Base rate curve

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The base interest rate curve is an interest rate curve that results from the risk-free returns that can be achieved on the valuation date and capital market investments with equivalent maturities compared to the cash flow of the company to be valued. It is a model yield curve that cannot be directly observed on the market. This curve is used in company valuation in accordance with the recommendations of the Institut der Wirtschaftsprüfer in Deutschland eV (IDW) .

The base rate in the company valuation

When evaluating an investment property, the cash flows are compared with the achievable return of the best alternative capital market investment. Capital market models such as the CAPM can be used to estimate the achievable return . This has established itself particularly in company valuation practice. In this model framework, the resulting discount rate is made up of a risk-free base rate and a risk premium. The base interest rate can in principle be determined on the basis of an interest rate structure curve relating to the reporting date. In practice, the approach developed by Nelson and Siegel and expanded by Svensson has established itself . This approach is recommended by the Institut der Wirtschaftsprüfer in Deutschland eV (IDW) .

Yield curves in valuation theory

When evaluating an investment property on the basis of one of the discounted cash flow methods or the income value methods , the valuation-relevant cash flows in the numerator are compared with the best alternative capital market investment. The expected payments from the alternative investment must be equivalent to the payments to be expected from the investment in terms of time structure (equivalence of maturity), availability (key date principle) and risk (principles of equivalence in the valuation).

Risk equivalence of the base rate

The base interest rate is the return that can be achieved on the valuation date on a risk-free capital market investment with a maturity equivalent to the cash flow of the company to be valued. The risk-free alternative investment must not have any significant default, forward or currency risks. Since there is no risk-free debtor in the narrow sense of the word, in practice the base interest rate is determined on the basis of “quasi-secure” returns on long-term coupon bonds from countries with good credit ratings. The default risk of countries with an AAA rating was mostly viewed as negligible and came very close to the ideal of (credit default) risk-free bonds. In the current environment of the sovereign debt crisis, however, this assumption has to be viewed more and more critically. B. on the basis of the CDS market.

Term equivalence of the base rate

The theory demands future payments with congruent times, i.e. H. maturity-specific, discount rates to be realized. In Germany, this procedure is basically confirmed by the IDW for the purposes of company valuation. In current valuation practice, however, the cash flow is often discounted with only a constant rate of return over the term. B. was derived from a Bundesbank bond with a term of 20 years. The cash flows to be discounted in the context of company valuations are i. d. Usually long-term or include an infinite period of time ( going concern premise , principle of going concern ); therefore, bonds with terms of 20 or 30 years are often viewed as a sufficient approximation to meet the required term equivalence for this long-term cash flow on average. However, this simplification largely neglects the current interest rate structure. In addition, this approach is quite arbitrary in practice, as the choice for 10-, 20- or 30-year bonds is often inadequately justified and is treated quite differently on a case-by-case basis. Nevertheless, it is also the dominant approach internationally.

Difference between yield structure vs. Yield curve

In addition to the risk and maturity equivalence, the difference between the yield and the interest rate structure must be taken into account. While all cash flows are discounted to present values at the same rate ( effective interest or yield to maturity ) when calculating the yield, each cash flow is discounted with the interest rate that is to be expected depending on the reinvestment date and period according to the current market conditions ( so-called spot rate , zero coupon yields , or zerobond rates ). Spot rates are the yields on zero coupon bonds with a term from the valuation point to the payment point. In the case of non-flat interest structures, the latter are the alternative returns to be compared with the time-specific (safe or security-equivalent) corporate surpluses. The relationship between the (spot) interest rates and the terms of zero coupon bonds without credit default risk is known as the interest rate structure. The use of the yield structure instead of the interest structure, on the other hand, neglects the reinvestment risk of coupon payments. The yields and interest rates on coupon bonds are therefore only identical if there is a horizontal interest rate structure. The use of yield curves is only acceptable with a flat interest rate structure. For this reason, zero coupon yields are more suitable for calculating the present value of cash flows that arise over a period of time, such as in the context of company valuations.

Methods for estimating the yield curves

A continuous yield curve would be directly observable on the bond market if a zero coupon bond with a low risk of default were quoted for each maturity. The interest rates for the respective terms can be read directly from the prices of zero-coupon bonds , since the price of a zero-coupon bond is identical to the value of the discount function of the corresponding interest rate. In other words, the discount function describes the present value of a unit that will be paid at a future point in time. This is why the discount factor is also known as the zero coupon bond price.

