Taxable gift (tax paid by giver) vs Charitable gift

[adidas4628]

Hello all,
just a quick question regarding Taxable gift (tax paid by giver) and Charitable gift, anyone can explain why the tax saving part： Tg*(1-Te)* (1+Rg(1-Tig)^n (for Taxale gift, tax paid by giver) is deducted from total value, however, Toi*(1-Te)* (1+Rg(1-Tig)^n is added to total value for charitable gift, or I just need to memorize it? thx

 

[Galli]

I think the primary idea here is that the total “value” of a taxable gift is lower by the inherent cost of taxing the gift. A Charitable gift is a tax deducation therefore it will have a higher “value”.
Are these equations from the Relative After-Tax Values of Gifts section?

 

[cpk123]

read the book - it is pretty well explained.
The first term in the numerator has no deduction for either gift tax or taxes on investment returns. The second term of the numerator represents the additional value created in the estate associated with the income tax deduction. Toi is the tax rate on ordinary income and represents the current income tax benefit associated with a charitable transfer. The tax advantages of charitable giving allow the donor to either increase the charitable benefit associated with a given transfer of excess capital from the estate, or to use less excess capital to achieve a given charitable benefit.