Borrowing bitcoins and converting them to fiat to invest in a business is a bad idea because of the exchange risk that bitcoins may shoot up in value against the fiat and you can never pay it back.
One solution I came up with is to place bitcoins in a low interest bearing account of a third party as escrow. You would then receive USD to the value of those coins to invest. The coins earn bitcoin interest in the meantime which can be used to offset fiat interest payments or increase your collateral backing the loan.
To do this needs a lender who deals with fiat denominated loans who will accept btc collateral.
If you then invest the fiat in a business you essentially have twice the collateral to back the loan.
Alternatively you could do this through the same person (if you trust them) where they pay interest on the btc which they can use to offset fiat repayments on the loan which might mean you dont need to pay fiat at all - the bitcoin interest covers your repayments so you have more fiat cashflow. The main thing is to not sell the bitcoins but use them as collateral.
If only fiat banks accepted btc as collateral!
I have a future glbse project called Alpacastocks
https://bitcointalk.org/index.php?topic=59961.0 I was thinking this model could be used for. If we can find a lending partner for the fiat the IPO would raise the bitcoin collateral needed. Thoughts ?