Base Rate under IDW S1: Calculation and Rounding

8
Min Read
Under IDW S1, the risk-free base rate is generally rounded to 0.10 percentage points when below 1.0% and to 0.25 percentage points when above 1.0%. The rate is derived from a risk-free yield curve and must also be applied consistently with the maturity structure of the forecast cash flows.
#Base Rate
#IDW Standard
#Risk-free Rate
#Yield Curve
Peter Schmitz
on
15.1.20
The founder and Managing Director of smartZebra GmbH. Formerly head of company valuation at Deutsche Bahn (DB) AG, Peter also advised at ACXIT Capital Partners.

What is the risk-free base rate?

The risk-free base rate is the long-term return that can be achieved from a virtually default-free capital market investment. In German business valuation practice, it is a central component of the capitalization rate and therefore directly affects the value of a company.

IDW S1 requires the valuation to be based on an appropriate risk-free rate. In practice, German valuers generally use capital-market data published by the Deutsche Bundesbank. The Bundesbank’s term-structure data represents estimated zero-coupon rates derived from observed yields on outstanding coupon bonds.  

How is the IDW S1 base rate determined?

The determination can be understood as a sequence from the market yield curve to the rate ultimately used in the valuation.

1. Start with the risk-free yield curve

The first step is to obtain the relevant risk-free term structure. The Deutsche Bundesbank publishes a daily term structure for listed German Federal securities using the Svensson method, including zero-coupon rates for different residual maturities (Deutsche Bundesbank, 1997).

The advantage of using the term structure rather than a single observed bond yield is that the valuation can reflect the relationship between interest rates and different maturities.

2. Match the rate to the forecast cash flows

The principle of maturity congruence is important: a cash flow should be discounted using a risk-free rate corresponding to its maturity.

For example, a cash flow expected in five years should be discounted using the appropriate five-year risk-free rate rather than simply applying the current ten-year government bond yield.

For a valuation involving many future cash flows, the complete yield curve can therefore be used directly. In practical IDW S1 valuations, however, it is also possible to derive a single present-value-equivalent uniform base rate that produces approximately the same present value as the maturity-specific curve.

This is particularly relevant for DCF valuations, where cash flows extend over many years.

3. Derive the present-value-equivalent uniform base rate

A single uniform rate is selected so that discounting the forecast cash flows at that rate produces the same present value as discounting them using the individual maturity-specific rates.

Conceptually:

Present value using the yield curve = Present value using the uniform base rate

The resulting rate therefore represents a simplified equivalent of the underlying term structure rather than simply being an arithmetic average of individual interest rates.

This distinction matters. A simple average would ignore the different timing and economic significance of the individual cash flows. A present-value-equivalent rate instead weights the term structure according to the cash-flow profile of the valuation.

4. Check the long-term growth assumption

The IDW’s clarification on the present-value-equivalent uniform base rate is particularly relevant when the valuation extends beyond 30 years.

The original smartZebra analysis notes that, for the standard present-value-factor calculation, the interest rate in year 30 needs to exceed the assumed long-term growth rate. If this condition is not satisfied, the valuation period needs to be extended sufficiently to derive the equivalent uniform base rate appropriately.  

This issue becomes especially important in a low-interest-rate environment, where a long-term growth rate can approach or even exceed the relevant risk-free rate.

5. Apply the IDW rounding convention

Once the relevant base rate has been determined, the IDW rounding convention is applied.

Rounding the risk-free base rate under IDW S1 (smartZebra)
Base rate Rounding
Below 1.0% 0.10 percentage-point increments
Above 1.0% 0.25 percentage-point increments

For example, a calculated rate of 0.83% would be rounded to 0.80%, while a calculated rate of 2.13% would be rounded to 2.25%.

The underlying smartZebra article documents this distinction with reference to the IDW’s 2016 guidance: rates below 1.0% are rounded to 0.10 percentage points, while rates above 1.0% follow the FAUB recommendation of 0.25 percentage-point increments.  

Why is rounding required?

Rounding may appear minor, but it can have a material effect on a business valuation.

The base rate is a component of the capitalization or discount rate. A change of only a few basis points can therefore affect the present value of a company’s future cash flows, particularly where the valuation involves long forecast periods.

The rounding convention also provides a degree of consistency between valuations. Rather than allowing small movements in market data to produce an apparently excessive level of precision in the final capitalization rate, the IDW approach creates a standardized convention for practical valuation work.

The present-value-equivalent base rate in practice

The present-value-equivalent approach is particularly useful when the valuation model contains a large number of future cash flows but the final capitalization rate is intended to be expressed as a single percentage.

