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!