Discounted Cash Flow (DCF) and Growth Models

Welcome to DCF and Growth Models

In the previous chapter, Introduction to Equity Valuation, we learned that a stock's value can be estimated in several ways. In this chapter, we focus on Discounted Cash Flow (DCF) valuation. The core idea is simple: the value of an investment today is the sum of all the cash it will give you in the future, adjusted for the time value of money.

Think of it like buying a fruit tree. The tree's value isn't just the wood it's made of; it’s the value of all the apples you expect to pick from it over the coming years, discounted because an apple today is worth more than an apple five years from now.

1. The Dividend Discount Model (DDM)

The Dividend Discount Model (DDM) is the most basic DCF model. it assumes that the only cash flows a shareholder receives are dividends. If you plan to hold a stock forever, the value of that stock is the present value of all future dividends.

A. The Gordon Growth Model (Constant Growth)

If a company is mature and we expect its dividends to grow at a steady, constant rate forever, we use the Gordon Growth Model (GGM). This is a favorite for the CFA exam because it is simple yet powerful.

The formula for the intrinsic value \(V_0\) is:

\(V_0 = \frac{D_1}{r - g}\)

Where:
- \(D_1\) = The expected dividend next year (Note: \(D_1 = D_0 \times (1 + g)\))
- \(r\) = The required rate of return on equity
- \(g\) = The constant dividend growth rate

Important Rule: For this formula to work, \(r\) must be greater than \(g\). If the growth rate is higher than the required return, the formula breaks (and the stock would theoretically be worth an infinite amount!).

Quick Tip: Watch out for the "timing" trap in exam questions. If the question gives you the "dividend just paid," that is \(D_0\). You must multiply it by \((1+g)\) to get \(D_1\) before plugging it into the formula!

B. Valuing Preferred Stock

Preferred stock is a special case. Most preferred stocks pay a fixed dividend forever and have no maturity date. Because the growth rate \(g\) is zero, the GGM formula simplifies to a perpetuity:

\(V_0 = \frac{D}{r}\)

2. Multistage Growth Models

Real-world companies rarely grow at a constant rate forever. A tech startup might grow at 30% for five years (High Growth) and then settle down to 3% as the industry matures (Stable Growth). To value these, we use Multistage Models.

Steps for Multistage Valuation:

1. Forecast: Predict the dividends for each year during the high-growth period.
2. Discount: Find the Present Value (PV) of those specific dividends.
3. Terminal Value: Use the Gordon Growth Model to find the value of the company at the moment it reaches stable growth. This is called the Terminal Value.
4. Total Value: Add the PV of the high-growth dividends to the PV of the Terminal Value.

Shortcomings of DCF Models:
- They are very sensitive to inputs. Small changes in \(r\) or \(g\) can lead to massive changes in the estimated value.
- If a company doesn't pay dividends, the DDM is difficult to use (though we can use other cash flow measures, as seen below).

3. Free Cash Flow Models (FCFE and FCFF)

What if a company doesn't pay dividends? Or what if it pays out much less than it actually could? In these cases, analysts use Free Cash Flow.

Free Cash Flow to the Firm (FCFF)

FCFF is the cash flow available to all capital providers: both bondholders (debt) and stockholders (equity). It is the "size of the whole pie."

- Discount Rate: Because FCFF belongs to everyone, we discount it using the Weighted Average Cost of Capital (WACC).
- Outcome: This gives us the Firm Value. To find the value of just the equity, we would subtract the value of the company's debt.

Free Cash Flow to Equity (FCFE)

FCFE is the cash flow left over for common stockholders after the company has paid its operating expenses, taxes, interest to bondholders, and made necessary investments in the business.

- Discount Rate: Since this cash belongs only to shareholders, we discount it using the required return on equity (\(r\)).
- Outcome: This gives us the Equity Value directly.

4. Residual Income Models

Residual Income (sometimes called Economic Profit) takes a different approach. It asks: "How much profit did the company make above and beyond the minimum return its investors required?"

The value of a firm using Residual Income is:
Value = Current Book Value + Present Value of Future Expected Residual Income

- Input: It focuses on Book Value and Accounting Earnings.
- When to use: This is particularly useful for companies that do not pay dividends and do not have predictable free cash flows.

5. Estimating the Inputs: The Growth Rate (\(g\))

To use any of these models, we need to estimate the growth rate. A common method is the Sustainable Growth Rate formula:

\(g = b \times ROE\)

Where:
- \(ROE\) = Return on Equity (Net Income / Equity)
- \(b\) = Retention Ratio (The percentage of earnings the company keeps to reinvest. This is equal to \(1 - \text{dividend payout ratio}\)).

Analogy: If a company earns a 15% return on its projects (ROE) and keeps 60% of its earnings to reinvest (\(b\)), it will grow its earnings by \(0.60 \times 0.15 = 9\%\) per year.

Summary & Key Takeaways

- DDM: Best for stable, dividend-paying companies. \(V_0 = \frac{D_1}{r - g}\).
- Preferred Stock: Treated as a fixed perpetuity. \(V_0 = \frac{D}{r}\).
- FCFF: Cash for everyone (Debt + Equity holders); discount at WACC.
- FCFE: Cash for shareholders only; discount at Required Return on Equity.
- Residual Income: Values the firm based on earnings in excess of required returns added to current Book Value.
- Growth: Can be estimated as \(ROE \times \text{Retention Ratio}\).

Quick Review: Common Pitfalls to Avoid
1. Mixing up \(D_0\) and \(D_1\): Always check if the dividend is "just paid" (\(D_0\)) or "expected next year" (\(D_1\)).
2. Mismatched Discount Rates: Never discount FCFF at the cost of equity, and never discount FCFE at WACC. Equity cash flows need an equity return; firm-wide cash flows need a firm-wide return (WACC).
3. Unrealistic \(g\): Remember that in the Gordon Growth Model, the long-term growth rate (\(g\)) cannot be higher than the overall growth rate of the economy (usually 2-4%).