Solve the simple-interest budget
With year fraction t = holding days ÷ 365, gross yield equals principal × yield APR × t. The amount available for borrowing interest is gross yield − fixed cost. Break-even borrow APR equals that amount ÷ (principal × t). Equivalently, subtract fixed cost ÷ (principal × t) from yield APR. Principal and holding days must be positive. The fixed cost belongs to the whole modeled holding period, not automatically to a year.
Work through a ninety-day scenario
For a hypothetical $10,000 principal, 90 days, and 10% yield APR, modeled gross yield is about $246.58. After $100 of fixed costs, about $146.58 remains for borrowing interest. Dividing by $10,000 × 90 ÷ 365 gives a break-even borrow APR of approximately 5.94%. A higher borrowing rate produces a modeled loss; a lower rate leaves a positive amount before other excluded effects.
Interpret negative and variable-rate results
If fixed costs exceed gross yield, the calculated threshold is negative: no nonnegative borrowing rate breaks even under those assumptions. Reporting that condition is more informative than presenting zero as profitable. The calculation assumes a constant borrowing rate, constant principal, and yield accruing throughout the full period. It excludes reward-token price changes, borrowing origination charges not entered as costs, compounding, and liquidation losses. A rate threshold is a scenario output rather than a borrowing recommendation.