Give both paths the same job
Suppose you hold 1 BTC, Bitcoin is assumed to be $100,000, and you need $20,000 of cash. Selling 0.2 BTC provides that cash and leaves 0.8 BTC. Borrowing $20,000 provides the same cash while retaining 1 BTC, but creates a $20,000 liability and collateral obligations.
You keep 1 BTC until you sell or lose collateral
In this example, selling leaves you with 0.8 BTC. Borrowing leaves you with 1 BTC and a dollar debt. A change in Bitcoin’s price does not change those BTC holdings. The borrower keeps an extra 0.2 BTC compared with the seller, as long as no BTC is sold or liquidated.
The debt can become smaller in BTC terms
A $20,000 debt equals 0.2 BTC at $100,000 per BTC. At a hypothetical $1,000,000 per BTC, the same $20,000 equals 0.02 BTC. The dollar debt has not fallen. It represents a smaller fraction of your 1 BTC.
Interest increases the dollar balance. With 10% interest added over one year and no repayments or new borrowing, you owe $22,000. At $1,000,000 per BTC, that balance equals 0.022 BTC. Your holdings remain 1 BTC; converting debt into BTC does not repay it.
A higher modeled price is an assumption
Debt shrinks in BTC terms only when the BTC price rises faster than the debt grows. If the price falls, the same dollar debt represents more BTC. A power-law floor price used in a model is an assumed price path, not a guaranteed minimum market price.
Holdings and net value answer different questions
BTC held tells you how much Bitcoin you own. Subtracting the debt’s BTC equivalent gives a debt-adjusted value for comparison with selling. For example, 1 BTC minus a 0.022 BTC debt equivalent is 0.978 BTC of net value, not a reduction of your holdings to 0.978 BTC. If you actually sold BTC to repay the loan, your holdings would then decrease. Repaying from other funds would not require that sale.
The missing costs still matter
This simplified comparison excludes taxes, fees, spreads, sale limits, changing rates, and liquidation. Borrowing also creates collateral and repayment obligations. Selling can have tax consequences depending on your situation, which this example does not calculate. Neither path is presented as the better choice for every person.