Discounted cash flow

Developed by Oliver Skou Schwarz

This page refers to the discounted cash flow (DCF) method regarding projects and investments. Discounted Cash Flow (DCF) is a method used to estimate the value of an investment or a project by projecting its future cash flows and then discounting them back to their present value. The reason for using DCF is that an investment's value is equal to the sum of its expected future cash flows, discounted at an appropriate rate to account for the time value of money and the investment's level of risk. The sum of the discounted cash flow is the Net Present Value (NPV).

History

Origin

• Origin of the method
• Why was it "invented"?
• Who "invented" it?

The concept of discounted cash flow (DCF) has been used in various forms for centuries, but the modern version of DCF used in finance and investment analysis can be traced back to the early 20th century.

One of the earliest uses of DCF in its modern form was by Irving Fisher, an American economist, in his 1930 book "The Theory of Interest." Fisher used DCF to calculate the present value of a stream of future cash flows, which he called the "net present value" of an investment.

Fisher's work on DCF was groundbreaking and became an important part of finance theory. Since then, DCF has been widely used in financial analysis and valuation, including in corporate finance, investment banking, and portfolio management.

Use throughout history

How has it been used before?

• In the 1930s, DCF was used by economists such as Irving Fisher and John Maynard Keynes to analyze the impact of interest rates on investments and economic growth.
• In the 1950s, DCF gained popularity in the oil and gas industry as a tool for valuing oil and gas reserves. This was known as the "net present value" (NPV) method, which calculates the present value of expected cash flows from oil and gas reserves.
• In the 1960s and 1970s, DCF was used by corporate finance professionals to evaluate capital investment projects and to value businesses for mergers and acquisitions.
• In the 1980s and 1990s, DCF became widely used in the field of equity research, where it is used to value stocks and make investment recommendations to clients.
• Today, DCF is still widely used in all of these areas, as well as in other fields such as real estate investment and project finance.

Overall, DCF has been an important tool for investors, analysts, and managers in making informed decisions about investments, capital allocation, and strategic planning.

Math section

A section describing the mathematical expression in detail, so it is broken down into understandable parts. Including examples of how the calculation method works.

• Discounted Cash Flow (formula)
• Free cash flow
• Discount Rate

Application

A section explaining how and when to use the method, and what it is used with

Time value of money

The time value of money refers to the concept that monetary value changes over time. Practically, this means that an equal amount of money available at different points in time has different values due to many various factors such as changing inflation and interest rates.

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The general concept is that money available today is worth more than the same amount of money available in the future, because it can be invested smartly or used immediately to generate returns. On the other hand, money available in the future is worth less than the same amount of money available today, because it cannot be used or invested until that future time.

Therefore, the time value of money is an important concept in project work and when investing in them, as it helps project managers and businesses make better decisions about how to allocate their resources in the right points in time.

Free Cash Flow

The free cash flow (FCF) is the cash flow that is available to equity holders and debt holders after a business pays for the costs of continued operations, like operating expences and capital expenditures. Generally, the more free cash flow a business or a project has, the more attractive it will be for investors, as it will be able to invest in new opportunities. There are multiple ways of calculating the free cash flows depending on the level of precision and complexity. A simple model for calculating this can be seen below.

$F C F = Sales Revenue - (OPEX + Taxes) - CAPEX$

The sales revenue is the money going into the project or the business, hence the positive sign. The Operational Expenditure (OPEX) is the short-term cost of maintaining operations on a daily basis. This could be the cost of running the machines in a factory, which need operators and electricity.

CAPEX is the Capital Expenditures, which refers to the amnount fo money a company or a project need to invest in acquiring its long-term assets needed to start operations. This can include assets such as property, equipment, or technology. In other words, CAPEX refers to the long-term spending a company undertakes, typically in advance, to buy its fixed assets that are expected to provide benefits over an extended period.

Capital expenditures are typically larger and more long-term in nature than other expenses, such as operational or maintenance expenses, and are considered investments in the company's future growth and profitability. Examples of capex include the purchase of new machinery or equipment, the construction of a new building, or the acquisition of another company. The Capital Expenditures (CAPEX) is the long-term investment needed to start operations. This is typically paid for in advance, and includes things like investing in the machinery and buildings in a factory.

Net Present Value (NPV)

Net Present Value (NPV) is a financial metric used to estimate the current value of an investment based on its expected cash flows and the time value of money. It measures the difference between the present value of cash inflows and the present value of cash outflows over a specified period of time.

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To calculate the NPV, the expected cash flows of the investment are discounted back to their present value using a discount rate that reflects the time value of money and the risk of the investment. The discounted cash inflows are then subtracted from the discounted cash outflows to arrive at the net present value of the investment.

If the net present value is positive, it means that the investment is expected to generate more cash inflows than outflows and is considered profitable. Conversely, if the net present value is negative, it means that the investment is expected to generate less cash inflows than outflows and is considered unprofitable.

NPV is a commonly used financial metric in capital budgeting, where it is used to evaluate the financial viability of long-term investment projects such as the construction of a new plant or the development of a new product. It helps decision-makers determine whether an investment will create value for the company and whether it is worth pursuing.

Working Average Cost of Capital (WACC)

The Weighted Average Cost of Capital (WACC) is a financial method used to measure the cost of capital. It uses the cost of both debt and equity financing, as well as the proportion of each in the company's capital structure.

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The WACC formula calculates the average cost of capital by multiplying the cost of each capital component (debt and equity) by its weight in the company's capital structure.

The WACC is an important financial metric as it is used to evaluate the financial feasibility of potential investment opportunities. The WACC is typically used as the discount rate in discounted cash flow (DCF) analysis to determine the present value of future cash flows.

A higher WACC indicates a higher cost of capital and a greater risk associated with an investment opportunity. On the contrary, a lower WACC indicates a lower cost of capital and a lower risk associated with an investment opportunity.

Terminal Value

The Terminal Value (TV) is another term that is used when trying to calculate the present value of a firm or an investment.

Investments in Projects (references to NPV as well)

A section with specific reference to projects and investments in these, possible examples from real life application of it and other methods that are similar or (better/worse) in certain cases.

• Projects
• Real example
• How and when similar models were used

Limitations

A section describing the cons of the methods, with a critical perspective on possible assumptions of the model.

How to calculate

A brief section with concrete advice on how it should be applied for the reader - this may need to not be the last section.

• example of how to use the formula, with numbers
• Assumptions

References

Possible Sources:

https://www.investopedia.com/terms/d/dcf.asp

https://www.investopedia.com/terms/c/cashflow.asp

https://www.streetofwalls.com/finance-training-courses/investment-banking-technical-training/discounted-cash-flow-analysis/

https://www.pmi.org/learning/library/project-investment-9384

(PROJECT INVESTMENT https://esfccompany.com/en/articles/economics-and-finance/investment-project-management/)

(HISTORY https://www.jstor.org/stable/2490123?seq=8)

(TIME VALUE OF MONEY https://www.investopedia.com/terms/t/timevalueofmoney.asp)

(NET PRESENT VALUE https://www.investopedia.com/terms/n/npv.asp)

(Weighted average cost of capital WACC https://www.investopedia.com/terms/w/wacc.asp)