Proper Method for Splitting up an Inheritance among Four Siblings (including myself)

[keppela]

Hi there. I'm having difficulty finding the right method to split up an inheritance. Unfortunately, it involves a long post (apologies for that), but I believe it's basically a simple math problem at heart. OK, here goes: I recently sold an inherited piece of property and want to split the proceeds among 4 siblings (including myself). Before the property was sold, two of the siblings had contributed to repairs and would like to recover that money. In trying to figure out how to correctly split up the proceeds, I come up with two possible methods - both of them seem legitimate, but they lead to completely different answers! I'm hoping someone with better math skills than me could let me know which is the correct method to use.

Here is the background information:

- The total proceeds from the property sale were $5000

- The split arrangement is 28.33% for siblings 1, 2, & 3, and 15% for sibling 4 ([28.33% x 3] + 15% = 100%)

- Sibling 1 wants to recover $1000 spent on repairs

- Sibling 2 wants to recover $500 spent on repairs

Split Method 1:

1. Subtract the $1K and $500 needed to repay siblings 1 & 2 from the $5K total ($5K - $1.5K = $3.5K)

2. Split the remaining $3.5K up between the siblings (next two steps)

3. Sibs 1, 2, & 3 receive 28.33% of 3.5K = $992 each (rounding up)

4. Sib 4 receives 15% of 3.5K = $525

5. Sib 1 recovers his $1K by adding it to $992 and receives $1992

6. Sib 2 recovers her $500 by adding it to $992 and receives $1492

7. Sibs 3 and 4 amounts don't change

8. Totals for sibs 1 + 2 + 3 + 4 = $1992 + $1492 + $992 + $525 (= $5K)

Split Method 2:

1. Split the $5K up between the sibs (next two steps)

2. Sibs 1, 2, and 3 receive 28.33% of $5K = $1417 each (rounding up)

3. Sib 4 receives 15% of $5K = $750

4. Sib 1 recovers his $1K by adding it to $1417 and receives $2417

5. Sibs 2, 3, & 4 each have 1/3 of this $1K subtracted from their totals, so $1417 - $333 = $1084 (sibs 2, 3) and $750 - $333 = $417 (sib 4)

6. Sib 2 recovers her $500 by adding it to $1084 and receives $1584

7. Sibs 1, 3, & 4 each have 1/3 of this $500 subtracted from their totals, so $2417 - $167 = $2250 (sib 1), $1084 - $167 = $917 (sib 3), and $417 - $167 = $250 (sib 4)

8. Totals for sibs 1 + 2 + 3 + 4 = $2250 + $1584 + $917 + $250 (= $5K)

As you can see, in both methods, the totals correctly add up to $5K, but the amount each sibling receives is different! Which of these is the correct method (assuming both aren't wrong)? Thanks very much for helping me solve this problem!

 

[blamocur]

I see Method 1 as more fair: the amounts that 1 and 2 contributed to repairs should not be a subject to distribution, i.e. they should recover their amounts first, then the rest is the actual estate. Imagine the case where repairs were financed not by some of the siblings but, say, a bank -- they would be no question that the bank gets its money first, then the rest is divided. But siblings 1 and 2 are no different from a bank in this respect.

P.S. One could argue in real life that those $1500 repairs could increase the value of the estate by even higher amount, which would complicate the computations, but this does not seem to be a consideration in this problem.

 

[keppela]

I see Method 1 as more fair: the amounts that 1 and 2 contributed to repairs should not be a subject to distribution, i.e. they should recover their amounts first, then the rest is the actual estate. Imagine the case where repairs were financed not by some of the siblings but, say, a bank -- they would be no question that the bank gets its money first, then the rest is divided. But siblings 1 and 2 are no different from a bank in this respect.

P.S. One could argue in real life that those $1500 repairs could increase the value of the estate by even higher amount, which would complicate the computations, but this does not seem to be a consideration in this problem.

Thank you very much for your input! I agree, recovering the contributions of siblings 1 and 2 first does seem to be more fair, but notice that they end up with less if you follow Method 1 than if you follow Method 2. This is what throws me - in prioritizing the recovery of their amounts, it seems like they get shortchanged in the end.

 

[blamocur]

Thank you very much for your input! I agree, recovering the contributions of siblings 1 and 2 first does seem to be more fair, but notice that they end up with less if you follow Method 1 than if you follow Method 2. This is what throws me - in prioritizing the recovery of their amounts, it seems like they get shortchanged in the end.

In Method 1 sibling 2 ends up with $500 + $992 = $1492, whereas in Method2 she/he gets $1417.

 

[keppela]

In Method 1 sibling 2 ends up with $500 + $992 = $1492, whereas in Method2 she/he gets $1417.

If you look at the totals in Line 8:

Method 1, sib 2 = $1492 ($500 + $992)
Method 2, sib 2 = $1584 ($500 + $1084)

Again, it appears that sibling 2 (like sibling 1) gets shortchanged by Method 1.

 

[blamocur]

If you look at the totals in Line 8:

Method 1, sib 2 = $1492 ($500 + $992)
Method 2, sib 2 = $1584 ($500 + $1084)

Again, it appears that sibling 2 (like sibling 1) gets shortchanged by Method 1.

You are right, I did not look carefully at method 2, but assumed that there is no compensation for repairs there -- sorry. But whether a particular siblings gets more or less does not in itself make a particular method more or less fair.

 

[keppela]

You are right, I did not look carefully at method 2, but assumed that there is no compensation for repairs there -- sorry. But whether a particular siblings gets more or less does not in itself make a particular method more or less fair.

Well, the issue of fairness came up in your original comment "I see Method 1 as more fair." My original and primary concern is which method is correct! Can you provide any insight/clarification as to which of these methods is correct?

 

[khansaheb]

Well, the issue of fairness came up in your original comment "I see Method 1 as more fair." My original and primary concern is which method is correct! Can you provide any insight/clarification as to which of these methods is correct?

As was suggested in response #2, suppose the money from repair came from Bank (counted as liability of estate). The liabilities must be cleared by the estate, prior to any calculation of the asset of the estate.

So method is correct and is fair.

 

[blamocur]

Well, the issue of fairness came up in your original comment "I see Method 1 as more fair." My original and primary concern is which method is correct! Can you provide any insight/clarification as to which of these methods is correct?

I am not sure I see any difference between correct and fair, at least not in this context.

 

[keppela]

As was suggested in response #2, suppose the money from repair came from Bank (counted as liability of estate). The liabilities must be cleared by the estate, prior to any calculation of the asset of the estate.

So method is correct and is fair.

OK, thank you for your help!