However, there are only a small number of such bonds, so that the majority of the bonds in circulation are coupon bonds. In addition, the observable yield structure curve shows gaps in the maturity range over 10 years. Even separately traded interest claims (so-called strips), which have the character of zero coupon bonds, are usually not seen as an alternative in practice due to the lack of liquidity of the prices, tax-induced clientele effects or the higher convexity at the long end. Alternatively, the interest rates could also be read directly from the prices of interest rate swaps, forward rate agreements and interest rate futures . This would avoid the possible estimation error of an interest rate model, but has the disadvantage that prices from very different instruments are aggregated and compared, which creates problems with regard to the homogeneity of the data. In addition, these instruments carry a not insignificant counterparty risk (Engl. Counterparty risk ). Therefore, the indirect derivation of the yield curve from the yields of coupon bonds is theoretically the better and more consistent approach.

In the case of a multi-year coupon bond, it is not possible to read the interest rate directly because payments are made at different times. In order to be able to determine zero coupon interest rates, these individual payments do not have to be discounted with constant, but rather with term-specific interest rates. The equation that determines the price of the coupon bond contains several unknowns, which is why the interest rates have to be determined iteratively . For this purpose, theoretical yields are calculated from a given yield curve and compared with the observed yields. For the estimation of continuous yield curves from the yields of coupon paper, as in the case of the estimation of continuous yield curves, a model assumption about the functional relationship between interest rates and maturities must be made. From the large number of existing model approaches, the approach developed by Nelson and Siegel and expanded by Svensson has established itself as a good compromise solution. In the Nelson / Siegel / Svensson model, the interest rate is defined as the sum of a constant and various exponential terms and as a function of a total of six parameters. The model estimates a continuous, steady yield curve. Therefore, the constant interest calculated using the Svensson method must be converted into discrete interest in order to be used as discrete discount factors in the valuation as usual.

The Bundesbank, the European Central Bank and the Federal Reserve (FED) estimate the parameters for the Svensson equation on a daily basis. The working group for company valuation (AKU) of the IDW recommends to use the data of the Bundesbank for reasons of comprehensibility and objectivity for the model parameters. If you use the data from the Bundesbank, however, it should be noted that the parameters published by the Bundesbank lead directly to discrete interest rates, as the Bundesbank calculates the discounting function differently from the Svensson approach.

Updates of the yield curve

Yield curves can in most cases be estimated over at least 30 years due to the observable returns. To discount payments that are further away, an assumption about the further course of the yield curve must be made. In practice as in theory, the parameters of the Bundesbank and the Svensson formula are used to extrapolate the interest rates. The long-term extrapolated interest rates converge to the value of the constant β 0 , since the contribution of the exponential terms tends to zero with increasing maturity. This limit value therefore represents a long-term interest rate. It should be noted, however, that the Svensson model has limits with regard to the predictability of the yield structure. Against the background of its application in company valuation, however, the simplifying assumption that the Svensson model can also be used to extrapolate the interest rate structure for a term of more than 30 years is acceptable in most cases.

Runtime-specific vs. Term constants base rates

For practical company valuation, the IDW suggests using a (standardized) uniform basic interest rate with a constant term instead of interest rates specific to the term for the case of moderately growing financial surpluses. The aim is to facilitate comparability and at the same time reduce the complexity of the modeling, since the practitioner can thus fall back on the final calculated base interest rates on the key date (see e.g.) and costly period-specific discounting does not have to be carried out. The uniform base rate results from the requirement for present value equivalence. It corresponds to the interest rate that, for a given payment structure, delivers the same cash value as discounting with interest rates specific to the term. From August 2008 the IDW will calculate this so-called present value equivalent uniform base rate based on the data estimated by the Deutsche Bundesbank for 30 years. In addition, the IDW assumes constantly growing payments and recommends using a typical growth rate of 1% in most cases. From the 31st year the yield curve is constantly updated on the basis of the 30th year. The formula for the typified present value equivalent basic rate is:

This constant base interest rate equivalent to the present value has established itself as a quasi-standard in German valuation practice, but is discussed controversially in theory and practice.

