Sigma Bank has the following balance sheet in millions of dollars.Unless mentioned otherwise, all assets are associated with corporate customers (not governments or sovereigns).Values are in millions of dollars.Refer to table 20-8 for appropriate risk weights. $$\begin{array} { | l | r | l | r | }
\hline \text { Cash } & \$ 40 & \text { Deposits } & \$ 370 \
\hline \begin{array} { l }
\text { Municipal General } \
\text { Obligation Bonds }
\end{array} & \$ 60 & & \
\hline \begin{array} { l }
\text { Residential Mortgages } \
\text { 1-4 family } \
\left( 80 \% { - 90\% } \text { LTV } \right)
\end{array} & \$ 100 & \begin{array} { l }
\text { Perpetual Preferred } \
\text { Stock }
\end{array} & \$ 20 \
\hline \begin{array} { l }
\text { Commercial loans } \
\text { BB + rated }
\end{array} & \$ 200 & \text { Equity } & \$10\
\hline \text { Total Assets } & \$ 400 & & \$ 400 \
\hline
\end{array}$$ Off balance sheet contingent liabilities (Refer to Table 20-10) $40 million direct-credit substitute standby letters of credit issued to a U.S.corporation.
$40 million commercial letters of credit issued to a corporation
Off-balance sheet derivatives (Refer to Table 20-11)
$200 million 10-year interest rate swaps
$100 million 2-year forward DM contracts
What is the minimum required Tier I and Total risk-based capital for the on-balance-sheet assets in order for the DI to be adequately capitalized?

Question

Sigma Bank has the following balance sheet in millions of dollars.Unless mentioned otherwise, all assets are associated with corporate customers (not governments or sovereigns).Values are in millions of dollars.Refer to table 20-8 for appropriate risk weights. $$\begin{array} { | l | r | l | r | } 
\hline \text { Cash } & \$ 40 & \text { Deposits } & \$ 370 \
\hline \begin{array} { l } 
\text { Municipal General } \
\text { Obligation Bonds }
\end{array} & \$ 60 & & \
\hline \begin{array} { l } 
\text { Residential Mortgages } \
\text { 1-4 family } \
\left( 80 \% { - 90\% } \text { LTV } \right)
\end{array} & \$ 100 & \begin{array} { l } 
\text { Perpetual Preferred } \
\text { Stock }
\end{array} & \$ 20 \
\hline \begin{array} { l } 
\text { Commercial loans } \
\text { BB + rated }
\end{array} & \$ 200 & \text { Equity } & \$10\
\hline \text { Total Assets } & \$ 400 & & \$ 400 \
\hline
\end{array}$$ Off balance sheet contingent liabilities (Refer to Table 20-10) $40 million direct-credit substitute standby letters of credit issued to a U.S.corporation.
$40 million commercial letters of credit issued to a corporation
Off-balance sheet derivatives (Refer to Table 20-11)
$200 million 10-year interest rate swaps
$100 million 2-year forward DM contracts
What is the minimum required Tier I and Total risk-based capital for the on-balance-sheet assets in order for the DI to be adequately capitalized?

Quizplus · Accepted Answer

The minimum required Tier I and Total risk-based capital for the on-balance-sheet assets is calculated based on the risk weights of the assets and the required capital ratios. For a depository institution (DI) to be adequately capitalized, it must maintain a Tier I capital ratio of at least 4% and a Total capital ratio of at least 8% of its risk-weighted assets. - Cash has a 0% risk weight.- Municipal General Obligation Bonds typically have a 20% risk weight.- Residential Mortgages with 80%-90% LTV have a 50% risk weight.- Commercial loans rated BB+ have a 100% risk weight.- Off-balance sheet items and other assets like Perpetual Preferred Stock and Equity are not directly mentioned in the question for their risk weights, but they are not typically included in the calculation for minimum required capital for on-balance-sheet assets.Calculation:- Cash: $40 million * 0% = $0- Municipal Bonds: $60 million * 20% = $12 million- Residential Mortgages: $100 million * 50% = $50 million- Commercial Loans: $200 million * 100% = $200 million- Total Risk-Weighted Assets = $0 + $12 million + $50 million + $200 million = $262 millionTier I Capital Requirement = 4% of $262 million = $10.48 millionTotal Capital Requirement = 8% of $262 million = $20.96 millionThe closest match to these calculations is option C, which suggests a slight difference in calculation or rounding, but it indicates the need for both Tier I and Total risk-based capital to be above the calculated amounts to be adequately capitalized.

Sigma Bank Has the Following Balance Sheet in Millions of Dollars.Unless