# Discounted cash flow method explained – examples

Discounted Cash Flow Method – Calculation, Formula and Examples

Discounted cash flow is used to determine the intrinsic (fair) value of a company. The ratio uses the discounting of cash flows to determine a current net present value. The expected Cash flow of a company is discounted in order to provide forecasts for the future. Different variants are available for the calculation. Internationally, the discounted cash flow indicator is considered to be highly informative, which is why it is important for investors and shareholders.

## The cash flow as a basis

Before the discounted cash flow can be defined and derived, the knowledge about the Cash flow as a business balance sheet indicator. This short excursus is necessary in order to understand the calculation and the significance of the discounted cash flow. In a company, cash flow refers to the flow of funds within an accounting period.

In contrast to profit, only the money that has actually flowed is counted and fictitious expenditures are excluded. The cash flow indicates how much money was actually generated within an accounting period. Roughly speaking, it is a simple difference calculation between income and expenses. Of course, there can also be a deficit at the end of this calculation and the cash flow can therefore be negative. In contrast to profit, cash flow is considered to be the more honest value.

.

## Discounted Cash Flow by Definition:

Discounted cash flow indicates, from the future cash flows of a businesshow much it is actually worth today. It is important to understand that a company is to be seen as an investment object, which uses the available capital to increase its value. For the valuation of a company according to discounted cash flow, forecasts about the future are included, which is why the result will vary depending on the forecast model.

Thus, there is no right or wrong, but the discounted cash flow provides a good indication for a fair company valuation. In addition, the chapters on the different calculation methods provide information on the fact that a different result can arise depending on the calculation method. The calculation of the discounted cash flow serves primarily investors, who thus get a real view of the company to be analyzed. In addition, the ratio is useful for small investors. It can be used to check whether the current share price of a company is rather overvalued or undervalued. The discounted cash flow is thus a decision-making aid for the selection of shares.

### Underlying values for the discounted cash flow

As already mentioned, the discounted cash flow works with future earnings rates of a company. The actual current value is rather irrelevant. It is used to forecast future cash flows. Therefore, the current balance sheet and income statement are only used to transfer the corresponding figures into the future. Since discounted cash flow always focuses on the future, the expected cash flows of a company are not simply added up.

Although this would lead to a result, the aspect of inflation would not be considered in any way. For this reason, the values are discounted. In a first step, however, the cash flows of the coming years must be determined. These form the basis for calculating future company values. The following chapters deal with the forecasting of future cash flows and the discounting approach.

### Cash flow discounting

Money loses value over time at Value, which may be due to inflation or interest rates. For this reason, cash flows must be discounted from their respective year of origination to the present date. Discounting is the opposite of compound interest. In contrast to a continuous increase, there is a continuous decrease in the value of the amounts. The result of discounting is the present value of a company or in this case the present value from the cash flow.

The cash flow is used for Discounting divided by a discount rate. This rate is the same for all years and must be calculated individually for each company. The discount rate is calculated from equity, debt, the respective cost rates and income tax. All this is determined by a formula in the WACC method. More detailed explanations follow in the chapter “WACC approach“.

### Forecasting the cash flow

In order to calculate the discounted cash flow, it is first necessary to forecast the cash flows of the yearswhich are to be included in the desired calculation period. This forecast is important because it has a significant influence on the results of the discounted cash flow. The deviations in the result thus depend to a large extent on how well a cash flow can be forecast. This varies from company to company.

A company that has had a steady business for years can budget more easily than a young start-up. Many companies rely on financial models to forecast cash flow. These include a budgeted balance sheet, a budgeted P&L and a budgeted cash flow. These can often be calculated precisely for individual items for three to five years. Following to after this period, the company’s growth is measured using only percentage figures and the cash flow is forecast accordingly.

.

## Calculating the discounted cash flow

After the required values for the discounted cash flow have been explained, the formula can be established. As already stated, the cash flow from the respective year must be discounted. The cash flow is divided by increasingly higher values, since the exponent of the formula corresponds to the year from which the cash flow originates. Thus, the cash flows in the distant future are worth less when calculated in terms of today. The formula for discounted cash flow is:

.

.

DCF = {\frac{CF1}{(1+r)}} + {\frac{CF2}{(1+r)^2}} + {\frac{CF3}{(1+r)^3}} + ……… + {\frac{CFn}{(1+r)^n}}

.

.

The discounted cash flow is calculated from the discounted cash flows using the formula presented. However, this does not complete the internal valuation of a company. The infinity of a company and its debt capital are also included in the formulas. Four different methods are available for calculating company values in connection with discounted cash flow, which can lead to different results and follow different approaches. The following chapters describe the respective methods, which are divided into the two headings “Gross” and “Net”. The gross method is again divided into three approaches.

