calculation logic for the Tree Diagram

I understand the purpose for creating a tree diagram, but I am unclear about how the numbers are derived. I am unable to paste the diagram here, but one can be viewed either on page 338 (Reading 8- Figure 2 BankCorp’s Forecasted EPS) on the CFAI book or page 202 (Reading 8: Figure 3: A Tree Diagram) on the Schweser book. Question: how are the forecasted EPS numbers (total of 4) on the right derived from the one expected EPS on the left? Steps for the calculations would help…thanks!

You’ll have to gimme some time on this one… I dont have the text on me right now

No problems…take your time…

From your question, I think you are wondering how the 4 EPS figures are derived, not how the associated probabilities are calculated. The four EPS figures (e.g. $2.60, $2.45 etc on pg 338 of the TB) are just assumptions. They are not deriving them. What they are deriving is the probability of each of the 4 possible EPS actually occurring. For example, the probability of an EPS of $2.60 is 0.60*0.25 = 0.15

Thank you Beat The CFA. Your explanation makes sense to me. Just to confirm my understanding though the 4 EPS on the right could then be any number as long as the percentage total (prob * EPS) adds up to $2.34? And I suppose the logic they are using for their artificial number from highest of $2.60 to low of $2.00 is purely based on the circumstantial change of interest rates - declining interest rates triggering a possible initial boom in the economy and the stable interest rates possibly causing the economy to cool down…

I think you’ve got it. The total all of the four PROBABILITIES on the right should equal 1 (0.15+0.45+0.24+0.16). The EPS numbers just illustrate how the company’s earnings would be affected by the different interest rate scenarios. The sum of (prob*EPS) equals the expected EPS. (0.15*2.60) + (0.45*2.45) + (0.24*2.20) + (0.16*2.00) = E(EPS) = $2.34