# Goals Based Allocation - Optimal Subportfolios

CFAI has a practice problem in their Asset Allocation section that is throwing me off.
They show a client with a \$2.9MM investment portfolio.
She has 2 goals:

Goal 1 is \$120K / year for 20 years with 90% probability of success, and 2.5% annual inflation.
Goal 2 is donate \$1.5MM in nominal terms in 10 years with 85% probability of success.

The have 2 portfolios, and you’re asked which % allocation in each will match with her goals.

I am able to look @ the sub portfolios to determine the appropriate discount rate for each…

I can look @ Goal 2 and determine how to determine what amount of \$ is needed today…\$1.5MM/(1+DF)^10…

What is the formula they’re using for Goal #1, an inflation adjusted annual cash flow generated by a sub-portfolio and where is it in the curriculum?

K = 5.7% (from the sub portfolio time horizon/proability)
G = 2.5% (inflation from above).

The formula they use to calculate is:

\$1,827,000 x (0.057-0.025) / [ 1 + (1+.025/1+.057)^20] x 1.057 = \$120,432.04.

The \$1,827,000 figure is the 63% allocated to the portfolio with a 5.7% return.

What is this formula and where do I find it? Don’t understand the denominator.

Thank you!

That is the formula for the PV of a growing annuity.

I have a video here on it: https://youtu.be/KbUTi65Ev9I