> the value of that asset is at least the amount you borrowed

That assumption just isn't true: Loans are made based on risk and the expected ability to repay. Collateral is an optional and sometimes partial of reducing the lenders' risk, it bears no firm relationship to the amount being sought.

To illustrate, imagine a Debtor borrows $5,000 and offers up one of their child's crayon drawings as collateral. For private reasons we cannot see, the Lender accepts this deal. Do you truly believe the crayon-drawing has been proven to be "worth at least $5,000"? Would you joyfully jump at the chance to buy that crayon-drawing for a mere $1,250, confident that you could resell it for an easy $3,750 profit?

Probably not, and that's assuming everyone is acting ethically, we haven't even started to talk about how the Debtor and Lender could collude to game the system.

> So just use that amount.

At this point, you're probably thinking: "Very funny Terr_, but we both know the crayon-drawing obviously wasn't covering the full $5,000 loan here."

Yeah, but how did you reach that conclusion, what mathematical steps did you use?

I'm pretty sure you applied an independent judgement of what a likely crayon-drawing "should" fetch in some hypothetical future. That's quite reasonable, but the fact that you had to do it shows that the loan-basics are not sufficient to solve the problem.

That just doesn't happen. Either the lendor is happy with an uncollateralized loan, a significantly but partially collateralised loan (such as 50%) or a fully collateralised loan. And in each of those cases the lender knows exactly how much he thinks the collateral is worth. If the collateral doesn't cover the loan, there is a written agreement between both parties stating so. The borrower would be wise to use that as evidence, since it reduces his taxable gains. Otherwise it's assumed the collateral covers the loan. No need to do anything special.