Question

first bank has the following balance sheet in millions of dollars with the basel ii risk weights given in parentheses. u.s. govt t-bonds (0%) $150m deposits $1420m govt. agency fnma bonds (20m subordinated debt ((tier 2) $20m university dorm bonds (50%) $350m preferred stock (tier 2) $25m consumer loans aaa-rated (20%) $450m commercial loans bbb-rated (100%) $300m equity (tier 1) $35m total $1500m $1500m a. does the bank have enough capital to meet the requirements as specified by basel ii? b. the bank wishes to keep its tier 1 ratio at 6%. they will sell a portion of their commercial loans and invest them in u.s. government bonds. how much consumer loans should they sell?

Answer 1

To determine if the bank has enough capital to meet Basel II requirements, we calculate the Tier 1 and total capital ratios. The bank has enough capital to meet the requirements. To keep a Tier 1 ratio of 6%, the bank should sell approximately $534.86 million of consumer loans.

Step-by-step explanation:

To determine if the bank has enough capital to meet the requirements specified by Basel II, we need to calculate the Tier 1 and total capital ratios. The Tier 1 ratio is calculated by dividing Tier 1 capital by risk-weighted assets. The total capital ratio is calculated by dividing total capital by risk-weighted assets. The formulas for the Tier 1 and total capital ratios are:

Tier 1 ratio = Tier 1 capital / risk-weighted assets

Total capital ratio = total capital / risk-weighted assets

Given the information provided, we can calculate the Tier 1 and total capital ratios:

• Tier 1 capital = equity (tier 1) = $35m
• Total capital = equity (tier 1) + preferred stock (tier 2) + subordinated debt (tier 2) = $35m + $25m + $20m = $80m
• Risk-weighted assets = (U.S. govt T-bonds x 0%) + (deposits x 0%) + (govt. agency FNMA bonds x 20%) + (university dorm bonds x 50%) + (consumer loans AAA-rated x 20%) + (commercial loans BBB-rated x 100%) = ($150m x 0%) + ($1420m x 0%) + ($20m x 20%) + ($350m x 50%) + ($450m x 20%) + ($300m x 100%) = $0m + $0m + $4m + $175m + $90m + $300m = $569m
• Tier 1 ratio = $35m / $569m ≈ 6.14%
• Total capital ratio = $80m / $569m ≈ 14.05%

Based on the calculated ratios, the bank has enough capital to meet the requirements specified by Basel II.

To calculate how much consumer loans the bank should sell in order to keep its Tier 1 ratio at 6%, we can use the equation:

New Tier 1 capital = Tier 1 ratio × New risk-weighted assets

Let x be the amount of consumer loans to be sold:

$35m = 0.06 × ($569m - x)

From the equation, we can solve for x:

$35m = 0.06 × $569m - 0.06x

0.06x = 0.06 × $569m - $35m

0.06x = $34.14m

x = $34.14m / 0.06 ≈ $569m - $34.14m ≈ $534.86m

Therefore, the bank should sell approximately $534.86 million dollars of consumer loans in order to keep its Tier 1 ratio at 6%.