Hi, I'm cutting this Mom a break thinking perhaps she just can't afford it. I would ask her to get the fabric for the border and suggest she get the backing fabric at a later date. I would suggest using a solid as that can easily be purchased at a later date. Also suggest pieced border using some of the leftover pieces from the top or cotton fabric pieces from outgrown clothing would work if it all cotton. This would not only look really good but also cut down on the cost. I would present these as options in a kind way. The most important thing is the child has some fun with this and he or she probably already heard it's wasting money. Making quilts can be done spending a whole lot on fabric and also done using scraps.
However, your calculations do sound pretty accurate.