I came across this thread when researching EVM and decided to revive it as a distraction from studying for a few minutes.

I believe the paper you're referring to may have used confusing terminology.
I believe what is meant with "50% complete" is actually "50% funds spent" (AC/BAC).
In that case a CPI of 1,25 would make sense: if your project was underperforming by 25% (CPI 0,75) for the first half of the budget, it should overperform by 25% for the remaining half of the budget in order to stay within the BAC.

More conventionlally, if you consider "50% complete" to be "half the work done" (EV/BAC), then your project was underperforming by 25% during half of the work, which means you've spent 0,5/0,75 = 67% or 2/3 of your funds, therefore your funds remaining are 1/3 of BAC.
TCPI=(work remaining)/(remaining funds) = 0,5/0,33 = 1,5
So, in order to keep your project within initial budget you'll need to overperform by 50% for the remaining 50% of the work.

Hi,

I want to start a thread for discussing relation between CPI and TCPI. I came across an exam question where I was asked to demonstrate relation between CPI and TCPI. So the question goes if the project is 50% complete and current CPI is 0.75. What is the TCPI? According to my calculations which I am demonstrating below the answer comes out to be 1.51 but the correct answer is 1.25. Attached is the discussion paper as well.

My Answer:
Since project is 50% complete EV = 0.5 * BAC

CPI = 0.75 => AC = (EV/0.75) = (0.5 * BAC)/(0.75) = 0.67 * BAC

TCPI = (BAC-EV)/(BAC-AC) = (BAC - 0.5 * BAC)/(BAC - 0.67 * BAC) = 1.51