A client wants to lend Rs 50 lakh to a friend's business at 18%. If there is a 20% chance of default with 30% recovery, what is his expected return, and how do you have the conversation?

The expected return is about 0.4%, not 18%. Repaid, he gets Rs 59.0 lakh; in default, Rs 15.0 lakh. Weighted 80 to 20, that averages Rs 50.2 lakh on Rs 50 lakh. The loan only matches a 7% deposit if the default chance is below 12.5%, or if the rate is 26.2%. The conversation separates helping a friend from making an investment.

A shop that sells a hundred mangoes at Rs 20 profit each, but throws away twenty rotten ones at Rs 40 loss each, does not earn Rs 20 a mango. The coupon is what a loan pays if nothing goes wrong; the expected return weights every outcome by its chance. Here the good branch pays Rs 59.0 lakh and the bad branch Rs 15.0 lakh, and the 20% chance of the bad branch eats almost all of the extra interest.

Turn the question around, because it gives Yogesh something he can check. At 18%, the loan matches a 7% deposit only if the default chance is below 12.5%; at a 20% default chance, it would need a rate of about 26.2%. Then add what the average hides: one time in five, Yogesh loses Rs 35 lakh, over 11% of his portfolio, and possibly the friendship. A deposit has no bad branch at all.

Separate the two decisions he is making at once. Helping a friend is a legitimate choice; calling it an 18% investment is what goes wrong. If he wants to help, size the loan to an amount he could lose without changing his plans, say Rs 10 to 15 lakh, put it in writing with security over the machine, and count it outside the investment portfolio. If he wants a return, the numbers say this is not one.

Be honest about the soft number too. The 20% default chance is a judgement, not a measurement, and Yogesh may think his friend is safer than that. Run it at 10%: the expected return rises, but the Rs 35 lakh loss in the bad branch is unchanged, and so is the concentration in one borrower.