Stress the Assumptions, Not the Arithmetic

A closing habit, because it is the one this chapter has been quietly demonstrating. Every formula here is exact; every input is a guess. The Gordon model was correct all three times it valued the same business at $20\times$, $33\times$, and $50\times$ earnings — only $g$ changed, by two points. The NPV example flipped its verdict when the hurdle moved from 5% to 12%. The savings rate, the retirement target, and the leverage ceiling all inherit the same property: the arithmetic never fails, and the inputs never quite hold.

So before you trust any output — in this chapter or any that follows — move each input one point in each direction and watch the answer. The input that swings the result most is the one that deserves your research, your negotiation, or your hedge; the ones that barely move it deserve defaults and no further anxiety. And when a model’s verdict flips within the plausible range of a single input, the model has not given you a verdict at all — it has given you a sensitivity report, and the honest response is to decide on other grounds or build in enough margin that the answer survives being somewhat wrong. Every chapter after this one hands you models. Stress them the same way, and you will disagree productively with most of the confident numbers you are shown — including, occasionally, the ones in this book.