Certainly! Let’s break down the solution step by step as you requested. --- **STEP 1: Introduction to the Concept (Repricing Model and Interest Rate Sensitivity)** The **repricing model** (or gap analysis) is a tool banks use to measure their exposure to interest rate risk. It does so by comparing the amount of assets and liabilities that reprice (i.e., reset their interest rates) within a specific time frame. The difference is called the "repricing gap." - If assets that reprice in a given period exceed liabilities (positive gap), a fall in interest rates **reduces net interest income**. - If liabilities that reprice exceed assets (negative gap), a fall in rates **increases net interest income**. The bank's net interest income (NII) = Interest Income from Assets – Interest Expense on Liabilities. If interest rates fall, both asset and liability yields fall, but the impact depends on the timing and size of repricing. --- **STEP 2: Calculate the Change in Interest Rates on Assets and Liabilities** Let’s assume the cash rate **decreases by 1%** (for example, from 4.35% to 3.35%) over the year. (If you have a specific decrease, you can substitute it.) **Formulae:** - Interest rate on assets = 1.7 × Cash rate + 1.225% - Interest rate on liabilities = 1.2 × Cash rate + 0.75% Let’s do the calculations: **Before** (Cash rate = 4.35%): - Asset rate = 1.7 × 4.35% + 1.225% = 7.395% + 1.225% = **8.62%** - Liability rate = 1.2 × 4.35% + 0.75% = 5.22% + 0.75% = **5.97%** **After** (Cash rate = 3.35%): - Asset rate = 1.7 × 3.35% + 1.225% = 5.695% + 1.225% = **6.92%** - Liability rate = 1.2 × 3.35% + 0.75% = 4.02% + 0.75% = **4.77%** **Change:** - Asset rate decreases by: 8.62% – 6.92% = **1.70%** - Liability rate decreases by: 5.97% – 4.77% = **1.20%** --- **STEP 3: Calculate Impact on Net Interest Income Using the Repricing Model** **A. Identify Rate-Sensitive Assets (RSA) and Rate-Sensitive Liabilities (RSL) within 1 year** Assets repricing within 1 year: - Cash: $50 (assume immediately reprices) - Investments: - Treasury Bonds: $120 (maturing within 6 months) + $60 (maturing within 6-12 months) = $180 - Municipal Bonds: $0 (all beyond 1 year) - Corporate Bonds: $0 (all beyond 1 year) - Loans: - Floating-rate Mortgages: $300 (reprices every 9 months, so within 1 year) - Corporate Loans: $270 (maturing within 1-2 years; for 1 year, allocate roughly half: $135) - Consumer Loans: $180 (duration 0.5 years) - Other Long-term Assets: $0 (as duration is 2 years) **Total RSA within 1 year =** Cash ($50) + Treasury Bonds ($180) + Floating Mortgages ($300) + Corporate Loans ($135) + Consumer Loans ($180) = **$845 million** Liabilities repricing within 1 year: - Six-month Term Deposits: $465 - Certificates of Deposit: $115 (six-month) + $120 (two-year, half assumed within 1 year) = $175 - Short-term Borrowings: $130 **Total RSL within 1 year =** Six-month Term Deposits ($465) + Certificates of Deposit ($175) + Short-term Borrowings ($130) = **$770 million** **Repricing Gap (within 1 year) =** RSA – RSL = $845 million – $770 million = **+$75 million (positive gap)** **B. Calculate Change in Net Interest Income (NII)** ΔNII ≈ Gap × (Δ in rate on assets – Δ in rate on liabilities) Δ in rate on assets = –1.70% Δ in rate on liabilities = –1.20% Net change = –1.70% – (–1.20%) = –0.50% ΔNII = $75 million × (–0.50%) = **–$0.375 million** (i.e., net interest income decreases by $375,000 over the year due to the rate drop). --- **STEP 4: Final Summary (Few Sentences)** A 1% decrease in the cash rate reduces the bank’s asset yields by 1.70% and liability yields by 1.20%. Since the bank has a positive 1-year repricing gap ($75 million), the decrease in rates will reduce net interest income by approximately $375,000 over the year. --- **STEP 5: What We Did in Each Step (Summary)** 1. **Introduced** the repricing model and its role in measuring interest rate sensitivity. 2. **Calculated** the change in asset and liability rates resulting from a 1% drop in the cash rate. 3. **Identified** rate-sensitive assets and liabilities within one year and computed the 1-year repricing gap. 4. **Applied** the change in rates to the gap to estimate the impact on net interest income. 5. **Summarized** the key findings and steps clearly and concisely. --- **If you wish to use a different cash rate decrease or need further breakdown by different time buckets, let me know!**