Discounting a Ragi Bill versus a Gold Loan
A wholesale cooperative in Hubballi supplies 600 bags of ragi to a trader for ₹2,40,000. The trader accepts a bill payable 8 months hence. The cooperative needs cash now and considers three options. Bank X will discount the bill at 12% per annum banker's discount. Bank Y will discount the same bill at 13% per annum true discount for the same unexpired period. A gold-loan company will lend ₹2,20,000 for 8 months at 14% per annum simple interest and charge a ₹2,000 processing fee, deducted from the disbursement. The cooperative can use only one option. The treasurer wants the largest immediate cash and the lowest finance charge, but is confused because Bank X quotes a lower rate than Bank Y. Assume 1 year = 12 months, no other charges, and that the bill is certain to be paid. Compare the three options and advise.
1. Compute the immediate cash proceeds under Bank X and Bank Y. Which gives more cash?
Read the worked answer
The unexpired period is n = 8/12 = 2/3 year.
Bank X, banker's discount at 12%: BD = F n i = 2,40,000 × (2/3) × 0.12 = ₹19,200. Proceeds = 2,40,000 − 19,200 = ₹2,20,800.
Bank Y, true discount at 13%: First, n i = (2/3) × 0.13 = 0.0866667. TD = F n i/(1 + n i) = 2,40,000 × 0.0866667 / 1.0866667 = ₹19,141.10. Proceeds = 2,40,000 − 19,141.10 = ₹2,20,858.90.
Bank Y gives ₹58.90 more immediate cash. The rupee finance charge is also lower under Y by the same ₹58.90.
2. Compute the net cash and total finance charge for the gold loan. Compare it with the two bill options.
Read the worked answer
Gold loan: Interest = 2,20,000 × (2/3) × 0.14 = ₹20,533.33. Processing fee = ₹2,000. Total finance charge = 20,533.33 + 2,000 = ₹22,533.33. If the fee is deducted from disbursement, net cash now = 2,20,000 − 2,000 = ₹2,18,000. Repayment at maturity = 2,20,000 + 20,533.33 = ₹2,40,533.33.
Comparison of immediate cash: Bank X ₹2,20,800; Bank Y ₹2,20,858.90; gold loan ₹2,18,000. Comparison of finance charge: Bank X ₹19,200; Bank Y ₹19,141.10; gold loan ₹22,533.33.
The gold loan is worst on both stated criteria: it gives the least cash now and carries the highest rupee charge.
3. Explain why Bank X's 12% quote is not cheaper than Bank Y's 13% quote. Compute effective annual finance cost for each option and recommend.
Read the worked answer
Banker's discount is charged on the face value, but the borrower receives only the net proceeds. True discount is effectively charged on the present value actually received. So quoted rates are not directly comparable.
Bank X effective annual cost = (19,200/2,20,800) × (12/8) = 0.0869565 × 1.5 = 0.130435, or 13.04%.
Bank Y effective annual cost = (19,141.10/2,20,858.90) × 1.5 = 0.0866667 × 1.5 = 0.13, or 13.00%.
Gold loan effective annual cost = (22,533.33/2,18,000) × 1.5 = 0.103364 × 1.5 = 0.15505, or about 15.51%.
Bank Y is cheapest on an effective basis, even though its quoted 13% is higher than Bank X's 12%. Recommend Bank Y: it gives the largest immediate cash, the smallest rupee finance charge, and the lowest effective annual cost.