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The capitalised earnings method according to §§ 27-34 ImmoWertV is market-oriented and divides the value of a property into a building value and a land value. An annual present value is used for the building value and a perpetual annuity is implicitly used for the land value. The calculation interest rate is market-oriented and is called the object-specific property interest rate.
To calculate the business value using the capitalised earnings method, click here.
According to § 27 ImmoWertV, there are three variants for the capitalised earnings method for real estate valuation: the general, the simplified and the periodic capitalised earnings method. The capitalised earnings method according to §§ 27-34 ImmoWertV is market-oriented and the calculation interest rate is called (property-specific) property interest rate.
The following presentation refers to the data of the initial scenario of the capitalised earnings method for the business valuation and is of a purely explanatory nature with a focus on the mathematical calculation. The property interest rate corresponds to the calculation interest rate. The three variants are presented first and then the calculation of the property interest rate is discussed. A conclusion is drawn at the end.
Firstly, an annual net income (annual gross income less operating costs) is calculated (ImmoWertV § 31). In the example, this is an annual net income of 12000 MU.
The land value is essentially determined on a market-oriented basis (§§ 40 to 43 ImmoWertV). Perpetual use is implied for the land value. To differentiate between the building and the land value, you can imagine that both are rented separately. Let’s say that half of the annual net rent is attributable to the land 12000*0.5 = 6000 MU. This results in a land value of 6000/0.05 = 120000 MU (perpetual annuity) for the following explanations.
The land value interest amount represents the share of the annual net income that would theoretically be attributable to the ” rental” of the land if the building and land were rented separately. With a land value of 120000 MU and a property-specific property interest rate of 0.05, this is 12000*0.05 = 6000 MU.
The so-called preliminary capitalised earnings value of the buildings is calculated from the annual net amount less the land value interest amount, i.e. 120000 – 6000 = 6000 MU.
This amount is discounted over the remaining utilisation period of the building, resulting in an annuity present value. To do this, the annuity present value factor (PVF) is first calculated and multiplied by the above value. The formula for this is PVF = ((i+1)^n-1)/((1+i)^n*i), where i stands for the interest rate and n for the years. With a remaining utilisation period of 50 years and a property-specific property interest rate of 0.05, this results in a PVF of 18.26. The capitalised annual net income share of the buildings is 6000*18.26 = 109535.55 MU. In §34 ImmoWertV the formula is slightly rearranged.
For the capitalised earnings value, the capitalised annual net income share of the buildings of 109535.55 MU and the land value of 120000 MU are added together, resulting in a capitalised earnings value of 229535.55 MU.
Note: In the general capitalised earnings method in accordance with § 28 ImmoWertV, the annual net income is corrected by a land value interest amount and the preliminary capitalised earnings value of the buildings is discounted to a present annuity value using the property-specific property interest rate. The land value is added to the capitalised earnings value.
First, the annuity present value of the annual net amount is calculated. (No land value interest amount is deducted here.) In our example, the annuity present value of the annual net amount is 18.26*12000 = 219071.10 MU.
Added to this is the land’s residual value as a perpetual annuity at the end of the remaining utilisation period (6000/0.05)*(1+0.05)^(-50) = 10464.45 MU. The first part represents the perpetual annuity and the second part discounts the perpetual annuity to the current reference date.
Together this results in 229535.55 MU.
The capitalised earnings method according to § 29 ImmoWertV is therefore only a transformation of the general capitalised earnings method according to § 28 ImmoWertV.
Note: For the simplified capitalised earnings method in accordance with § 29 ImmoWertV, the annuity present value of the net annual amount is added to the residual value of the land at the end of the remaining utilisation period of the building.
Within the planning horizon, a maximum of 10 years in accordance with Section 30 (2) ImmoWertV, the periodic annual net amount is to be discounted. The initial values are provided to show the relationship. (No period-specific property interest rate is mentioned in § 30 ImmoWertV). For reasons of clarity, the period under consideration is set at two years.
Year 1: 12000 * (1+0.05)^-1 = 11428.57 MU
Year 2: 12000 * (1+0.05)^-1 * (1+0.05)^-1 =10884.35 MU
An annuity present value is to be recognised between the planning horizon and the remaining utilisation period of the building. This in turn must be discounted to the reference date. The period is 50-2 = 48 years.