### DCF Example: Discounted Cash Flow of Ruby GmbH

Ruby GmbH manufactures briefcases and would like to determine the present value of future cash flows. Using the forecasting tool Financial Modelin, the future cash flows of the years 2022 – 2026 were determined. These can be taken from the following table. The company calculates with a discount rate of 5%.

2022: EUR 644,000
2023: 778,000 EUR
2024: – 229,000 EUR
2025: 312,000 EUR
2026: 875,000 EUR

Entered into the formula, the following calculation results:

.

.

DCF = {\frac{644.000}{(1+0,05)}} + {\frac{778,000}{(1+0.05)^2}} + {\frac{-229.000}{(1+0.05)^3}} + {\frac{312,000}{(1+0.05)^4}} + {\frac{875,000}{(1+0.05)^5}}

.

.

DCF = 613,333 + 705,668 + (-197,818) + 256,683 + 685,585

.

.

DCF = 2,063,451 EUR

.

.

The future cash flows of Ruby GmbH over the next five years have a value of EUR 2,063,451 today. These are included in the calculation of the enterprise value using different methods.

### The entity methods

The entity methods are a way to calculate the real enterprise value including its future projections. What the methods have in common is that they initially assume full Financing with 100 % equity capital is assumed. Only then is the deduction made from borrowed capital. Normally, only the assets required for operations are calculated using the entity methods. Additional fixed or capital assets are then added to the discounted enterprise value.

This step is understandable, as non-operating assets do not provide any information about the future success of a company. Within the entity methods, a distinction is made between three approaches. The WACC (Weighted Avarage Cost of Capital), APV (Adjusted Present Value) and TCF (Total Cash Flow) methods will be described in detail below.

### WACC approach

The primary purpose of the WACC approach is to determine the discount rate for projected cash flow in future years. Thus, the result of the formula is initially a percentage that can be used for further company valuation. The percentage in itself can be sufficient for investment activities, as it describes the return distributions that a company pays its capital providers and investors on average. Various influencing factors are needed to calculate the discount rate. These include:

Equity
Debt capital
Total capital
Cost of equity
Cost of debt
Income tax

The factors equity, Debt capital and total capital can easily be read from a balance sheet of the company. It becomes more difficult with the cost rates. The cost of debt can best be calculated using the average interest rates that a company has to pay for its borrowed capital. Alternatively, a comparison with the coupons of corporate bonds from the same industry can help. The cost of equity, on the other hand, must be calculated, which is done using the Capital Asset Pricing Model (CAPM).

The formula for the CAPM is as follows:

.

.

Expected\thinspace return = Risk-free\thinspace interest rate + Beta * (expected\thinspace market return – risk-free\thinspace interest rate)

.

.

The risk-free interest rate describes the return from government bonds of the respective country, the number beta is used to classify the risk of the company compared to the market, and the expected market return can be predicted from an industry corresponding Stock index corresponding to the industry.

### Example: Calculating the cost of equity

Ruby GmbH is in a market environment whose risks are derived from the government bonds of Germany. The interest rate for this is 0.1 %. The company is robust and is hardly subject to fluctuations, which is why the Beta figure was set at 0.9. The shares of the sector generated a plus of 7% in the past year.

.

.

Cost of equity = risk-free\thinspace interest rate + beta * (expected\thinspace market return – risk-free\thinspace interest rate)

.

.

Cost of equity = 0.1 + 0.9 * (7 – 0.1)

.

.

Cost of equity = 6.31%

.

.

After the components of the WACC formula have been broken down and derived, the formula can be set up in the next step. Here, the equity ratio is offset against the return on equity from the CAPM formula. In addition, the debt ratio is offset against the coupon. Subsequently, the result from borrowed capital must be offset against the income tax rate, as the interest on borrowed capital is tax deductible.

The formula for the discount rate is:

.

.

WACC = {\frac{Equity}{Total capital}} * Cost of equity + {\frac{debt}{total capital}} \newline * (cost of debt capital * (1 – income tax rate)

.

.

Once the average cost of capital has been calculated from the WACC approach, this can be used to determine the enterprise value. All that remains to be done is to divide the free cash flow by the cost of capital. The debt capital is then deducted and the enterprise value is determined.

### Example: Calculating the discount rate

Ruby GmbH would like to calculate its discount rate using the WACC method so that it can determine its enterprise value. For this purpose, the following values were determined:

Equity: 120 million
Debt capital: 40 million
Total capital: 160 million
Cost of equity from CAPM formula: 6.31 percent
Cost of debt capital: 2.5 %
Income tax: 30 %

.

