# Capitalised Earnings Method Calculation

The capitalised earnings method is a heuristic method of business valuation used to determine the value of a business (valuation object). For this purpose, the future net cash flow is discounted using a tax-corrected calculation interest rate and condensed to a value.

The capitalised earnings method can be divided into the subjective capitalised earnings method (in accordance with IDW S 1), the objectified capitalised earnings method in accordance with IDW S 1, the simplified capitalised earnings method in accordance with Section 202 BewG and the capitalised earnings method in accordance with Sections 27-34 ImmoWertV.

In the subjective capitalised earnings method (in accordance with IDW S 1), the net cash flow is discounted using an individual tax-corrected calculation interest rate (endogenous marginal interest rate) of the person concerned in the respective period. If necessary, the net cash flow is corrected by a risk discount or the discount rate is increased by a risk premium. The subjective capitalised earnings method existed long before IDW S 1 and is the original capitalised earnings method.

The objectified capitalised earnings method in accordance with IDW S 1 derives the base interest rate and the risk (market risk premium*beta factor) from a model called Tax-CAPM, which is then used to discount the net cash flow, corrected for tax.

The simplified capitalised earnings method in accordance with § 202 BewG originates from German tax law. The profit of the last three years is corrected, totalled, divided by three and taxed at a flat rate of 30%. This sustainable profit is currently multiplied by a capitalisation factor of 13.75, which corresponds to a calculation interest rate of 7.27%. The capitalisation factor can be calculated using the reciprocal of the discount rate and vice versa.

The capitalised earnings method according to §§ 27-34 ImmoWertV is explained separately in the capitalised earnings method according to ImmoWertV.

## Capitalised Earnings Method Calculation with Example

### Baseline Scenario

The subjective capitalised earnings method (in accordance with IDW S 1) is explained using a simple example. Too much “theory” should be avoided at this point. New aspects are added to this example bit by bit.

A company generates a cash flow of 12000 monetary units (MU) per year to the owner. Growth and taxes are excluded for now. The investment interest rate (endogenous marginal interest rate) is 5%. If the company is sold, the same cash flow must be realised through an alternative investment of the sale price.

If 240000 MU are deposited at a bank at 5%, one also receives 240000*0.05 = 12000 MU per year. The value of the company is therefore 240000 MU. Mathematically this is calculated as follows 12000/0.05 = 240000 MU. This is a perpetuity.

At a value of 240000 MU, the money from the company can be substituted by a bank investment without any disadvantage or advantage.

Table 1: Company Value Calculation Baseline Scenario

Name Year 1 Year 2 Year 3 Year...
capital 240000 240000 240000 ...
interest revenue 12000 12000 12000 ...
withdrawal -12000 -12000 -12000 ...

Source: own representation.

It is important that the calculation interest rate, in technical language the endogenous marginal interest rate, is used for discounting. In the case of a sale, this is often an investment interest rate, unless only a portion of existing debt is being paid off. In the case of an acquisition, it is often the credit interest rate (borrowing rate), unless the acquisition is made exclusively from own funds. The endogenous calculation interest rate must be estimated per period and lies between the debit and credit interest rate in the case of infinite investment and borrowing possibilities. In examples, a debit interest rate of 5% and a credit interest rate of 10% are often used. The endogenous marginal interest rate is a net interest rate. Since there are no taxes in the above example, the net interest rate is equal to the gross interest rate.

### Extension by Growth

Growth is added to the initial example. The company’s cash flow increases annually by 2% (inflation). A purchasing power equalisation is to take place. The value is determined as follows:

12000/(0.05-0.02) = 400000 MU. The company is worth 400000 MU. Specifically, not all of the interest income can be distributed because the investment must be increased to compensate for the increase in cash flow.

If the investment interest rate had now increased by the inflation rate (5%+2%=7%), the company would be worth12000/(0.07-0.02) = 240000 MU. In practice, the interest rate is strongly dependent on inflation.

Table 2: Company Value Calculation inc. Growth

Name Year 1 Year 2 Year 3 Year...
capital 400000 408000 416160 ...
interest revenue 20000 20400 20808 ...
withdrawal -12000 -12240 -12484.8 ...