Year 3 to remaining utilisation period: 12000 * ((0.05+1)^48-1)/((1+0.05)^48*0.05) * (1+0.05)^-1 * (1+0.05)^-1 = 196758.18 MU
After the residual utilisation period, the residual value of the land must be taken into account.
(6000/0.05) * (1+0.05)^(-50) = 10464.45 MU
Together this gives 229535.55 MU. Provided there are no periodic differences, the result corresponds to the above two values according to §§ 28 and 29 ImmoWertV.
Note: For the periodic capitalised earnings method in accordance with § 30 ImmoWertV, periodic discounting is applied in the planning horizon. An annuity present value is calculated between the planning horizon and the residual utilisation period, which is discounted to the reporting date. After the residual utilisation period, the residual value of the land is taken into account. All three partial values together result in the capitalised earnings value.
In accordance with section 33 ImmoWertV, the property-specific adjusted property interest rate is to be determined in accordance with section 21(2) ImmoWertV, taking into account section 9(1) sentence 1 ImmoWertV and, if necessary, adjusted in accordance with section 9(1) sentences 2 and 3 ImmoWertV.
For the calculation of the property interest rate (i), the formula(s) of the capitalised earnings method is used and this is converted to i. Market data is used for this purpose. n stands for the residual utilisation period. The formula for the property interest rate is shown below.
i = net income/(purchase price +- adjustment) – ((1+i)^n*i)/((i+1)^n-1)*(1+i)^-n * (purchase price – land value +- adjustment)/(purchase price +- adjustment)
If a standard market property has a value of 229535.55 MU, a land value of 120000 MU, a net income of 12000 MU, a remaining utilisation period of 50 years and a property-specific adjustment of 0, the following calculation results for our example.
i = 12000/( 229535.55 – 0) – ((1+i)^50*i)/((i+1)^50-1)*(1+i)^-50 * ( 229535.55 – 120000 – 0)/( 229535.55 – 0)
The determination of i is done iteratively. If 0.06 is used for i, the result is 0.05064 and if 0.06 is used for i, the result is 0.04915. If 0.05 is used for i, the result is 0.05.
The property interest rate implies all market expectations, such as the future interest rate level, price increases and increases in value. In our example, the interest rate level is constant (flat yield curve) and the prices and values are constant.
Let us return to the example of the original capitalised earnings method with taxes and growth. Suppose the market property has a value of 480000 MU, a land value of 240000 MU (half of the property value), a net income of 12000 MU (sic!), a residual utilisation period of 50 years and a property-specific adjustment of 0. (Net income is not adjusted for income taxes.)
i = 12000/(480000 – 0) – ((1+i)^50*i)/((i+1)^50-1)*(1+i)^-50 * (480000 – 240000 – 0)/(480000 – 0)
The property interest rate is approximately 0.0189 and implicitly includes all the factors from above.
In the capitalised earnings method in accordance with §§ 27-34 ImmoWertV, a standardised capitalised earnings value (property value) is determined in a market-oriented manner and may be justified in its intended legal scope.
It is rather unsuitable for investments, as the personal net marginal interest rate is not used. In the case of rental income, your personal tax rate is also not taken into account. If the differential tax rate were 30%, the net cash flow would be != annual net income and only 8400 MU. A large amount of information such as the yield curve, price increases, value increases and possible taxes are implied in the property interest rate. The property interest rate is therefore a “black box”.
For investments, it is better to use the original capitalised earnings method. The personal net marginal interest rate, taxes, growth and risk are taken into account. In contrast to the capitalised earnings method in accordance with §§ 27-34 ImmoWertV, the opportunities and risks are (more) visible in the original capitalised earnings method. The modelling is theoretically clean and preferable. The calculation is also not significantly more complicated. The functional business valuation is also excellently suited to modelling and allows much more detail.
Important! It is unlikely that the capitalised earnings value according to the capitalised earnings value method in accordance with §§ 27-34 ImmoWertV and that of the original capitalised earnings value method are congruent.
Explanations of the real estate value in the cases of letting vs. selling and renting vs. acquiring can be found on the linked page.
The explanations are abbreviated and focus on the maths. In legal terms, the presentation of the law (ImmoWertV) applies, which is very well written.
General information on the calculation of the property value using the comparative value method, the capitalised earnings method and the material value method can be found under the link (German).
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