Flat rate versus reducing balance on a vehicle purchase
A trading company needs a delivery van costing Rs. 1,500,000 and has two financing offers, both with no down payment and 36 equal monthly instalments. Dealer A quotes '9% per annum', computed on the original amount financed, added to the principal and spread evenly over the 36 instalments. Dealer B quotes '15% per annum on the reducing balance', which produces an instalment of about Rs. 52,000 per month. The company's treasurer applies a hurdle effective annual cost of funds of 13% to asset-finance decisions and has asked for a like-for-like comparison. Dealer A's salesman has told the board that his 9% is 'six percentage points cheaper' than Dealer B's 15%. Assume instalments are paid at the end of each month and ignore tax, depreciation and residual value.
1. Compute Dealer A's monthly instalment and total outlay, compare it with Dealer B's total outlay, and say which offer is cheaper in cash terms.
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Dealer A: interest is charged on the original principal for the whole term. Interest = 1,500,000 × 0.09 × 3 = Rs. 405,000. Total payable = 1,905,000, so instalment = 1,905,000 / 36 = Rs. 52,916.67.
Dealer B: total payable = 52,000 × 36 = Rs. 1,872,000, instalment Rs. 52,000.
Dealer B is cheaper by 1,905,000 − 1,872,000 = Rs. 33,000 on identical cash-flow timing (same 36 end-of-month instalments, same nil deposit).
The comparison is legitimate precisely because the instalment schedules are structurally identical - only the amounts differ. If the terms had differed (e.g. a deposit, or a balloon), the raw totals would no longer be comparable and a present-value approach would be required.
2. Assess the salesman's 'six percentage points cheaper' claim and state the approximate reducing-balance equivalent of A's 9% flat rate over 36 months, and the effective annual cost of B's 15% offer.
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The claim is wrong, and wrong in the direction that matters. A flat rate charges interest on the full Rs. 1,500,000 for all 36 months, even though the outstanding balance falls to near zero. The average balance over the term is roughly half the principal, so a flat rate of 9% is worth roughly double that on a reducing balance.
Standard conversion for an n-instalment loan: reducing rate ≈ flat rate × 2n / (n + 1) = 9 × 72/37 ≈ 17.5% per annum.
Dealer B: monthly rate = 15%/12 = 1.25%, so effective annual = 1.0125^12 − 1 = 16.08%.
So A's 9% is really about 17.5% against B's 16.1% - A is the more expensive of the two, exactly as the Rs. 33,000 outlay gap shows. Both figures are above the treasurer's 13% hurdle, so strictly neither offer clears it, and the recommendation should be to take B only if the van's returns exceed 13% or to seek a third quote.
3. The company can afford no more than Rs. 45,000 per month. On Dealer B's terms (15% reducing, 36 months), what minimum down payment closes the gap? Use an instalment factor of 0.034665 per rupee of principal.
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Maximum principal that Rs. 45,000 per month will service:
P = 45,000 / 0.034665 = Rs. 1,298,128 (approximately Rs. 1,298,000).
Required down payment = 1,500,000 − 1,298,128 = Rs. 201,872, i.e. about Rs. 202,000.
Check: 1,298,128 × 0.034665 = Rs. 45,000.00 per month, so total instalments 1,620,000 plus deposit 201,872 = Rs. 1,821,872 - about Rs. 50,000 less than the nil-deposit version of the same offer, because the financed principal is smaller.
Two cautions belong in the answer rather than the arithmetic: the Rs. 202,000 must come from the company's own funds, which has an opportunity cost at the 13% hurdle; and a lower instalment with a deposit is not automatically 'cheaper' for liquidity purposes if the cash is needed for working capital. Rounding the deposit up to Rs. 205,000 gives a small buffer against rate movement.