What does CPI really mean, and why can it predict your final budget?

Well, Cost performance index (CPI) may help you find the performance of project based on budget, CPI is project health indicator for a point of time, if CPI is less then1 then project in over budget and if CPI is greater the1, this means project is under budget, you divide earned value with actual cost to find project CPI.

Another term is schedule performance index (SPI) which provides the project health based on schedule, if SPI is greater then1, your project is doing fine and within schedule,  otherwise  your project is ahead of schedule which is  bad indicator. you can divide earned value with planned value to find SPI.

As discussed above CPI may provide project status of "As of today" however if you want  to predict project budget during project execution, you will have to use other techniques, like finding EAC.

There are several ways to find Estimate at Complete (EAC) based on situation or assumption made,

like 

EAC = AC + Bottom up ETC

We mostly use this  formula when current status of project required new estimating.

EAC = BAC/CPI

This  formula is used to calculate Estimate at Complete when you will continue with current rate of BAC.

EAC = AC + (BAC - EV)

We mostly use this formula when existing variances are atypical to be used for future.

EAC = AC + ((BAC-EV)/CPI*SPI)

This formula uses actual cost to date plus remaining budget based of project performance. and where project schedule is constrain and may not change.

Hope this answer the question.

Dosent it  seem a little weird that you can come up with a pretty accurate forecast of what you will BAC, or the total amount that you  are planning to spend on the project , but when you think about it it actually makes sense . lets say that you are running% over budget today , if your budget is $ then your CPI will be $0 =%

One good way to predict what your final budget will look like is to assume that you will keep running% over budget 

CPI Really mean the performance of resources utilization

Given the value of the work earned for each1$ Actually spended 

CPI is one of the earned value formulas, and it cannot predict your final budget, it predict you grossing cumulative cost against the budget