Source: own representation.

### Expansion by Taxes

In the following, taxes are added to the initial example. (Growth is excluded again for now.) The tax rate on the cash flow is 30%. The income from the interest investment is not taxed for the moment.

The net cash flow is 12000*(1-0.3) = 8400 MU.

The company is therefore worth 8400/0.05= 168000 MU and thus valued lower than in the initial scenario.

Let us now assume that the interest income is also taxed at 25%. The net interest rate is therefore 0.05*(1-0.25) = 0.0375. The company is therefore worth 8400/0.0375 = 224000 MU.

Why is the value higher than in the initial situation? Since the interest income is taxed and the net income is therefore lower, the initial amount for the interest investment must be higher.

Note: In order to correctly determine the net interest, the respective taxes must be taken into account. There are special tax formulas for e.g. natural persons, for corporations and for partnerships. These are always tied to a legal system and a specific period of time. Since the determination requires a rather profound knowledge of tax law, this will not be discussed in any further detail here. If necessary, please refer to Schneeloch et al. (2020).

Table 3: Company Value Calculation incl. Taxes

Name Year 1 Year 2 Year 3 Year ...
capital 224000 224000 224000 ...
interest revenue (gross) 11200 11200 11200 ...
taxes -2800 -2800 -2800 ...
withdrawal -8400 -8400 -8400 ...

Source: own representation.

### Expansion by Growth and Taxes

The initial example is now extended to include both growth and taxes. If both growth and taxes are taken into account, the value of the company is as follows:

8400/(0.0375-0.02) = 480000 MU. The calculation assumes that the cash flow increases by 2% but is also subject to 30% taxation.

Table 4: Company Value Calculation incl. Growth and Taxes

Name Year 1 Year 2 Year 3 Year...
capital 480000 489600 499392 ...
interest revenue (gross) 24000 24480 24969.6 ...
taxes -6000 -6120 -6242.4 ...
withdrawal -8400 -8568 -8739.36 ...

Source: own representation.

### Expansion by Risk

Risk can be included in the calculation in two different ways in particular. Firstly, through a lower cash flow (safety equivalent method) and secondly, through a higher interest rate (risk premium method) (Terstege, 2023). Both methods can be converted into each other. The lower cash flow explicitly accounts for the risk, while a risk premium on the calculation interest rate implicitly accounts for the risk.

The cash flow is corrected in the payment series and is now only 10000 MU. Consequently, after tax (30%) 7000 MU is applied. The value of the company is 7000/(0.0375-0.02) = 400000 MU.

The cash flow is further estimated at 12000 MU before taxes and 8400 MU after taxes. However, a risk premium of 0.35% is assumed. The company value is 8400/(0.0375-0.02+0.0035)=400000 MU. In this example, the risk premium was calculated by a mathematical reformulation.

The problem with the risk premium is that the risk in future periods is taken disproportionately high into account. An explicit correction in the payment series, in the sense of scenarios, is better estimable and prevents unnecessary estimation errors.

Reference should be made to Table 4 above. Conceptually, the cash flow is “simply” replaced by the risk-corrected cash flow.

### Capitalised Earnings Method with Detailed Planning Period

Let us now assume that the flow of money continues to grow in line with inflation and is taxed at 30%. There is no risk and if there was, it would be corrected directly in the cash flow. However, the investment interest rate is 7% in year one, 6% in year two and 5% starting in year three (perpetuity). The investment interest is again taxed at 25%, so the net interest is 5.25%, 4.5% and 3.75%. Each period and, at the end, the perpetuity, must be discounted individually. Compound interest is also taken into account.

Year 1: 8400 * (1+0.0525)^-1 = 7981 MU

Year 2: 8568 * (1+0.045)^-1 * (1+0.0525)^-1 =7790.06 MU

Year 3: 8739.36/(0.0375-0.02) * (1+0.045)^-1 * (1+0.0525)^-1 = 437638.06 MU

The total is 469820.55 MU. This is the amount that has to be invested to get the same cash flow as through the company. The example illustrates this. It can be seen that the data from year 3 onwards in Table 5 is the same as the data in Table 4.

