You are given the balance sheet of the First National Bank (FNB) below. Yield Duration (years) Yield Amount in million USD 31 150 200 250 Amount in million USD 253 50 Duratior (years) 460 1.25 0.5 0.2 50 0.95 175 375 350 0.02 0.22 7.55 4.25 0.42 3.78 0.55 1.65 250 Assets Cash Federal Funds 3-month T-bills 8-year T-bonds 5-year municipal bonds (munis) 6-month consumer loans 5-year car loans 7-month Cmmercial and Indistrial loans (C&I) 2-year C&l loans Fixed-rate mortgages (maturing in 5 months) Fixed-rate mortgages (maturing in 1 year) Fixed-rate mortgages (maturing in 5 years) Fixed-rate mortgages (maturing in 20 years) Premises and Equipment Total Assets Liablities and Equity Capital Demand Deposits Savings Accounts Money Market Deposit Accounts 3-month Certificate of Deposits (CDs) 1-year CDs 5-year CDs Federal Funds Repurchase Agreements (Repos) 6-month commercial paper Subordinated Notes: 1-year fixed rate Subordinated Debt: 7-year fixed rate Total Liabilities 350 2.05% 3.25% 6.50% 7.20% 5% 6% 4.80% 4.15% 5.10% 6.85% 5.30% 5.40% 225 0.50% 3.50% 3.20% 3.50% 5% 2% 2% 4.05% 5.55% 6.25% 200 275 450 4.85 0.02 0.05 0.55 0.97 6.6 290 300 200 100 2778 0.48 0.85 4.52 18.25 300 275 355 20 Equity Total Liabilities and Equity 378 3156 3156 a. What is the repricing gap if the planning period is One year? (5 points) b. What is FNB's duration gap? (5 points) c. What is the impact over the next year on net interest income if interest rates on rate-sensitive assets (RSAs) decrease 35 basis points and on rate-sensitive liabilities (RSLs) decrease 50 basis points? Explain the results. (Hint: 35 basis points is 0.35%). (10 points) d. Use the duration values to calculate the expected change in the value of the assets and liabilities of FNB for a predicted decrease of 0.35 percent in interest rates on assets and 0.50 percent on liabilities. (5 points) That is tho chonns in serierna faraonator from tho dentinn teolar fordonnann ofn 25 naunant in intrant entorno ansate and a. C. e. What is the repricing gap if the planning period is One year? (5 points) b. What is FNB's duration gap? (5 points) What is the impact over the next year on net interest income if interest rates on rate-sensitive assets (RSAs) decrease 35 basis points and on rate-sensitive liabilities (RSLs) decrease 50 basis points? Explain the results. (Hint: 35 basis points is 0.35%). (10 points) d. Use the duration values to calculate the expected change in the value of the assets and liabilities of FNB for a predicted decrease of 0.35 percent in interest rates on assets and 0.50 percent on liabilities. (5 points) W What is the change in equity value forecasted from the duration values for decrease of 0.35 percent in interest rates on assets and 0.50 percent on liabilities? (5 points) f. Use the duration gap model to calculate the change in equity value if the relative change in all market interest rates is a decrease of 50 basis points. (10 points) FNB's managers are expecting a larger shift in the yields on the fixed-rate mortgages. Particularly, they expect the yield on the 5 years fixed-rate mortgages to shift upward from 5.30% to 7%, that is a shift of 1.7 percentage points. Compute the convexity of this class of mortgages and show the impact of this shift on market value of these mortgages. Note that the principal value is 275 million, interest rate is 5.3% (equal to yield initially) and the mortgage is paid annually. (10 points) a op