.

WACC = {\frac{Equity}{Total capital}} * Cost of equity + {\frac{debt}{total capital}}\newline * Cost of debt * (1 – income tax rate)

.

.

WACC = {\frac{120.000}{160.000}} * 0.0631 + {\frac{40,000}{160,000}} * 0,025 * (1 – 0,3)

.

.

WACC = 0.75 * 0.0631 + 0.25 * 0.025 * 0.7

.

.

WACC = 0.047325 + 0.004375

.

.

WACC = 5.17%

.

.

Ruby GmbH must therefore pay 5.17% annually to to its providers of equity and debt capital in order to meet their requirements.

The enterprise value is then determined. For this purpose, the example table of the projected cash flows of Ruby GmbH can be used and corrected with the discount rate now calculated. This results in the following formula:

.

.

DCF = {\frac{644.000}{(1+0,0517)}} + {\frac{778.000}{(1+0,0517)^2}} + {\frac{-229.000}{(1+0.0517)^3}} + {\frac{312.000}{(1+0.0517)^4}} + {\frac{875.000}{(1+0.0517)^5}}

.

.

DCF = 612,341 + 703,389 – 196,861 + 255,027 + 680,062

.

.

DCF = 2,023,958 EUR

.

.

The future cash flows of Ruby GmbH for the next five years have a value of EUR 2,023,958 today. The borrowed capital would still have to be deducted from this, but this would only make sense if the perpetuity were also calculated. In the example a period of five years is given, whereby the perpetual annuity and thus also the outside capital are not to be considered.

### APV approach

The APV approach is used for company valuations and can be used if the borrowed capital is to be included directly in the formula. The calculation is divided into two steps. First, the future cash flow is discounted. Here, the already known cost of equity from the CAPM formula is used for the calculation. In a second step, the present value of the tax benefit resulting from debt financing must be determined.

This value is referred to as the tax shield and increases with increasing debt capital. The text shield is positive because it describes how much money is saved when borrowing. This is because debt is normally cheaper for a company than equity.

Various values are required to derive the formula, but these are known from the chapter “WACC-Approach” chapter and therefore do not need to be redefined. The following basic values are required:

Cash flow of the coming years
Cost of equity
Cost of debt
Income tax rate
Amount and timing of debt

The first part of the formula deals with the discounting of cash flows, for which a simple calculation of discounted cash flow is needed. The already known formula is:

.

.

DCF = {\frac{CF1}{(1+r)}} + {\frac{CF2}{(1+r)^2}} + {\frac{CF3}{(1+r)^3}} + ……… + {\frac{CFn}{(1+r)^n}}

.

.

The Tax Shield is added to this value. As mentioned, this indicates the savings from borrowing. Thus, all years in which there is constant debt capital in the firm must be discounted. The formula is:

.

.

Tax\thinspace Shield = {\frac{FK*FK\thinspace interest*tax rate}{(1+FK\thinspace interest)}} + {\frac{FK*FK\thinspace interest*tax rate}{(1+FK\thinspace interest)^2}}\newline + {\frac{FK *FK\thinspace interest*tax rate}{(1+FK\thinspace interest)^3}} + ……… + {\frac{FK*FK\thinspace interest*tax rate}{(1+FK\thinspace interest)^n}}

.

.

### Example: Enterprise value according to APV approach

Ruby GmbH wants to determine its enterprise value according to the APV approach. All already known values are applied. So does the list of projected cash flows. For this reason, the first part of the formula can be taken from the section “Example: Discounted Cash Flow of Ruby GmbH” can be can be used. The amount for this was EUR 2,063,451. In the second step, the tax shield is determined. In the third year, Ruby GmbH takes out a loan of EUR 1 million in the third year. Together with the already known further influencing variables, the following formula results, which deliberately starts in the third year, which can be recognized by the exponent.

.

.

Tax\thinspace Shield = {\frac{FK*FK\thinspace interest*tax rate}{(1+FK\thinspace interest)}} + {\frac{FK*FK\thinspace interest*tax rate}{(1+FK\thinspace interest)^2}}\newline + {\frac{FK *FK\thinspace interest*tax rate}{(1+FK\thinspace interest)^3}} + ……… + {\frac{FK*FK\thinspace interest*tax rate}{(1+FK\thinspace interest)^n}}

.

.

Tax\thinspace Shield = {\frac{1.000.000*0,025*0,3}{(1+0,025)^3}} + {\frac{1.000.000*0,025*0,3}{(1+0,025)^4}} + {\frac{1,000,000 *0.025*0.3}{(1+0.025)^5}}

.

.

