CRR Change and Loan Pricing at a Cooperative Bank
A district cooperative bank has demand deposits of ₹800 crore. It holds cash reserves of ₹80 crore with the Reserve Bank, has lent ₹700 crore, and holds government securities worth ₹20 crore. The cash reserve ratio (CRR) is 5 per cent. The bank's manager claims that because ₹80 crore is 'idle cash', the bank can immediately lend ₹40 crore more without any problem. The central bank then raises the CRR to 8 per cent to control inflation. In the same district, consumer inflation is running at 7.5 per cent, while the bank charges 11 per cent nominal interest on personal loans. Borrowers are demanding a cut in the loan rate, saying the bank is 'profiteering'. The manager asks you to assess the lending capacity before and after the CRR change, and to advise on the loan rate. Assume no currency leakage and that borrowers keep their accounts with the bank.
1. Calculate required reserves, excess reserves and the maximum additional lending the bank can support at CRR 5 per cent and at 8 per cent. Evaluate the manager's claim that ₹40 crore can be lent immediately at the original CRR.
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At CRR 5%: required reserves = 5% × ₹800 crore = ₹40 crore; excess reserves = ₹80 crore − ₹40 crore = ₹40 crore. The manager is right only about the first round: the bank can lend its ₹40 crore excess. But if borrowers keep the proceeds as deposits, each new loan creates a new deposit and a new required reserve. Total deposits the system can support from ₹80 crore of reserves = ₹80 crore / 0.05 = ₹1,600 crore, so additional lending capacity is ₹1,600 − ₹800 = ₹800 crore, not ₹40 crore.
At CRR 8%: required reserves = ₹64 crore; excess reserves = ₹16 crore. Maximum total deposits = ₹80 crore / 0.08 = ₹1,000 crore; additional lending capacity = ₹200 crore. The ₹40 crore of 'idle cash' is therefore not all lendable once the CRR is 8%; only ₹16 crore is excess. The claim confuses cash with excess reserves.
2. The manager says the CRR hike of 3 percentage points will contract credit by 3 per cent of deposits (₹24 crore). Is this correct? Explain the money multiplier and the actual effect in this bank.
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No. A 3 percentage point rise in CRR is not a 3% cut in deposits. The simple deposit multiplier is 1/CRR: at 5% it is 20; at 8% it is 12.5. With the same ₹80 crore of reserves, potential deposits fall from ₹1,600 crore to ₹1,000 crore, a contraction of ₹600 crore in this simplified system. In this bank, excess reserves fall from ₹40 crore to ₹16 crore, so its additional lending capacity falls from ₹800 crore to ₹200 crore. The manager's ₹24 crore figure (3% of ₹800 crore) treats the CRR as if it were a tax on the existing deposit base and ignores multiple deposit creation. Actual contraction may be smaller because banks may hold excess reserves, currency leakage may occur, and loan demand may be weak; but the direction and scale are much larger than ₹24 crore.
3. With inflation at 7.5 per cent and the nominal loan rate at 11 per cent, calculate the real interest rate. If the bank wants a real return of 4 per cent when inflation is expected to remain 7.5 per cent, what nominal rate should it charge? Assess the borrowers' claim and the risk of raising the rate.
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Real interest rate = (1 + nominal rate)/(1 + inflation) − 1 = 1.11/1.075 − 1 ≈ 0.0326, or 3.26%. The approximation 11% − 7.5% = 3.5% is close. A 4% real return requires 1.04 × 1.075 − 1 ≈ 0.118, or about 11.8% nominal. On these numbers, the borrowers' 'profiteering' claim is not supported: the bank's real return is only about 3.3%, below the 4% target. But raising the nominal rate to 11.8% has risks: it may deter creditworthy borrowers, worsen repayment problems, and if actual inflation falls below 7.5%, the ex post real rate will be higher than intended. The bank should also consider regulatory caps and the fact that expected, not past, inflation matters. A better response may be to index or reprice selectively rather than raise all loan rates.