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By selling the property for $75,000 when its worth $300,000, you are effectively gifting $225,000. Therefore, since the gift is in excess of the $12,000 annual per person limit, you will be required to file a gift tax return (i.e. Form 709) in the year you transfer the property to your daughter and son-in-law under these terms. You will owe gift tax on $201,000 (i.e. $225,000 - $24,000), however, you will not have to write a check. You will just use $201,000 of your $1,000,000 lifetime gifting exemption. Your daughter and son-in-law will take over 75% of your cost basis (i.e. $225,000/$300,000) and holding period on the gift portion of the transaction. The $75,000 your daughter and son-in-law are actually paying (by taking over the mortgage) is also added to their cost basis.
With respect to the sale portion of the property, yes you will owe capital gains tax if you do not qualify to use the IRC Sec. 121 exclusion for gain on sale of principal residences. Since you are selling for $75,000 and the property is worth about $300,000, you will allocate approximately 25% ($75000/$300,000) of your cost basis to the sale. Their cost basis would be comprised of their original purchase price plus non-recurring closing costs incurred on purchase or refi's plus improvements less any allowable depreciation. Gain would be calculated as selling price net of selling expenses less allocated cost basis.
Pursuant to IRC Sec. 121 if as of the date of sale you have owned and used the property as their personal residence for 24 out of the last 60 months, then you may exclude up to $250,000 of gain ($500,000 if married filing joint) if filing a single or MFS return.
Thus, unless you have used the property as your principal residence for at least 2 out of 5 years as of the date of sale, then the gain is taxable as a capital gain subject to a maximum federal tax rate of 15% (5% if the gain would otherwise be taxable in the 10% and 15% tax brackets).
Accordingly, if this is what you want to do you will need to prepare a sales contract for the specified price (i.e. $75K). I would talk with a real estate attorney to prep this and to find out if anything special needs to be done in your county with respect to recording a deed transfer for less then full consideration. Also, you will need to file a gift tax return so check with your accountant. One alternative is to sell to your daughter and son-in-law for full value and take back a 2nd trust deed for the sales price in excess of the mortgage. The note should carry a reasonable interest rate and your daughter and son-in-law should pay you interest (they deduct as mortgage interest and you recognize as income). Then you can gift them $24,000 worth of principal each year until the note is completely gifted away with no filing requirement or use of your lifetime $1,000,000 exemption. Also, if you are married you may split this gift with your spouse and double up on the annual exemption.
Because it is impossible for me to identify and consider ALL the relevant facts, this advice is not intended or written to be used for the purpose of avoiding penalties, and cannot be used for that purpose.
The installment sale rules apply in this situation. That means you only recognize gain as you receive cash (or as debt is relieved). To the extent you gift the note back you will in effect be transferring your cost basis in that portion of the debt to your daughter and son-in-law. The only tax difference between doing the immediate gift of the equity versus doing it via gifting of a note is that the note is gifted over time and your daughter must pay you a reasonable rate of interest on thenote as long as its outstanding. otherwise, the IRS will not respect the note.