Skip to main content
diversification.com
← Back to D Definitions

Discounted cash flow models

What Is Discounted Cash Flow Models?

Discounted cash flow (DCF) models are a class of valuation methods used to estimate the value of an investment based on its projected future cash flow. The core principle behind discounted cash flow models is the time value of money, which posits that a dollar received today is worth more than a dollar received in the future due to its potential earning capacity. Therefore, future cash flows are "discounted" back to their present value using a specific discount rate to determine an asset's intrinsic worth. This approach falls under the broader category of valuation methods in finance.

History and Origin

The concept of present value, which is foundational to discounted cash flow models, has roots in early financial thought, arguably implicit in works as far back as Leonardo of Pisa's Liber Abaci in 1202, and later formalized by economists like Irving Fisher in his 1907 theory, The Rate of Interest.11 However, the modern application of discounted cash flow as a systematic valuation tool gained prominence in the 20th century. Joel Dean, an American economist, is credited with introducing the discounted cash flow (DCF) approach as a tool for valuing financial assets, projects, or investment opportunities in 1951.10 This methodology was inspired by the well-established practice of bond valuation, where the price of a bond is determined by discounting its future coupon payments and principal back to the present.9

Key Takeaways

  • Discounted cash flow (DCF) models estimate an asset's value by projecting its future cash flows and converting them into today's dollars.
  • The fundamental concept underpinning DCF is the time value of money, recognizing that money available now is worth more than the same amount in the future.
  • A crucial input in DCF models is the discount rate, which reflects the riskiness of the projected cash flows and the opportunity cost of capital.
  • DCF analysis is widely used in investment decisions, corporate finance, and real estate.
  • Despite its theoretical rigor, DCF models are highly sensitive to assumptions about future cash flows and the discount rate, making accurate forecasting essential yet challenging.

Formula and Calculation

The basic formula for a discounted cash flow (DCF) model calculates the present value of all expected future cash flows. For a series of discrete cash flows, the formula is:

PV=∑t=1nCFt(1+r)t+TVn(1+r)n\text{PV} = \sum_{t=1}^{n} \frac{\text{CF}_t}{(1+r)^t} + \frac{\text{TV}_n}{(1+r)^n}

Where:

  • (\text{PV}) = Present Value (the estimated intrinsic value)
  • (\text{CF}_t) = Cash Flow in period (t)
  • (r) = The discount rate (representing the cost of capital or required rate of return)
  • (t) = The time period in which the cash flow occurs
  • (n) = The number of explicit forecast periods
  • (\text{TV}_n) = Terminal Value at the end of the forecast period

The terminal value represents the value of all cash flows beyond the explicit forecast period (typically 5-10 years). It can be calculated using a perpetuity growth model or an exit multiple method.

Interpreting the Discounted Cash Flow Models

Interpreting the results of discounted cash flow models involves comparing the calculated present value (or intrinsic value) to the current market price or cost of the asset. If the DCF valuation yields a value higher than the current market price, it suggests the asset may be undervalued. Conversely, if the DCF value is lower than the market price, it might indicate overvaluation.

For investment decisions, a positive net present value (NPV), which is essentially the sum of all discounted cash flows minus the initial investment, typically suggests a worthwhile project or asset. The interpretation also heavily relies on the quality of the inputs. A higher discount rate will result in a lower present value, reflecting a higher perceived risk or opportunity cost, while lower future cash flow projections will similarly reduce the valuation. Analysts often create a range of valuations by using different assumptions to provide a more robust assessment.

Hypothetical Example

Imagine an investor is considering buying a small business, "GreenTech Solutions," and wants to use a discounted cash flow model to estimate its value. The investor projects the following Free Cash Flow to Firm (FCFF) for the next five years:

  • Year 1: $100,000
  • Year 2: $120,000
  • Year 3: $140,000
  • Year 4: $160,000
  • Year 5: $180,000

After Year 5, the investor assumes GreenTech Solutions will grow its FCFF at a perpetual rate of 3% per year. The investor determines the appropriate Weighted Average Cost of Capital (WACC) for GreenTech Solutions to be 10%.

