A bank is pricing an unsecured personal loan with a 4% default probability and 70% loss given default. Build the minimum rate from its costs, including capital, and judge a proposal to undercut a competitor's 13% offer.

The floor is about 12.76%, so the competitor's 13% clears it by only 0.24 points, and the proposed 12.5% does not clear it at all. Funding costs 7.00%, running the loan 2.00%, expected loss 2.80% and the capital charge 0.96%. At 12.5% the loan earns 12.8% on its capital against a 15% hurdle. Allow for defaulters also skipping interest and the floor is nearer 13.3%, so undercutting would lend below cost.

A shopkeeper pricing a product adds what it cost to buy, the rent, an allowance for breakages, and a return on the money tied up in the shop. A loan is priced the same way. Funding costs 7.00%, servicing 2.00%, expected loss is 4% x 70% = 2.80%, and the capital charge is 0.96%: a floor of 12.76% before any profit above the hurdle. The expected lossThe average credit loss a lender should plan for: the probability of default times the share of the loan lost if default happens. It is a cost of doing business, priced in, not a risk held capital against. is a cost, like breakages: across many loans it will happen, so it belongs in the price.

The capital charge needs one more sentence because it is where candidates go wrong. Of every Rs 100 lent, Rs 12 is funded by shareholders and Rs 88 by deposits. The 7% funding line already charges for all Rs 100 as if it were deposits. Shareholders want 15% on their Rs 12, which is 8 points more than deposits cost, so the extra charge is 12% x 8% = 0.96%.

Turn each rate into the return on the capital it uses. Profit per Rs 100 is the rate less Rs 6.16 of deposit cost on Rs 88, less Rs 2 of servicing and Rs 2.80 of expected loss, all divided by the Rs 12 of capital. At 12.5% the loan earns 12.8% on capital, below the 15% shareholders require; at 13% it earns 17.0%. Because capital is only 12% of the loan, every 0.1 point of rate moves the return on capital by about 0.8 points, so small pricing decisions have large effects on value.

Two things, and both push the floor up. First, the additive build assumes a defaulter still pays the year's interest. Over one year, a borrower who defaults pays neither interest nor the lost 70% of principal, so the rate must be earned on the 96% who repay. Solving it exactly, the floor is about 13.29%, which puts even the competitor's 13% slightly below full cost. Second, adverse selectionWhen a lower price attracts a disproportionate share of the riskier customers, because they are the ones most often turned down or overcharged elsewhere.: if Chandrakor undercuts the market, it attracts borrowers other lenders priced higher or declined. If the true default rate in that pool is 5% instead of 4%, expected loss rises to 3.50% and the floor to 13.46%.

So the judgement is clear on these numbers. Undercutting at 12.5% lends below cost from the first day, and the shortfall widens if the cheaper price draws in weaker borrowers. Matching 13% is roughly break-even once defaults are treated properly. The bank should hold its price at or above 13% for this grade and compete on speed and service, or tighten the grade so that the default rate supports a lower rate. The limitation of the whole exercise is that the 4% and 70% are estimates from the bank's own history; a new segment deserves a margin for being wrong about them.