Note: The planning period is divided into a clearly plannable period, e.g. 5-10 years, and then a perpetual annuity is applied to the planning horizon.

Table 5: Company Value Calculation with Detailed Planning Period

Name Year 1 Year 2 Year 3 Year...
capital 469820.55 486086.12 499392 ...
interest revenue (gross) 32887.44 29165.17 24969.6 ...
taxes -8221.86 -7291.29 -6242.4 ...
withdrawal -8400 -8568 -8739.36 ...

Source: own representation.

### Formulas for the Capitalised Earnings Method

The formula for the discount factor is shown here. ρ stands for the discount factor, t for the respective year, τ is a running variable for the time, i for the interest rate and r for the risk. If the risk in the cash flow is taken into account by a discount, no risk premium may be added to the interest rate.

The discounting of the cash flow of a company with a perpetual life is represented by the following formula.The first part shows the discounting in the planning period, and the second part represents the annuity on the planning horizon. C stands for the net present value, t for the respective year, T for the planning period, e for the cash flow, ω for the growth rate.

If a finite lifespan is assumed instead of a perpetual lifespan, a present value is applied to the planning horizon. n stands for the years.

## Objectified Capitalised Earnings Method According to IDW S 1

The capitalised earnings method in accordance with IDW S 1 is described in particular in margin nos. 102-123. It is divided into a subjective and an objectified capitalised earnings method. The subjective form is described in margin no. 123.  In addition to this subjective approach, there is also the objectified capitalised earnings method (margin no. 114-122), which is described below.

The objectified income capitalisation approach in accordance with IDW S 1 proceeds as follows in simplified form:

1. A planning period is defined (e.g. 5 years) and then a perpetual annuity (or a present value) is applied.
2. Projected balance sheets and projected P&Ls are prepared in order to determine the sustainable profit.
3. The calculation interest rate is determined and derived from a model called Tax-CAPM (Brennan, 1970). Specifically, a risk-free base rate is determined, which is augmented by a risk premium (market risk premium*beta factor). This interest rate is then discounted with a (standardised) personalised tax rate. Furthermore, the interest rate is corrected by a growth factor for the perpetual annuity.
4. The net cash flow is discounted with the calculated calculation interest rate.

Planning period

Base interest rate +
market risk premium * beta factor =
Gross interest rate
Gross interest rate * (1 – tax rate) =
Net interest rate

At the planning horizon (perpetual)

Base interest rate +
Market risk premium * beta factor =
Gross interest rate
Gross interest rate * (1 – tax rate) –
Growth rate =
Net interest rate

The procedure is similar to the subjective capitalised earnings method (in accordance with IDW S 1). The difference is that the starting point is not the individual calculation interest rate, but an objectified interest rate consisting of base rate + market risk premium * beta factor. Although the value is therefore more “objective”, it is irrelevant for the valuation subject. Detailed and accurate criticism of why the objectified capitalised earnings value method according to IDW S 1 should not be used for decision-making purposes can be found in Matschke and Brösel (2013).

This will be illustrated here using an example. The gross cash flow for the company is 12000 MU and 8400 MU after tax (30%). The cash flow trends in line with inflation of 2%.

In the subjective capitalised earnings method (in accordance with IDW S 1), the interest rate for 5% before and after tax is set at (25%) 3.75%. This is what he actually gets from his bank. The value is 8400/(0.0375-0.02) = 480000 MU. As the example shows, the sale price compensates for the lost cash flow through the interest income. In this example risks are not taken into account due to subjectively certain expectations ( (expectancy value).

Table 7: Company Value Capitalised Earnings Method (Subjective)

Name Year 1 Year 2 Year 3 Year...
capital 480000 489600 499392 ...
interest revenue (gross) 24000 24480 24969.6 ...
taxes -6000 -6120 -6242.4 ...
withdrawal -8400 -8568 -8739.36 ...

Source: own representation.

