Distributing An Estate (or anything) Equitably — A Formula

Introduction

When considering your estate distribution following your death, there are many strategies to take. Some of the most popular include:

  • Distribute the estate via an equal percentage — I’ll give John, Paul, George, and Ringo all 25%
  • Distribute via a set percentage — I’ll give John 35%, Paul 35%, George 20%, and Ringo 10%
  • Distribute specific amounts — I’ll give John $35,000, Paul $35,000, George $20,000, and Ringo $10,000

This post explains another option, one that I haven’t found yet after scouring the internet. This option is to distribute an estate through a calculated equitable percentage.

Thought Process

The questions that I asked myself when distributing money were:

  • What is the relative value of a dollar to each individual?
  • How can I distribute funds in an equitable way?
  • How can I remind my descendants I’m a nerd at heart one last time?

To accomplish this, I decided to make a formula (or more accurately, a series of formulas) to determine with an estate of X value, how would I want to distribute my funds to N number of people based on their relative wealth. I also wanted to create a system other people could use based on their own preferences.

I prioritized 2 things:

  1. Equitable distribution
  2. Adjustable variation

I chose not to focus on:

  1. Relative familial value (child vs. cousin, first child vs. second child, etc…) — All relatives are treated the same
  2. The “Protestant Work Ethic” — AKA: “Maybe someone is poor because they deserve to be, and we shouldn’t reward bad behavior with more money.”
  3. How to calculate salary or wealth — I’m not sure how to do it fairly, so I’m ignoring it for now
  4. The method of distributing the estate — trust funds, etc…
  5. Taxes

These topics should be explored further prior to using the formula for practical application.

The Short Version

Use the Excel spreadsheet found here to input your own amounts and see it for yourself.

Adjust the INPUTS:

Inputs: Distribution Level and Estate Value
  • Distribution Level: The distribution level adjusts how equally distributed the funds are. The closer to 1, the more evenly distributed, the further from 1 the more equitably distributed. Here is a graph showing the distribution of $1,000,000 based on different distribution levels —
Distribution level adjustment example
  • Estate Value: The amount of money you have to distribute to your beneficiaries.

The Formula(s) — Explanation

Below are the symbols referenced in the formula(s):

Pw = Person initial Wealth
N = Number of People
D = Distribution Level
Pwavg = Average of Pw
Pwadj = Adjusted wealth based on V
Pwout = Pwadj with outliers accounted for
Proportion = the proportion of the estate each person receives
% of estate = the percent of the estate each person receives

To start, you will take the yearly salary (or whatever measure of wealth for each individual you choose) of each beneficiary, represented by Pw. I then averaged all of the Pw’s, which is represented by Pwavg.

Pwavg = {Pw/N

From there, you may want to bring everybody a little together, which is why I use the below equation to create an adjusted wealth (while also solving the issue of dividing by zero for those with no wealth). This adjusted wealth is represented by Pwadj.

This is represented by the distribution value D. The closer to one, the less distributed, and more than one the more distributed.

Pwadj=IF(Pw<Pwavg, (Pw+(Pwavg-Pw)^(1/D)),(Pw-(Pw-Pwavg)^(1/D)))

This brings all the distributions closer together.

I then look for low outliers in the Pwadj (adjusted wealth). I do this via this formula —

Pwout=IF(Pwadj<(Pavg/N),(Pavg/Pn),Pwadj)

Pwout being the adjusted wealth after another adjustment to account for outliers.

This solves the problem of vastly overdistributing funds to people with little to no wealth. **(show example)**

From there, I take the outlier Pwout and use the following formula to get the Proportion of the estate each person should receive —

Proportion = 1/(Pwout/{Pwout)/100

Then divide each Proportion by the sum of those Proportions to get the % of estate for each individual.

% of estate = Proportion/{Proportion

Finally, take the % of estate for each person and multiply it by the total amount of the estate. And there you have it: the amount each person gets, distributed in an equitable way.

Bit of a mouthful right? If you prefer, you can just use the Excel formula found here to get it as well.

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Kyle Scheer

Kyle Scheer

I like writing about things that interest me. I’m hoping some of it may be interesting to you as well. Keep up with me and my projects at www.kylescheer.com