net effect of the new regulatory burden on Bank A?

Answer 1

Initially, Bank A's net interest income is calculated to be $4.05. After the imposition of new regulations, despite the $1 deposit insurance cost and an increased capital requirement leading to a change in capital structure, the bank's profitability increases to $5.15 due to a lower cost of debt.

Step-by-step explanation:

Calculating the bank's profitability initially:

1. Interest income from loans: $195 × 5% = $9.75
2. Interest expense on deposits: $190 × 3% = $5.70
3. Net interest income: $9.75 - $5.70 = $4.05

After the new regulations:

1. New capital requirement assets: 10% × $200 = $20 (assuming total assets are $200, loans + cash)
2. New capital raised: $20 - $5 (existing cash) = $15
3. New cost of debt: $190 × 2% = $3.80
4. Net interest income after regulations: ($195 × 5%) - $3.80 - $1 (deposit insurance) = $5.15

The net effect of the new regulatory burden on Bank A is an increase in profitability since net interest income increases from $4.05 to $5.15, even after accounting for deposit insurance and the change in capital structure.