Can someone give me a hand with understanding how the \$640,000 and \$695,000 figures are derived in the below example?

Even in jurisdictions with relatively small annual exclusions, a gifting program that is started early and implemented over long periods of time can transfer substantial wealth in a tax-efficient manner. In the United States, for example, a donor’s annual gift exclusions are currently limited to US\$13,000 per year (for 2009), per donee (e.g., a parent may annually transfer US\$13,000 to each child or US\$26,000 from both par- ents). Exhibit 4 shows that an annual gifting program of transferring US\$13,000 per year tax free implemented over a 30-year period transfers over US\$640,000 inflation- adjusted dollars at an 8 percent nominal return that is taxed at 25 percent annually with a 2.5 percent inflation rate (i.e., 5.5 percent real rate of return).19 The dashed line in Exhibit 4 represents the accumulated value of the gifts themselves, excluding investment returns. After 30 years, gifts total US\$390,000 = US\$13,000 × 30. If the donor had kept this amount, any future appreciation would have increased the value in his estate and hence the estate tax liability. Assuming an 8 percent nominal pretax return that is subject to a 25 percent annual tax would add an additional US\$305,000 of real appreciation (after adjusting for inflation), for a total value of US\$695,000. A tax-efficient investment strategy that defers the 25 percent tax until the end of the investment horizon increases the accumulated sum to almost US\$843,000.

For the ‘over \$640,000’ figure I used the after tax nominal return of 6% and adjusted it to 3.4% after tax real return, by 1.06/1.025 and the FV of a 30 year \$13,000 payment stream gives me \$660,158 but I’m not sure if this is even what they’re getting at. As for the \$695,000, clueless.

Thanks!

Hi Andrew,

You may want to take a look at this

http://www.analystforum.com/forums/cfa-forums/cfa-level-iii-forum/91320497

The last comment is a good explanation of how one could get to ‘over \$640,000’.

No luck there with the \$695,000 and I, like you, am clueless.

Regards, Carlo

Yeah the 640 makes sense if I think about it as an immediate annuity, the first 13k would be gifted right away and not wait until the end of the period to start. That’s cool but yeah, still stuck on the 695. Thanks for the link though, it at least cleared up the first part.

-Andrew