establishing an optimal take profit

External question — Quantitative Finance Stack Exchange Author: adriano Original post: https://quant.stackexchange.com/questions/64163 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. Please let me know what you thoughts are on this. Say for example that you have a perpetuity, which guarantees you indefinite payments of a certain amount. Say then that you also have the opportunity to reinvest all your earnings by buying an even larger perpetuity that will then guarantee even larger payments indefinitely. Provided that the only costs you have would be transaction fees and spread charged by some broker, at what gain level would you close your position in the first perpetuity to establish the position in the new one?