present value

Present Value - Present value (also known as the current value) represents the current value of a future payment or series of payments, which is determined by discounting the payments at a specific interest rate. In real estate valuation, present value is the key calculation in the income approach: Future rental income and the residual value of the property are discounted to the valuation date to determine the market value.

Calculation and Formula

The present value of a single future payment is calculated using the following formula:

Present Value = Future Amount ÷ (1 + Interest Rate)^n

Here, n is the number of years until payment. For a recurring, equal payment (e.g., annual net rent), the multiplier (also known as the present value factor in annuity calculations) is used, which combines all future payments into a single factor:

Multiplier = [1 - (1 + i)^-n] ÷ i

Here, i is the property interest rate and n is the remaining useful life in years.

Present Value Calculation in the Income Approach

In the income approach according to ImmoWertV (§ 17 ff.), the present value of net income is calculated as follows:

1. Gross Income = Annual net rent (actually earned or market rate)
2. Operating costs = Management + Maintenance + Loss of rent + Depreciation (approx. 15-25% of gross income)
3. Net income from the building = Gross income minus operating costs minus return on land value
4. Capital value of the building = Net income × Multiplier (based on remaining useful life + property interest rate)
5. Capital value = Capital value of the building + Land value

Calculation example - Nuremberg apartment building:

Item	Amount
Annual net rent	€45,000
Management costs (20%)	- €9,000
Gross income according to BWK	€36,000
Return on land value (land value €200,000 × 4%)	- €8,000
Net income from building	€28,000
Remaining useful life 40 years, property interest rate 4%
Multiplier (from ImmoWertV table)	19.79
Capitalized value of building	€554,120
Land value	+ €200,000
Total income value	approx. €754,000

Significance of the property interest rate

The property interest rate is the interest rate at which the market value of real estate is capitalized in accordance with market practice. It is derived by appraisal committees from actual sales transactions and published in the real estate market report. It varies depending on the type of property, location, and market conditions:

Property type	Typical property interest rate (Nuremberg metropolitan region)
Condominiums	2.0-3.5%
Multi-family homes	3.0-4.5%
Mixed-use buildings	4.0-5.5%
Commercial real estate	5.0-7.0%

A low cap rate results in a higher multiplier and thus a higher present value-the property is more valuable. This reflects lower risk and higher market acceptance. A high cap rate indicates higher risk (e.g., vacancy risk, poor location) or lower growth expectations and reduces the present value accordingly.

Present Value vs. Purchase Price Factor (Multiplier)

In practice, present value is often simplified using the purchase price factor (also known as the annual rent multiplier):

Purchase Price Factor = Purchase Price ÷ Annual Net Rent

The reciprocal is the net rental yield. In Nuremberg, purchase price factors for multi-family homes in the 2020-2024 period ranged from 20 to 30 depending on location and condition (corresponding to yields of 3.3-5.0%). The present value represents the scientifically sound, discounting-based method-the purchase price factor is the practical, quick-reference version.

Practical Tip for Property Owners in Nuremberg and Franconia

We recommend that property owners in the Nuremberg metropolitan region understand the present value calculation when appraising their property, even if the calculation is performed by an appraiser. The Appraisal Committee of the City of Nuremberg regularly publishes current property interest rates in its annual real estate market report-available at the City Planning Office or online on the Nuremberg city website.

Anyone wishing to roughly estimate the income value of their property can multiply the annual net income by the appropriate multiplier. For a multi-family home with a remaining useful life of 40 years and a 4% property interest rate, this results in a multiplier of approximately 19.8-this is the number by which the net income must be multiplied to determine the income value of the building excluding land value.

Frequently Asked Questions

Why is future income worth less today?

Money that will be received in the future is worth less than money available today-because today’s money can be invested and earn interest (opportunity cost principle). This principle is known as the time value of money. Discounting reflects this effect: The further a payment lies in the future and the higher the interest rate, the lower its present value. At an interest rate of 4%, a payment of 10,000 euros in 20 years is worth only 4,564 euros today. This explains why properties with a longer remaining useful life and secure rental income achieve higher present values than short-lived or precariously leased properties.

How does the remaining useful life affect the present value?

A longer remaining useful life significantly increases the present value, as income is generated over a longer period. A building with a remaining useful life of 50 years has a significantly higher income value than one with only 20 years, assuming the same net income and the same property interest rate. With a 20-year remaining useful life and a 4% interest rate, the multiplier is only 13.59-whereas with a 50-year remaining useful life, it is 21.48. Renovation measures that extend the remaining useful life (e.g., roof renovation, pipe replacement) therefore directly increase the market value. These relationships are also covered in the regular Appraisal Committee report for Nuremberg.

Can I calculate the present value of my property myself?

A rough estimate is possible. Determine the annual net income (net base rent minus management costs-approx. 18-22% of the annual net rent), multiply it by the multiplier (tables can be found in the ImmoWertV appendix or in reference books), and add the discounted land value. However, for a reliable market value assessment-such as for a sale, a mortgage, an inheritance proceeding, or a divorce settlement-we recommend an appraisal by a real estate valuation expert recognized under Section 194 of the German Building Code (BauGB) or publicly appointed and sworn by the Chamber of Commerce and Industry (IHK).

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