Step 1: Calculate the Present Value of Explicit Cash Flows

  • PV (Year 1) = $100,000 / (1 + 0.10)(^1) = $90,909.09
  • PV (Year 2) = $120,000 / (1 + 0.10)(^2) = $99,173.55
  • PV (Year 3) = $140,000 / (1 + 0.10)(^3) = $105,185.76
  • PV (Year 4) = $160,000 / (1 + 0.10)(^4) = $109,240.24
  • PV (Year 5) = $180,000 / (1 + 0.10)(^5) = $111,761.54

Sum of PV of explicit cash flows = $90,909.09 + $99,173.55 + $105,185.76 + $109,240.24 + $111,761.54 = $516,270.18

Step 2: Calculate the Terminal Value (TV)

Using the perpetuity growth model at the end of Year 5:
(\text{TV}_5 = \frac{\text{FCFF}_6}{r - g} = \frac{\text{FCFF}_5 \times (1+g)}{r - g})
(\text{TV}_5 = \frac{$180,000 \times (1+0.03)}{0.10 - 0.03} = \frac{$185,400}{0.07} = $2,648,571.43)

Step 3: Discount the Terminal Value back to Present Value

PV of Terminal Value = $\frac{$2,648,571.43}{(1+0.10)^5} = $1,644,482.50$

Step 4: Calculate the Total Intrinsic Value

Total Intrinsic Value = Sum of PV of explicit cash flows + PV of Terminal Value
Total Intrinsic Value = $516,270.18 + $1,644,482.50 = $2,160,752.68

Based on this DCF model, the estimated intrinsic value of GreenTech Solutions is approximately $2,160,752.68. The investor would then compare this value to the asking price of the business to make an investment decision.

Practical Applications

Discounted cash flow models are widely applied across various domains in finance and business due to their robust theoretical foundation rooted in the time value of money. Key applications include:

  • Corporate Finance: Companies utilize DCF for capital budgeting decisions, evaluating potential projects, mergers and acquisitions (M&A), and determining the fair value of a business for sale or acquisition. It helps management assess whether a new investment will generate sufficient returns to justify its cost of capital.
  • Equity Valuation: Investors and analysts commonly employ DCF to estimate the intrinsic value of publicly traded stocks. By forecasting a company's future Free Cash Flow to Equity (FCFE) or Free Cash Flow to Firm (FCFF), they can arrive at a target price for the shares.
  • Real Estate Investment: In real estate, DCF models are used to value properties by projecting rental income, operating expenses, and eventual sale proceeds, then discounting these cash flows to determine a property's current worth.
  • Fair Value Accounting: Regulatory bodies and accounting standards, such as ASC 820 ("Fair Value Measurement") in the U.S. Generally Accepted Accounting Principles (GAAP), acknowledge the use of income approaches like discounted cash flow when determining the fair value of assets and liabilities, particularly for less liquid or unobservable investments. ASC 820 provides a framework for how fair value should be defined, measured, and disclosed, requiring entities to categorize assets based on the observability of inputs used in their valuation techniques.8 Large institutional investors, such as Norges Bank Investment Management, the manager of Norway's sovereign wealth fund, also emphasize the use of industry-standard models with observable market inputs for valuation where market prices are not available, consistent with international financial reporting standards (IFRS) and fair value principles.7
  • Litigation and Expert Witness Testimony: DCF is often used in legal settings to estimate damages, lost profits, or business valuations in disputes, drawing on its comprehensive approach to future economic benefits.
  • Financial Modeling: DCF is a cornerstone of advanced financial models, integrating detailed financial projections with valuation methodologies to provide comprehensive analyses for strategic planning and investment analysis.

