Estate Distribution

Date: 05/10/99 at 10:22:21
From: John I. Brichacek
Subject: Estate distribution

For a decedent's estate, the Will provides that after payment of debts 
and estate taxes the estate should be divided as follows:

A: 30% of net estate to child
B: 60% of net estate to grandchild
C: 10% of net estate to church

The net estate after payment of debts, but before taxes, is 
$121,403.09.

The estate tax rate is $2,600.00 + 4% of the excess net estate over 
$100,000.00.

The problem that I have is that the bequest to the church is a 
charitable deduction to the estate, and is not to be used in 
calculating the taxes.

I can't calculate the 10% to the church without knowing the amount of 
taxes, and I can't calculate the estate taxes without knowing the 
charitable amount to deduct from the net estate.

Can you give me a formula for doing this, or advise as to someone who 
might help me?

Date: 05/10/99 at 13:21:18
From: Doctor Peterson
Subject: Re: Estate distribution

Hi, John. Unusual question!

I'll assume you've checked the legal and financial aspects thoroughly; 
I can't quite believe that the government wouldn't have some standard 
way to interpret this to their own benefit; on the other hand, I'd 
think it could be interpreted so that 10% before taxes went to the 
church, and the taxes were taken out of the other parts only. I'm sure 
this isn't the first time this has happened.

To keep the typing simple, let's call the net estate before taxes 
N = $121,403.09. Then call the amount given to the church C.

Now the taxable amount will be (N - C), and the taxes are

    T = 2600 + 0.04 * ((N - C) - 100000)

(as long as N-C is greater than 100,000).

On the other hand, if it's true that the church gets 10% of what is 
left after taxes, we want

    C = 0.10 * (N - T)

Plugging in the expression for T,
    C = 0.10 * (N - (2600 + 0.04 * ((N - C) - 100000)))
      = 0.10 * (N - (2600 + 0.04N - 0.04C - 4000))
      = 0.10 * (N - 2600 - 0.04N + 0.04C + 4000))
      = 0.10 * (0.96 N + 0.04C + 1400)
      = 0.096N + 0.004C + 140

Subtracting 0.004C,

    0.996C = 0.096N + 140
         C = (0.096N + 140) / 0.996
           = (0.096 * 121,403.09 + 140) / 0.996
           = 11842.06

To check this, the taxable amount N-C is 109561.03 (which is in fact 
greater than 100,000; otherwise I would have to go back and change 
that equation). The tax T is

    T = 2600 + 0.04 * 9561.03 = 2982.44

and the amount after taxes is N-T = 118420.65, of which 10% is 
11842.06.

That works out just right. The church would lose $300 by having the 
taxes taken out before the distribution.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/