Consider a simplified example:

  • Cash flows are forecast over 30 years.
  • Each year has a different risk-free rate according to the Bundesbank yield curve.
  • The resulting present value is calculated using these maturity-specific rates.
  • A single rate is then solved for that produces the same present value when applied consistently to the entire cash-flow stream.
  • That rate becomes the present-value-equivalent uniform base rate.
  • The applicable IDW rounding convention is then applied.

This approach preserves the economic information contained in the yield curve while producing a single rate that can be used conveniently in the valuation model.

The method is therefore different from simply selecting the ten-year Bund yield or calculating an unweighted average of observed interest rates.

Why the Bundesbank data matters

The Deutsche Bundesbank provides the underlying German term-structure data used extensively in German valuation practice. Its published data describe the relationship between interest rates and maturities of default-free zero-coupon bonds and are estimated from observed yields on coupon bonds (Deutsche Bundesbank, 1997).

The Bundesbank also publishes the underlying Svensson-based term structure for listed Federal securities, with daily observations extending across a broad range of maturities (Deutsche Bundesbank, 2026).

This provides a transparent market-data foundation for deriving the risk-free base rate rather than relying on an isolated bond yield.

For a broader explanation of the underlying risk-free rate, see smartZebra’s Risk-Free Interest Rate in Business Valuation. For the mathematical construction of the yield curve itself, the related Svensson Method article can be used as part of the same Basiszins content cluster.

Low-interest-rate environments require particular care

The present-value-equivalent approach becomes more technically important when interest rates are low.

If the long-term growth rate approaches the interest rate used for discounting, the terminal value can become increasingly sensitive to small changes in assumptions. The IDW clarification therefore addresses how the valuation period and present-value factor should be handled when the year-30 rate does not sufficiently exceed the assumed long-term growth rate.  

The practical implication is straightforward: the equivalent base rate should not be calculated mechanically without checking whether the underlying assumptions satisfy the relevant conditions.

Base rate and the capitalization rate

The risk-free base rate is only one component of the capitalization rate.

A simplified cost-of-equity structure can be expressed as:

Cost of equity = Risk-free base rate + Risk premium

The risk premium captures the additional return required for bearing systematic and other relevant investment risks. Depending on the valuation framework, this can include the market risk premium, beta factor and, for international valuations, an appropriate country risk premium.

The resulting capitalization rate is then applied to the forecast cash flows to determine their present value.

This is why consistency between the base rate, beta, market risk premium, growth assumptions and the valuation date is essential.

Wrap it up!

The IDW S1 base rate is not simply an observed government-bond yield. In German business valuation practice, it is derived from a risk-free term structure, typically using Bundesbank capital-market data, and may be converted into a present-value-equivalent uniform rate when a single capitalization rate is required.

The practical process is:

  1. Obtain the relevant Bundesbank risk-free yield curve.
  2. Match rates to the maturities of the forecast cash flows.
  3. Derive a present-value-equivalent uniform base rate where appropriate.
  4. Check the long-term growth and valuation-period assumptions, particularly for periods beyond 30 years.
  5. Apply the applicable IDW rounding convention: 0.10 percentage points below 1.0% and 0.25 percentage points above 1.0%.

For valuation teams, the key is therefore not merely obtaining a current base rate, but documenting how the rate was derived, how maturity congruence was addressed, and how the IDW rounding requirements were applied.

Update at 13 August 2026

Questions & Answers

What is the riskfree base rate and why is it important?

The riskfree base rate corresponds to the long-term achievable yield on public bonds without default risk. It forms the basis for calculating the weighted average cost of capital (WACC) and is therefore decisive for the business valuation.

How is the riskfree base rate rounded in accordance with IDW S1?

Interest rates below 1.0% are rounded to 0.10 percentage points, while interest rates above 1.0% are rounded to 0.25 percentage points.

What sources does the IDW recommend for determining the riskfree base rate?

The IDW recommends using the capital market data published by the Bundesbank.

What is the IDW S1 standard?

The IDW S1 Standard is a guideline issued by the Institute of Public Auditors in Germany (Institut der Wirtschaftsprüfer) that codifies the principles for conducting business valuations and has become established as a standard in practice.

How is the riskfree base rate integrated into the accounting?

The riskfree base rate and the company values determined are integrated into the accounting under commercial law in accordance with the requirements of IDW RS HFA 10.

How can smartZebra help in determining and applying the riskfree base rate?

smartZebra provides tools and data that simplify the complex process of determining and applying the riskfree base rate, enabling accurate analysis and ensuring compliance requirements are met.

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