Key date versus averaging, standardized rounding according to IDW

The Svensson estimation procedure enables the theoretically precise determination of a zero bond interest rate for each term. The IDW recommends, however, to use the daily yield curves of the last three months to determine average interest rates for each term and also to round the typical present value equivalent base interest rate to 25 basis points. Two goals are pursued with averaging. Firstly, this is intended to minimize estimation errors. Second, short-term market or price fluctuations should be smoothed out. The main reason, however, is presumably to make the base rate less volatile and thus, in practice, to reduce the comparability of capital costs over time and, above all, to reduce the cost of updating for the practitioner.

The 3-month period is based on the case law for determining an average stock exchange price for the assessment of severance payments or other legally motivated valuation reasons. Rounding off to 25 basis points is additional smoothing. The averaging fundamentally contradicts the reference date principle, but just like the typified rounding, it is in most cases a justifiable simplification for the valuation practice.

Company valuations for inheritance and gift tax purposes

In the case of company valuations for the purposes of inheritance and gift taxes using the simplified income value method, the base interest rate is specified once a year on the basis of the interest structure (federal securities with annual coupon payments and a remaining term of 15 years) on the first trading day of the year by the Federal Ministry of Finance (BMF). The base rate is to be used for all valuation cases in the current year and has been 0.99 percent since January 2, 2015. The procedure is regulated in Section 203 (2) BewG.

See also

bibliography

  • Working group for company valuation: key data for determining the capitalization rate for company valuation - base rate. In: IDW-Fachnachrichten. No. 8, 2005, ISSN  0937-4019 , pp. 555-556.
  • Wolfgang Ballwieser : On the risk-free interest rate for company valuation. In: Frank Richter, Andreas Schüler, Bernhard Schwetzler (Hrsg.): Capital provider claims , market value orientation and company value. Festschrift for Jochen Drukarczyk on his 65th birthday. Vahlen, Munich 2003, ISBN 3-8006-3023-0 .
  • Wolfgang Ballwieser: company valuation. Process, methods and problems. Schäffer-Poeschel, Stuttgart 2004, ISBN 3-7910-2156-7 .
  • Deutsche Bundesbank: Estimation of interest rate structure curves. In: Deutsche Bundesbank. Monthly report. October 1997, ISSN  0012-0006 , pp. 61-66, online, (PDF; 204 kB) .
  • Jochen Drukarczyk: Company valuation. 4th, revised and expanded edition. Vahlen, Munich 2003, ISBN 3-8006-2880-5 .
  • IDW, Institute of Auditors in Germany: IDW standard. Principles for conducting company valuations. (IDW S 1 as amended 2008). IDW-Verlag, Düsseldorf 2008, ISBN 978-3-8021-1364-2 .
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  • Leonhard Knoll: Base interest rate and interest structure, comments on a methodical realignment of the IDW. In: Economics Studies. WiSt. 35th year, issue 9, ISSN  0340-1650 , pp. 525-528, here 527.
  • Charles R. Nelson , Andrew F. Siegel: Parsimonious Modeling of Yield Curves. In: The Journal of Business. Vol. 60, No. 4, 1987, ISSN  0021-9398 , pp. 473-489.
  • Robert Obermaier: Company valuation, base rate and interest structure. Capital market-oriented determination of the risk-free base interest rate with a non-flat interest structure (= Regensburg discussion contributions on economics. No. 408, ZDB -ID 1124610-8 ). Status: November 28, 2005. University of Regensburg, Regensburg 2005, online .
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  • Raimo Reese, Jörg Wiese: The capital market-oriented determination of the base rate for company valuation - operationalization, estimation procedures and application problems (= Munich business contributions. 16, 2006). Ludwig-Maximilians-Universität München, Munich 2006, http://cosmic.rrz.uni-hamburg.de/webcat/hwwa/edok07/f10970g/WP2006-16.pdf (link not available).
  • Eli M. Remolona, ​​Philip D. Wooldridge: The Euro Interest Rate Swap Market. In: BIS quarterly report. March 2003, ISSN  1683-0172 , pp. 53-64, online (PDF; 81 kB) .
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  • Suresh M. Sundaresan: Fixed Income Markets and their Derivatives. 2nd edition. South-Western College Publishing, Cincinnati OH 2002, ISBN 0-538-84005-6 .
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  • Wolfgang Wagner, Martin Jonas, Wolfgang Ballwieser, Andreas Tschöpel: Company Valuation in Practice - Recommendations and Notes on the Application of IDW S 1. In: Die Wirtschaftsprüfung. WPg. Vol. 59, 2006, ISSN  0340-9031 , pp. 1005-1028, here p. 1016.

