# Valuation

**FUND-08 · Fundamentals · Core**

**Lesson question:** What expectations does the purchase price require?

Original fictional examples; educational writing, not live market data, orders or production approval.

## By the end

- Explain the mechanism in the lesson question.
- Reproduce the worked comparison and recognize its failure case.

**Prerequisites:** FUND-01

A good company can be a poor purchase at a price requiring exceptional outcomes. A low multiple can be justified by deteriorating economics. Valuation connects a forecast to the price of the relevant claims.

No single ratio removes forecast uncertainty.

## Understand the mechanism

Equity measures such as P/E pair with equity value. Enterprise measures pair with operating cash or earnings before financing. Mixing them can distort comparisons. DCF results depend heavily on reinvestment, discount rates and terminal assumptions.

Use scenario ranges and reverse valuation: ask what assumptions the current price needs, not only what your preferred forecast produces.

## Walk through the process

Match definitions across peers and time. Consider growth, margins, leverage and capital intensity before comparing multiples. Build an independent range and inspect its sensitivity.

A margin-of-safety percentage is a judgment about uncertainty, not a guaranteed protection mechanism.

## Evidence and decision boundary

These are original fictional teaching figures, not a company screen. Actual analysis should use primary disclosures and distinguish management's explanation from your inference. Favorable or unfavorable evidence depends on the specific business, valuation and risk; no single ratio establishes a recommendation.

## A worked example

An independent fictional enterprise DCF projects unlevered cash flows 110, 120, 132, 145 and 160 million. At r=9% and terminal g=2.5%, forecast PV is 510.558, year-five terminal value 2523.077, and enterprise value 2150.385.

Subtract 250 net debt and divide by 50 million shares: 38.008 per share. This is a model output, not true value. The graph varies discount rate while retaining the other stated assumptions.

## Calculation popup: Reproduce the financial calculation

```text
EV=Σ FCFF_t/(1+r)^t + [FCFF_5(1+g)/(r−g)]/(1+r)^5; equity/share=(EV−net debt)/shares
```

Fictional figures; definitions and periods must match.

1. Forecast PV=510.557927165.

2. Year-five terminal value=2523.076923077.

3. EV=2150.384809518.

4. Subtract 250 and divide by 50.

**Result:** Illustrative value 38.007696 per share.

## Graph: Valuation—worked comparison

**Horizontal:** Discount rate (decimal)  
**Vertical:** Modeled equity value per share (USD)

Fictional data from the written example. The chart organizes the comparison; its shape is not a forecast.

Complete numerical data are embedded in `scripts/fundamentals/FUND-08.js` and displayed as an accessible table in the HTML lesson.

## What would invalidate the reading?

A precise output can conceal uncertain terminal value. Discounting levered equity cash flow as enterprise cash or subtracting net debt twice creates a more basic error.

## Check your understanding

### What is subtracted from enterprise value in this simplified equity bridge?

**Answer:** Net debt of 250 million, with other non-equity claims assumed absent.

**Why:** Align claims before dividing by shares.

### What is the critical failure to avoid?

**Answer:** A precise output can conceal uncertain terminal value. Discounting levered equity cash flow as enterprise cash or subtracting net debt twice creates a more basic error.

**Why:** Explain this risk before treating the example as a decision rule. A correct calculation does not guarantee a favorable market outcome. **Critical risk check.**

## Takeaway

Return to the question: What expectations does the purchase price require? State the observed facts, the assumptions and the failure condition separately.

## References and provenance

The cited references support definitions and conventions. The teaching prose, tickets and numerical scenarios are original; they are not attributed as historical market observations.

- [SEC Financial Statements Guide](https://www.sec.gov/about/reports-publications/beginners-guide-financial-statements)