RV of a Charitable Gift

Reference to BB, example 7 on page 299 of volume 2.

Trying to digest these formulas in a way that is easy to remember. Looking at this example, I understand the left side of the numerator is the supposed to be the FV of the investment that isn’t subject to tax since it’s a gift to a charity today that is expected to return 6% over 20-years

What I can’t make sense of is:

  1. Right side of the numerator for the ‘gain’ the gifter receivers in current year tax benefits. What is the intutition here? Is it current year tax benefit invested over the same 20-year duration * investment gains tax rate * estate tax rate?
  2. Why do we assume the gift grows at the provided investment growth rate? Isn’t the charity unlikely to invest in the same manner as the inidividual?

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.

Thanks CPK.

Why do we assume the gift (left side of the numerator) grows at the expected return though? Doesn’t the charity already posses the gift?

it invests the amount received in charity and earns the rate of return with no taxes.

It is just like a gift from donor to donee - and that gift earning returns, but paying taxes - in the earlier formula … .RV Gift, etc. etc.

Still feel confused about numerator second term. Is it because of donations to charitable organizations are income tax deductible?