CFA Vol II, p245 (charitable gifts) first, care, understand, represents, relative

SFoyil

I feel stupid….I don’t understand the formula (8) they give for the relative value of charitable gifts. The first term in the numerator and the denominator are straightforward, but what the heck is the second term in the numerator???`It says in the text that it represents the value created by the tax-free status of a charitable organization, but that doesn’t explain the formula.
Anyone care to elaborate?

Fdez

I messed it up a bit in my previous explanation. Sorry for the confusion. I think following is a better explanation:
Say your “net income before taxes” is $ 125,000 and your income tax rate on it is 20 %.
you are considering two options..
Option 1: Donate $ 100,000 to a charity, NOW.
Option 2: Put $ 100,000 in an account (call it account S) which would ultimately (say after n years) bequeathed to your Son.. and ask him to donate the funds in this account to the same charity.
Let’s see what difference it makes to the Charity at the end of all transactions i.e. after n years.
Option 1:
:: You give $ 100,000 to charity. This amount which you are donating is tax exempted.
:: After n years this would become 100,000*(1+Rc)^n. This is because even the returns generated by accounts of Charity are tax exempted.
:: You pay 20 % tax for remaining amount i.e. $ 25,000.
:: After paying taxes on $ 25,000, you are left with $ 20,000.
:: Put this $ 20,000 in account S. After n years and after the bequest it becomes 20,000 [{1+Rs(1-Ts)}^n]*[1-Te]. If your son donate this amount to charity as asked by you, the total amount the charity gets at the end is: [100,000*(1+Rc)^n] + 20,000*[{1+Rs(1-Ts)}^n]*[1-Te]
Option 2:
:: You pay taxes on the whole amount i.e. $ 125,000
:: You are left with $ 100,000
:: Put this $ 100,000 in account S. After n years and after the bequest it becomes 100,000 [{1+Rs(1-Ts)}^n]*[1-Te]. If your son donate this amount to charity as asked by you, the total amount the charity gets at the end is: 100,000*[{1+Rs(1-Ts)}^n]*[1-Te]
Thus the relative value is: [100,000*(1+Rc)^n] + 20,000*[{1+Rs(1-Ts)}^n]*[1-Te] upon 100,000*[{1+Rs(1-Ts)}^n]*[1-Te]
P.S.
:: $ 125,000 is used just to simplify the situation. Logic holds irrespective of the amount of net income. Let me know if some one needs an explanation on this.
:: In my earlier explanation I wrote, you get tax benefits on (a) the part of the income which you donated and in addition to that (b) on an equivalent amount from your remaining income. This is wrong. You get only (a).

cityboy

I read the chapter , and now I understand:
The tax on after-tax income that is bequeathed to relatives while you are alive is called Gift Tax. ( I think there is an annual limit on this in US). It is charged because people might bypass estate taxes ( which are paid upon death) by gifting while they’re alive.
When you make a Gift , it is taxed at Gift Tax rate . The donee does not have to pay income taxes on the amount received ( no double taxation) . The donor pays the tax and then gets to write off income equal to the taxes paid ( by claiming a rebate) , which reduces the overall taxes .
The income is really taxed twice for the donor , when he earns it and again when he gifts it .Second time he pays , he gets a rebate

dyga

look at the example in the text book…. there is one on a left side page (do not have the book with me) - somewhere around 240-245 I believe.
They leave a gift of 100 Mill Yen to their child, out of their 500 Million estate.
100 Mill goes to child.
They are left with 400 Mill. But taxes are considered only on 355 Million (100 * .45 rebate provided) and so they are left with 355 * (1-Te) which is given to the son as estate.
Son ends up with 100 + 355 * (1-Te).
if they bequeathed - without the gift - they pay the estate taxes on the full 500 Mill and son gets less.
Janakasri - the deduction on the donation is present even for our personal taxes.

Darien

Can you give me an example?
I’ll try:
$200 K in pre-tax funds
30% tax rate.
$100K donated to charity.
Pre-tax left over income= $100K
After-tax left over income = $100K( 1-0.3) = $70K .
Do you get additional rebate on donated money ( $100 K) , even though you did not pay taxes on it?
How can you get rebate ( i.e. deduction ) if you did not pay taxes?

brain_wash_your

You do get tax deduction.
CP is spot on.

NakedPuts

I think he means to say:
you had 200K in your income. you donated 100 K.
for the 100 K that you donated - you pay NO tax.
but you get a tax rebate on the 100K that is left over… (and that 100K after taxes is what is bequeathed/gifted).
essentially the $PV being talked about is pre-tax funds.

former

I don’t get this part:
:: Since you gave $ PV to charity, Government forgoes tax (T oi) on equal amount of your income. For example, if you donate 100,000 to a charity, you don’t need to worry about paying taxes on the 100,000 which you are donating, and IN ADDITION TO THAT you get a tax exemption on 100,000 of your, OTHER, income . So, in your case you saved ( PV * Toi ) on taxes, because of your donation.
The 100K should be coming from after-tax funds. You already paid taxes on it. Your post gives the impression that you get a tax deduction on part of PRE-TAX income which is impossible

Zestt

Say you have $ PV. You are considering two options:
Option 1: Give this PV to a Charity, NOW.
Option 2: No donations. Just give what ever you earn from this PV to your Son, AFTER n years.
Now let’s see how your $ PV behaves in above two actions:
Action 1:
:: You give PV to Charity. In n years, PV becomes [ PV * (1+Rg)^n ] . Rg is the expected return on the assets in the Charity’s portfolio.
:: Since you gave $ PV to charity, Government forgoes tax (T oi) on equal amount of your income. For example, if you donate 100,000 to a charity, you don’t need to worry about paying taxes on the 100,000 which you are donating, and IN ADDITION TO THAT you get a tax exemption on 100,000 of your, OTHER, income . So, in your case you saved ( PV * Toi ) on taxes, because of your donation.
In n years, This [ PV * Toi ] becomes [ PV * Toi ] * [ { 1 + Re ( 1 - Tie) } ^ n ]. Re is the return on your investment and Tie is the tax rate on your investment income.
At the end of n years, you can give the above amount to your Son. Value of the amount your Son will receive is: [ PV * Toi ] * [ { 1 + Re ( 1 - Tie) } ^ n ] * [ 1- Te ] . Te is estate tax.
Thus, at the end of n years, after all the transactions, TOTAL future value of your initial $ PV is:
[ PV * (1+Rg)^n ] + [ PV * Toi ] * [ { 1 + Re ( 1 - Tie) } ^ n ] * [ 1- Te ]
Action 2:
After n years your PV becomes [ PV * { 1 + Re ( 1 - Tie) } ^ n ]. Give this to your son. Value of the amount your Son will receive is: [ PV * { 1 + Re ( 1 - Tie) } ^ n ] * [ 1- Te ], which is also the total future value of your initial $ PV.
Relative Value is just the ratio:
[ PV * (1+Rg)^n ] + [ PV * Toi ] * [ { 1 + Re ( 1 - Tie) } ^ n ] * [ 1- Te ] / [ PV * { 1 + Re ( 1 - Tie) } ^ n ] * [ 1- Te ]

cityboy

Second term is Bequest*T oi
The T oi is the taxes on ordinary income , which would have been charged if you had not bequeathed you bequest to a charity.
The text says that you can donate early into a tax exempt structure , so that the amount donated grows without being taxed every year.
If you wait until your are about to die , all the gains are subject to taxation and you will get less bang for your donation. Put another way you might have to donate less today , than on your death bed , to get the same bang out of your bucks