The actual market value can only be determined if the property does actually go on the market but won't you/they be liable for the Auctioneers costs? The average mechanism is easier and less costly.
Just to clarify also what is happening - you do not buy someone out of their share of a mortgage. You buy their interest in the property, which is subject to a mortgage, and it is a condition of purchase that either the mortgage is discharged entirely or that you assume responsibility for their share of the mortgage and they are freed from any liability.
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