> ## Documentation Index
> Fetch the complete documentation index at: https://valuation-101.com/docs/llms.txt
> Use this file to discover all available pages before exploring further.

# Curve Shapes

> Six convergence curve types that control how forecast variables transition from current to terminal values over 10 years.

## Module: `lib/curve_shapes.py`

Controls the shape of convergence for the four forecast variables (revenue growth, operating margin, sales-to-capital ratio, cost of capital) as they transition from current values to terminal/stable values over the 10-year projection period.

## Why curves matter

A linear fade from 50% revenue growth to 3% tells a very different story than an S-curve that holds high growth for 3 years before dropping sharply. The curve shape encodes your belief about *when* and *how quickly* a company's performance normalizes.

## The six curve types

| Curve                  | Shape                                 | Best for                                                 |
| ---------------------- | ------------------------------------- | -------------------------------------------------------- |
| `exponential_decay`    | Fast initial decline, gradual tail    | High-growth companies decelerating as market saturates   |
| `linear_fade`          | Constant rate of change each year     | Steady, predictable convergence                          |
| `s_curve`              | Flat early → rapid middle → flat late | Companies with a moat that delays competitive pressure   |
| `step_down`            | Discrete drop at a specific year      | Margin cliff events (e.g., patent expiry, contract loss) |
| `delayed_deceleration` | Holds near start value, then drops    | Companies with strong near-term visibility               |
| `stable`               | No change — flat line                 | Already-mature companies where the variable doesn't move |

## Key functions

### `exponential_decay(start, end, n_years)`

Generates an exponentially decaying series from `start` to `end` over `n_years`. The rate of change is fastest in year 1 and slows over time.

### `s_curve(start, end, n_years, inflection=0.5)`

Generates an S-shaped (logistic) transition. The `inflection` parameter (0–1) controls where the steepest part of the curve falls — 0.3 means rapid change early, 0.7 means the transition is delayed.

### `linear_fade(start, end, n_years)`

Generates a straight-line interpolation from `start` to `end`.

### `step_down(start, end, n_years, step_year)`

Holds at `start` until `step_year`, then drops to `end` and stays flat.

### `delayed_deceleration(start, end, n_years, hold_years=3)`

Holds near `start` for `hold_years`, then decays exponentially to `end`.

### `stable(value, n_years)`

Returns a flat series at the given `value` for all years.

## How curves are selected

In **Expert mode**, the user can choose a curve type for each variable. In **Feeling Lucky** mode, the plugin uses rule-based classification that considers the company's growth trajectory, industry norms, and the gap between current and target values. A future [LLM-based classifier](/docs/skills/overview#experimental) is planned to incorporate narrative and competitive context.

The `populate_curve_data.py` utility module takes a curve type, start value, end value, and year count, and generates the full 10-year schedule that feeds into the DCF engine.