For the capitalised earnings method according to IDW S 1 in its objectified form, a base interest rate of 4% and a market risk of 4.5% apply. These data, as well as the beta factor of 1.05, are to be derived from the TAX-CAPM model. Added together and adjusted for taxes, the interest rate is (0.04+0.045*1.05)*(1-0.25) = 6.54%.

This results in a value of  8400/(0.0654-0.02) = 184869.36 MU.

The objectified capitalised earnings value method in accordance with IDW S 1 implies that the alternative investment is in the same risk class with the same level of debt.

Table 8: Company Value Calculation Capitalised Earnings Method According to IDW S 1 (Objectified)

Name Year 1 Year 2 Year 3 Year...
capital 184869.36 182939.75 180774.64 ...
interest revenue (gross) 9243.47 9146.99 9038.73 ...
taxes -2310.87 -2286.75 -2259.68 ...
withdrawal -8400 -8568 -8739.36 ...

Source: own representation.

However, the valuation subject invests its money with the house bank and attempts to obtain the same withdrawal flow as before the sale. His capital decreases every year because the interest income is not sufficient to compensate the former cash flow. The reason is that the objectified capitalised earnings method according to IDW S 1, like the DCF method, does not consider the subject’s real alternative investment, but a fictitious investment on the capital market. Decisions should therefore not be based on the objectified income capitalisation method according to IDW S 1. However, it does provide a good basis for argumentation, as it is widely used and respected in Germany.

It may be criticised that the figures in the example are arbitrarily chosen, but it nevertheless shows the following very well. The business value, which was calculated using the objectified capitalised earnings method according to IDW S 1 and not the subjective capitalised earnings method (according to IDW S 1), coincides at best with the decision value by chance. Wrong decisions happen frequently. Discrepancies are possible both upwards and downwards.

## Simplified Capitalised Earnings Method according to § 202 BewG

The simplified capitalised earnings method according to § 202 BewG aims at a generalised valuation.

1. The annual profit of the last three years is corrected for additions and deductions (§ 202 Abs. 1 BewG).
2. The fictitious sustainable profit before tax is then fictitiously taxed at a fixed tax rate of 30% (§ 202 Abs. 3 BewG).
3. The discount factor is determined, from which the reciprocal value, the capitalisation factor, is calculated. This is currently fixed at 13.75 (§ 203 BewG).
4. The fictitious sustainable profit after taxes is multiplied by the capitalisation factor.

Notes: The capitalisation factor of 13.75 corresponds to an interest rate of 7.27%. “Somewhere” in this is a so-called base rate, a risk premium and the growth rate, since calculation interest rate = base rate – growth rate + risk premium applies. The fictitious sustainable profit after tax is not corrected in the payment series.

The simplified capitalised earnings method according to § 202 BewG considerably simplifies work in tax law through standardisation. Under no circumstances should investment decisions be based on the simplified capitalised earnings method according to § 202 BewG, as there are all kinds of theoretical shortcomings, some of which are described in the next subsection.

## Theory and Derivation from the Total Model

The capitalised earnings method can be derived from a total model. A total model can be thought of as a kind of full financing plan that takes into account interdependencies between investment and financing objects. The use of money is optimised through a mathematical procedure (operations research). A so-called dual solution (dual variables) reveals the critical interest rate (endogenous marginal interest rate) of a respective period.

This endogenous calculation interest rate is estimated in the capitalised earnings method by finding so-called marginal objects in the respective periods. In the above example, it was the investment interest rate of 5%, which was tax-corrected at 3.75%. In the case of borrowing, it would have been the tax-corrected lending rate.

The capitalised earnings method is a strong simplification of the functional business valuation. For the full theoretical derivation see Laux and Franke (1969), Hering (2017), Hering (2021), Matschke and Brösel (2013) and Bitz et al. (2018).

For a payment of the price as a rate or as an annuity, reference is made to Toll (2011) and for an inclusion of progressive tax rates and loss carry-forwards in valuation models, reference is made to Walochnik (2021) (functional business valuation).

For the origin of the capitalised earnings method, the development of business valuation and the objectivism controversy, please refer to the dissertation by Quill (2016), which provides an excellent overview.