Multiple based and discounting connection
Multi-stage free cash flow valuation
Firm value to intrinsic value per share
Value investing is a disciplined approach built on the idea that every company carries an economic worth that can be estimated with reasonable precision. Market prices fluctuate around this worth, often moving for emotional, speculative or short term reasons that have little connection with the long run earning power of the business. When price falls meaningfully below a well supported estimate of intrinsic value, the difference becomes an opportunity for the patient investor. This simple philosophy, developed by Benjamin Graham in the mid twentieth century and refined by Warren Buffett and others, remains a coherent approaches in modern finance.
Although markets today are faster and data is more abundant, the core insight remains unchanged. A share is not a lottery ticket. It is a proportional claim on future cash flows generated by a real operating business. That claim has a rational price. The investor’s job is not to guess market sentiment but to understand the economics of the enterprise and compute what those future flows are worth today.
The material discusses general principles of value investing and the economic logic behind estimating the worth of a business. It is provided solely for educational and informational purposes. Nothing here should be interpreted as investment advice, a recommendation to buy or sell any security, or a guide to personal financial decisions.
Graham approached valuation from a defensive and highly conservative standpoint. Instead of trying to forecast detailed future scenarios, he focused on the current earning power of the company. If a business generated a sustainable level of earnings or cash flow, one could approximate its fair worth by applying a simple multiple. His classical approach treats the company as if its cash flow will continue with little or no growth. In that setting, the value resembles a not-growing annuity:
\text{Value} \approx \frac{\text{Cash Flow}}{r}
where r is the investor’s required return.
This method does not attempt to model long run improvements, technological advantages or network effects. Instead, it protects the investor by assuming stability and requiring a wide margin of safety. Graham emphasized that one should treat valuation not as a precise forecast but as an exercise in prudent estimation. If the numbers must be stretched to justify the purchase, the investment is rejected.
Buffett kept Graham’s logical structure but expanded it significantly. Instead of assuming that businesses are static, Buffett looked for companies with durable competitive advantages that allow them to grow their free cash flow for long periods. He recognized that many outstanding businesses compound their intrinsic value year after year. To ignore this process would undervalue them.
The key idea is that a firm with strong economics operates like a growing annuity. Future cash flows are not constant. They increase according to the firm’s competitive engine, market position, reinvestment capability and managerial discipline. The valuation must therefore reflect both current cash generation and the growth that will likely follow.
This is where discounting becomes central. Rather than applying a fixed multiple, Buffett evaluates the streams of future free cash flows and discounts them at a rate matching the opportunity cost of capital. In practical terms, value is computed as:
\text{Value} = \sum_{t=1}^{\infty} \frac{\text{FCF}_t}{(1+r)^t}
The philosophy remains conservative, but it allows excellence to be recognized. A high return on invested capital, a resilient business model and pricing power create long run growth that must be reflected in any rational valuation.
A multiple is a compact way to summarize a valuation, but it collapses many assumptions into a single number. The required return used in the denominator implicitly includes all expectations about risk, growth and reinvestment. For slow growing businesses this is acceptable since growth is barely relevant. For strong compounders, however, a multiple will always underestimate real worth unless adjusted manually.
Discounted cash flow analysis separates these components:
This structure allows a more transparent and mathematically consistent valuation. Each assumption can be inspected, challenged and stress tested. Different scenarios such as bearish, base and bullish can be evaluated cleanly without obscuring the mechanics.
Both Graham’s simplicity and Buffett’s more detailed analysis originate from the same mathematical idea. A perpetual stream of cash flows is a geometric series. A constant cash flow F discounted at rate r gives:
\frac{F}{r}
A growing stream with constant growth g (as long as g < r ) becomes:
\frac{F}{r-g}
This is the theoretical link between the multiple and discounted cash flow. A company with no growth corresponds to a multiple equal to 1/r. A company with moderate growth corresponds to a higher justified multiple equal to 1/(r-g). In practice, growth does not remain constant forever, so we apply multi stage models: five years of initial growth, five years of transition and a stable terminal regime. These reflect the real progress of a living business while maintaining analytical clarity.
Financial markets thrive on excitement and prediction. Most investors try to forecast price movements rather than understand economic value. Value investing is not about predicting the next quarter but assessing the long term capacity of the business to produce cash for its owners. The mathematics provides the structure, but the decision requires judgment.
Buffett often remarks that “price is what you pay and value is what you get”. Price changes every second. Value changes slowly with the underlying business. When the two diverge, opportunities appear. The combination of analytical tools and a patient temperament allows the value investor to take advantage of these discrepancies.
This project applies these principles to real companies using consistent, transparent calculations. By pairing Graham’s disciplined mindset with Buffett’s appreciation for quality and long term growth, we construct valuations that are both conservative and economically informed. The aim is not to produce artificial precision but to build a coherent framework that guides capital allocation in a rational way.
