Summary  
This chapter demonstrates how to implement mathematical formulas in code by assigning variables, performing arithmetic operations to calculate metrics using two different methods, and printing the results for comparison.

General domain of usage  
Financial modeling

Let's put the **CAPM** and **Build-Up Method** side-by-side using a real company—Tesla—to illustrate how different inputs affect your output.

#### Recap of the CAPM Formula

$$\text{Cost of Equity} = R_f + \beta \times (R_m - R_f)$$

Where:

* $$R_f$$ = 4.31% (risk-free rate);
* $$\beta$$ = 2.58 (Tesla's beta);
* $$R_m$$ = 9% (market return).

With these values:

$$\text{Cost of Equity} = 4.31\% + 2.58 \times (9\% - 4.31\%) \approx 16.14\%$$

The high beta reflects Tesla's volatility, which significantly amplifies the equity cost—something investors demand as compensation for risk.

#### Build-Up Method in Parallel

Let's assume for comparison:

- Risk-free rate: 4.31%;
- Equity Risk Premium: 5%;
- Size Premium: 1%;
- Industry Risk Premium: 2%;
- Company-Specific Premium: 1.5%.

$$\text{Cost of Equity} = 4.31\% + 5\% + 1\% + 2\% + 1.5\% = 13.81\%$$

Even though both methods are valid, they yield different results. The Build-Up Method often produces more conservative estimates for private firms or startups where beta isn't well-defined.

- **CAPM** is dynamic and market-based, suitable for public companies with reliable data;
- **Build-Up** is additive and more controllable, ideal for private or high-uncertainty contexts;
- The **cost of equity is not a fixed number**—it reflects your assumptions and context.

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Cost of Equity Calculation Example

Recap of the CAPM Formula

Build-Up Method in Parallel

Cost of Equity Calculation Example

Recap of the CAPM Formula

Build-Up Method in Parallel