A mortgage would be debt-financed, correct.
If not deb-financed, the income
would not be taxable per IRC Section 512(b).
If the rental income is derived from debt-financed property that is subject to outstanding acquisition indebtedness incurred in acquiring or improving the property, there could be tax
implications. There are some exemptions that would still exclude the rental income form taxation
. One is where more than 85 percent of the use of the debt-financed property is devoted to the church's exempt
purposes (see Income Tax Regulation
§1.514(b)-1(b)(1)). A second exception is where the rent is received from a related organization for an exempt purpose use (see ITR §1.514(b)-1(c)(2)). I do not think the latter would apply since you said this is a for-profit renter.
If you still determine the rental income is taxable, there is a complicated calculation as to how much Unrelated Business Income Tax (UBIT) would be reported and owed using Form 990-T. If this is the case, you should consult a local
tax professional with your exact details.
Please let me know if you have further questions.