Not every decision earns a discounted analysis. Three screens run in seconds, appear in every business case ever written, and each one is honest only if you say what it leaves out.

Simple payback: $t = \dfrac{C}{S}$ — t equals C over S. $C$ is the installed capital cost in dollars, $S$ the saving per year in dollars per year, and $t$ comes out in years because the currency cancels. What it ignores is stated in its own name: simple means no interest, no discounting, no inflation. It also ignores everything that happens AFTER the payback date, which is why it quietly favours short-lived equipment over long-lived equipment. Its honest limit is the same one-way street the units doctrine describes: a bad payback can rule a project out, but a good payback never proves a project right.

Return on investment: $\mathit{ROI} = \dfrac{G - C}{C}$, where $G$ is everything the investment gave back and $C$ is what it cost, both in dollars, and ROI is a bare fraction usually quoted as a percentage. Subtract the cost first — the money you put in was never profit. And notice what is missing: there is no $n$ anywhere. A 60% return over one year and over ten years read identically, which is why ROI on its own settles nothing. Do not confuse it with a profit margin, which divides the same profit by the revenue instead of the cost.

Break-even quantity: $Q = \dfrac{F}{p - v}$. Here $F$ is the fixed cost for the period — depot, insurance, licences, the costs that arrive whether you work or not — $p$ is the price per unit and $v$ the variable cost per unit, the material and labour that only exist if the job is done. Note the letter collision: $F$ is a fixed cost here, not a future sum. The denominator $p - v$ is the contribution margin, what each job leaves behind toward the depot, and it is the number the whole method turns on.

The nugget: if $p$ is at or below $v$, no quantity ever breaks even. Every additional job loses money, and volume makes it worse, not better. Underpriced service contracts fail exactly this way, and they fail faster the busier the crew gets.