Limitations and Criticisms

While discounted cash flow models are theoretically sound and widely used, they come with significant limitations and criticisms:

  • Sensitivity to Assumptions: DCF models are highly sensitive to the inputs, particularly the projected future cash flow and the discount rate. Small changes in growth rates or the Weighted Average Cost of Capital (WACC) can lead to vastly different valuations.6 Accurately forecasting financial results several years into the future is inherently challenging and prone to error, especially for dynamic businesses or uncertain economic conditions.5
  • Uncertainty of Terminal Value: A substantial portion of a DCF valuation often comes from the terminal value, which represents cash flows beyond the explicit forecast period. Estimating this value, whether through a perpetuity growth model or an exit multiple, requires significant assumptions about long-term growth and market conditions, introducing considerable uncertainty.4
  • Difficulty in Determining the Discount Rate: Selecting the appropriate discount rate is critical and complex. It involves estimating the risk-free rate, market risk premium, and specific company risks, which can be subjective and difficult to quantify precisely. For private companies, determining the WACC can be particularly challenging.3
  • "Garbage In, Garbage Out" (GIGO): The accuracy of a DCF valuation is directly dependent on the quality of its inputs. If the underlying financial projections or discount rate assumptions are flawed, the resulting valuation will be unreliable, regardless of the model's sophistication.
  • Applicability to Certain Companies: DCF may be less suitable for companies with unstable or unpredictable cash flows, such as early-stage startups or businesses undergoing significant transformation. It can also be challenging for companies with negative free cash flows for extended periods.
  • Untestability: Some critics argue that the DCF methodology is practically untestable in its ability to reliably predict market values. Because the inputs (expected cash flows and discount rates) are unobservable and future outcomes can be explained by an infinite number of possible paths, it is difficult to scientifically validate the model's predictive power.2 This can lead to DCF valuations being more akin to "quantitative narratives" rather than precise scientific estimates.1

Discounted Cash Flow Models vs. Net Present Value

While closely related and often used interchangeably in discussions, "discounted cash flow models" and "Net Present Value" represent different aspects of the same underlying principle.

Discounted Cash Flow Models refer to the broader category of valuation methodologies that use the concept of discounting future cash flows to the present. It encompasses various approaches, such as valuing a company based on its Free Cash Flow to Firm (FCFF) or Free Cash Flow to Equity (FCFE), or valuing a project based on its expected cash inflows and outflows. The output of a DCF model is typically an intrinsic value of the asset or entity being evaluated.

Net Present Value (NPV) is a specific metric calculated within a discounted cash flow framework, primarily used for capital budgeting and project evaluation. NPV explicitly measures the difference between the present value of all cash inflows and the present value of all cash outflows (initial investment and subsequent costs) associated with a project or investment. A positive NPV indicates that the project is expected to generate more value than its costs when both are brought to present terms, thus making it a financially attractive undertaking.

In essence, DCF models are the analytical framework, and NPV is a specific calculation or outcome derived from applying that framework to assess the profitability of a project or investment, usually in the context of an initial outlay.

FAQs

What is the primary purpose of a discounted cash flow model?

The primary purpose of a discounted cash flow (DCF) model is to estimate the intrinsic value of an asset, project, or business by projecting its future cash flow and then converting those future amounts into their present value using a specific discount rate. This helps in making informed investment decisions.

How is the discount rate determined in a DCF model?

The discount rate reflects the riskiness of the projected cash flows and the opportunity cost of capital. For valuing a company, it is often represented by the Weighted Average Cost of Capital (WACC). For equity valuation, the cost of equity might be used. It typically incorporates a risk-free rate (like a Treasury bond yield) plus a risk premium that accounts for the specific risks of the investment.

Can discounted cash flow models be used for all types of companies?

Discounted cash flow models are most effective for mature companies with relatively stable and predictable cash flow patterns. They are generally less suitable for early-stage startups, companies with highly volatile earnings, or those undergoing significant business model changes, where forecasting future cash flows accurately becomes extremely challenging.

What is terminal value in a DCF model?

Terminal value represents the present value of all cash flows that an asset or business is expected to generate beyond the explicit forecast period in a discounted cash flow model. This period typically extends indefinitely into the future, and the terminal value aims to capture the long-term sustainable value of the entity.

Why is forecasting cash flows so important and challenging in DCF analysis?

Forecasting cash flows is crucial because they are the primary input for determining value in discounted cash flow models. It is challenging because it requires making assumptions about future revenues, expenses, capital expenditures, and working capital needs, all of which are subject to economic conditions, competitive pressures, and management decisions that are inherently uncertain. Inaccuracies in these forecasts can significantly impact the final valuation.