Once the economic logic of value investing is understood, the next step is to compute intrinsic value with a structured and repeatable method. A company generates free cash flow (FCF) each year. This is the amount that, in principle, could be distributed to shareholders without harming the operations of the business. The task is to estimate the stream of these future cash flows and discount them to the present.
A single perpetual multiple is sometimes acceptable for stable, low growth firms, but it cannot capture the behavior of a business experiencing reinvestment cycles, competitive advantages, or diminishing returns. Real companies do not grow at the same speed in all phases of their life. Early years often feature higher expansion rates, followed by a gradual slowdown as the company matures, and eventually a long run trajectory close to the growth of the overall economy.
A three-stage model separates these periods and creates a valuation structure that is both analytical and intuitive.
This first stage (1Y \to 5Y) represents the near future, where the investor can form a reasonable view of how the company will evolve. Management guidance, sector conditions, reinvestment levels, and recent operating performance offer useful information. Growth rates in this period often reflect concrete business catalysts: new products, international expansion, cost optimization, active share repurchases, or structural tailwinds.
In practice, we assign a short-term annual growth rate g_1 and project FCF forward for the first five years:
\text{FCF}_{t} = \text{FCF}_{0} (1 + g_1)^t \quad \text{for } t = 1,\dots,5
This stage is the most impactful in many valuations, because it compounds from today’s base and reflects near-term business dynamics. However, it should remain grounded. An aggressive short-term growth assumption will distort the valuation and create a fragile estimate.
As the company moves beyond the high-visibility horizon (6Y \to 10Y), growth naturally decays. Competitive pressures increase, reinvestment opportunities become more limited, and the company’s market share tends to stabilize. The second stage captures this transition toward maturity.
We assign a lower rate g_2 for years six through ten:
\text{FCF}_{t} = \text{FCF}_{5} (1 + g_2)^{t-5} \quad \text{for } t = 6,\dots,10
The exact value of g_2 depends on the quality and scale of the business. A dominant digital platform or a company with strong pricing power may sustain moderate growth for longer. A commodity-linked or cyclical business may require a cautious assumption.
Stage 2 smooths the path between the short-term and the terminal regime, preventing unrealistic jumps in the valuation curve.
No company grows above the economy forever. Even the strongest compounders converge to a long run trajectory tied to GDP, inflation, and sector maturity. The final stage (11Y \to \infty) models this equilibrium. We assume a perpetual growth rate g_{\infty}, typically between 2\% and 3\% for developed markets.
The cash flow at the end of year ten is used to compute a terminal value via the standard perpetuity formula:
\text{TV}_{10} = \frac{\text{FCF}_{10} (1 + g_{\infty})}{r - g_{\infty}}
Here r is the required return, which includes the risk-free rate and the equity risk premium appropriate for the business.
This terminal value represents all cash flows from year eleven onward.
Each projected FCF and the terminal value must be discounted back to the present:
\text{PV} = \sum_{t=1}^{10} \frac{\text{FCF}_{t}}{(1+r)^t} + \frac{\text{TV}_{10}}{(1+r)^{10}}
The discount rate r captures the opportunity cost for a rational investor. In value investing, a 10\% required return is often used for high-quality large-cap companies, while adjustments can be made for riskier or more cyclical firms.
The future is not a single trajectory. Even a stable company faces uncertainties in demand, margins, regulation, capital allocation and competition. A simple way to assess robustness is to evaluate three scenarios:
For each scenario, we run the full multi-stage model and compute a valuation range. This reflects how sensitive intrinsic value is to the underlying assumptions. Companies with strong economics and stable cash flows often show a narrow valuation band. Businesses with volatile margins or high reinvestment uncertainty produce wide ranges, signaling caution.
Once the present value of the company is computed, we divide by the diluted share count to obtain intrinsic value per share:
\text{Intrinsic Value per Share} = \frac{\text{PV}}{\text{Shares Outstanding}}
The share count should include dilution from stock-based compensation, convertible securities and buyback effects. This step translates the economic value of the business into a quantity directly comparable with market price.
Even with a careful model, intrinsic value is an estimate. To protect capital, value investors apply a margin of safety, purchasing only when the market price sits meaningfully below their conservative estimate. The margin size depends on the confidence in the business model, the predictability of cash flows and the quality of the assumptions. Margins often range from 10\% to 30\%.
Although more analytical than Graham’s original multiples, the multi-stage FCF model preserves the same spirit. It forces us to focus on earning power, cash generation and economic reality rather than market noise. It avoids speculative forecasting by anchoring assumptions in business quality and long run dynamics. It is flexible enough to evaluate compounders such as CRM, Alphabet and other high-ROIC companies, while still applicable to steady firms like KO or PEP.
The method produces a repeatable valuation framework. I implemented a valuation template here.