Tax\thinspace Shield = 20,386 EUR

.

.

Finally, the discounted cash flow is added to the tax shield, resulting in an intrinsic enterprise value of EUR 2,083,837 according to the APV method. The debt capital would still have to be deducted from this, but this only makes sense if the perpetual annuity were also calculated. In the example, a period of five years is given, which means that the perpetual annuity and thus also the borrowed capital should not be considered.

### TCF approach

The total cash flow approach is almost identical to the WACC methodwhich is why it will not be considered in detail here. For the TCF approach, it can be stated that the positive effects of debt capital are not only taken into account in the formula, but already when forecasting the cash flow. This is already adjusted, which is why the TCF method does not require a final correction via the interest rate on borrowed capital.

### The equity method

The equity method of calculating the enterprise value is also referred to as the net method. This is because the cash flow to equity serves as the basis. This so-called CFE reflects the view of the equity investors. Future cash flows are forecast in such a way that the future debt ratio is predicted for the entire future in a market-oriented manner. The future CFE is discounted using the cost of equity of an indebted company. After adding up all discounted CFE, the result represents the enterprise value.

## Areas of application of discounted cash flow

Now that the various methods of calculating enterprise value using discounted cash flow have been made comprehensible, the next step is to look at how the value can be used in the free economy. This is mainly done in the field of mergers and acquisitions, i.e. in the case of mergers, takeovers or purchases of companies. Here, the intrinsic enterprise value is needed so that a company can be converted into a value determined in real terms.

Of course, the calculation steps involve risks, as described in the chapter “Disadvantages of Discounted Cash Flow” described isbut the calculations bring the investor very close to the actual enterprise value. Once the value has been determined, the companies can conduct negotiations or approach the existing shareholders with purchase offers. Discounted cash flow has the great advantage that it also considers the future of a company, which results in a fair valuation even for the seller.

However, the intrinsic company values can also be used by shareholders. To do this, the investor calculates the real enterprise value using the discounted cash flow. He divides this by the number of tradable shares and obtains a fair share price. If this price is below the real share price on the stock exchange, he should not make an investment.

If, however, the value is above the stock market price, it can be assumed that the shares are undervalued and will adjust to the fair share price in the long term. An investment is therefore advisable. In this way, the potential returns of shares can be compared very well. In this way, an investor finds out the shares with the best chances for the future on the basis of sound calculations.

### Example: Share comparison with company values

A shareholder wants to invest 5,000 EUR in shares of a company. For this purpose, he compares three companies and calculates the intrinsic company values using the discounted cash flow. The calculation yields the following figures for the companies’ values. In each case for the period of the next five years.

Zip AG: EUR 5,564,342
Alecho AG: EUR 44,256,000
Ramin Fulder AG: 894,000 EUR

Using the share capital and the nominal value of the shares, the shareholder finds out the number of shares in circulation:

Zip AG: 227,573
Alecho AG: 1,675,200
Ramin Fulder AG: 170,000

The enterprise value per share after division is:

Zip AG: EUR 24.45
Alecho AG: EUR 26.42
Ramin Fulder AG: 5.29 EUR

The current stock market price of the companies is:

Zip AG: 36.07 EUR
Alecho AG: 22.87 EUR
Ramin Fulder AG: 5.02 EUR

In the last step, the percentage deviation must now be calculated to obtain the best return opportunity for the respective share price.

Zip AG: + 32.21 % (Overvalued)
Alecho AG: – 15.52 % (Undervalued)
Ramin Fulder AG: – 5.38 % (Undervalued)

The shareholder should invest his EUR 5,000 in shares of the company Alecho AG. Here, the share price is 15.52 % below the fair enterprise value and thus offers the best return opportunity.

### Disadvantages of the Discounted Cash Flow

Finally, the disadvantages of discounted cash flow should be listed at this point. It is true that the method is recognized and one of the best when it comes to determining fair company values. However, every calculation has its pitfalls. In the case of discounted cash flow, the disadvantage becomes obvious very quickly because forecasts are used. It is difficult to look into the future and even with the best forecast models there is no certainty. In particular, it is difficult to look at the perpetual annuity, although this is a large part of the company valuation.

A small change in the percentage of the perpetual growth of the company has a significant impact on the valuation. For this reason, the previous examples and formulas were limited to a small period of time. This can most likely reflect the realistic data for a business valuation, even if then the business value is not calculated for an infinite activity.

In addition, the formulas for the discount rate and expected rate of return are subject to assumptions which can only approximate the real future. Statements about future market returns or borrowing costs in a few years are also estimates. Although these are made on the basis of real data, here too there is no certainty that they will be correct.

We will be happy to hear your thoughts