18 February 2012

Algebra can be useful

(This is a note I wrote to my brothers in June 2005.  My brother Jeff was saying at the time that the more items the rest of us brothers kept out of Mother's estate sale the less money he'd get overall  He chose not to keep any items himself in order to maximize the cash he'd get.  But he didn't consider that he'd get his full one-fifth of the appraised value of anything the others of us kept for ourselves, whereas the items in the sale were subject to the 30% fee of the company that handled the sale.)

The simplified estate sale formula



Let’s say the estate sale brings in $20,000.  This is an estimate based on Roy having said he hoped we’d leave in enough stuff for the sale to bring in $20,000.   E in the formula below represents this value, and is the same as (TX) in the formula I used earlier.   X is still what it was earlier, the total value of the items we keep out of the sale.  U is still the amount any individual keeps out, and $ is the amount an individual will get. 

From Kristin’s June 1st email, we currently have X = $16,593.

$ =  .70E/5 + X/5  U  =  14,000/5 + 16,593/5  U   =  6,118.60 – U .

With each brother’s value of U as shown in Kristin’s email, the proceeds from a  $20,000 sale would give

Jeff:      $ = 6,118.60 –       0.00  =  6,118.60

Greg:    $ = 6,118.60 – 4,385.00  = 1,733.60

Steven: $ = 6,118.60 – 2,431.00  = 3,687.60

Arch:    $ = 6,118.60 – 5,525.00  =    593.60

David:  $ = 6,118.60 – 4,252.00  = 1,866.60

The X/5 in the formula represents each persons 1/5 interest in the total amount of stuff we keep.  One thing this shows is that Jeff gets more money, not less, when the rest of us keep items out of the sale.  He gets his full 1/5 share of the items we keep, whereas if we put everything in the sale, he and the others of us would only get 70% of our 1/5 share. 

For the above figures, the amount we’d each get based on everything (including the car) selling for the appraised price and our getting 70% of the total is


$  =  .70(E + X)/5  =  .70(20,000 + 16,593)/5  = .70(36,593)/5  =  5,123.02

(If we sold the car on the open market for $3,600 we’d each get a little more than this, but not much—about $200 more.)  With the rest of us keeping $16,593 worth of stuff out of the sale, Jeff gets a little over about a thousand dollars more than he would if we put everything in the sale.