Individual evidence

  1. ↑ What is sought is the amount that an investor would have to invest in an alternative investment on the valuation date in order to achieve the same amount as from the valuation object at a certain future point in time. (Compare: Obermaier: Company Valuation, Base Rate and Interest Structure. 2005, p. 4). In practice one can still find valuation cases where historical (average) returns are used. This is to be rejected because of the non-compliance with the reference date principle. In the IDW S1 new version, the HFA clearly expressed its opinion that the orientation towards the current yield curve is preferred and that past interest rate developments are no longer relevant when determining the base interest rate.
  2. ↑ In this sense Wolfgang Ballwieser : company valuation. 2004, p. 82.
  3. ↑ See Drukarczyk: Company Valuation . 2003, p. 352.
  4. ↑ See Wolfgang Ballwieser : Company Valuation . 2004, p. 83.
  5. ^ Deutsche Bundesbank: Estimation of interest rate structure curves. In: Deutsche Bundesbank. Monthly report. October 1997, p. 63.
  6. ↑ See, inter alia, Drukarczyk: company valuation. 2003, p. 356; Ballwieser: On the risk-free interest rate for company valuation. In: Richter, Schüler, Schwetzler (Ed.): Claims to investors, market value orientation and company value. 2003, p. 24 and Wolfgang Dieter Budde: Wirtschaftsprüfer-Handbuch. Handbook for accounting, auditing and advice. Volume 2. 13th edition. IDW-Verlag, Düsseldorf 2008, ISBN 978-3-8021-1304-8 , p. 104, item 288.
  7. ↑ For a discussion of the various arguments cf. Obermaier: company valuation, base rate and interest structure. 2005, pp. 16-20.
  8. ↑ Reese, Wiese: The capital market-oriented determination of the base rate for company valuation. 2006, p. 3.
  9. ↑ Reese, Wiese: The capital market-oriented determination of the base rate for company valuation. 2006, p. 5.
  10. ↑ See Schich: Estimate of the German yield curve. 1997, p. 2.
  11. ^ Deutsche Bundesbank: Estimation of interest rate structure curves. In: Deutsche Bundesbank. Monthly report. October 1997, p. 63.
  12. ↑ See Deutsche Bundesbank: Estimation of interest rate structure curves. In: Deutsche Bundesbank. Monthly report. October 1997, p. 63.
  13. ↑ See Schich: Estimate of the German yield curve. 1997, p. 8.
  14. ^ Deutsche Bundesbank: Estimation of interest rate structure curves. In: Deutsche Bundesbank. Monthly report. October 1997, p. 63.
  15. ↑ See Schich: Estimate of the German yield curve. 1997, p. 2.
  16. ↑ Cf. Remolona, ​​Wooldridge: The market for euro interest rate swaps. In: BIS quarterly report. 2003, p. 60 f. and Sundaresan: Fixed Income Markets and their Derivatives. 2002, pp. 563-567.
  17. ↑ See Schich: Estimate of the German yield curve. 1997, p. 2; Reese, Wiese: The capital market-oriented determination of the base rate for company valuation. 2006, p. 7 and Obermaier: Company valuation, base rate and interest structure. 2005, p. 14.
  18. ↑ See Deutsche Bundesbank: Estimation of interest rate structure curves. In: Deutsche Bundesbank. Monthly report. October 1997, p. 63 and Schich: Estimation of the German yield curve. 1997, p. 17 f. and p. 25.
  19. ↑ , which see for further explanation Basiszinskurve.de . Retrieved November 28, 2011.
  20. ↑ Cf. Nelson, Siegel: Parsimonious Modeling of Yield Curves. In: The Journal of Business. Vol. 60, No. 4, 1987, pp. 473-489; Svensson: Estimating and Interpreting Forward Interest Rates. 1994; and Reese, Wiese: The capital market-oriented determination of the base rate for company valuation. 2006, p. 10.
  21. ↑ See Zinsen, Renditen ( Memento from December 9, 2011 in the Internet Archive ), The ECB's Directorate General Statistics releases euro area yield curves every TARGET working day at 12 noon Central European Summer Time (or Central European Time) ( Memento from 16. December 2011 in the Internet Archive ), and http://www.federalreserve.gov/pubs/feds/2006/200628/200628pap.pdf . Retrieved December 3, 2011.
  22. ↑ See working group on company valuation: key data for determining the capitalization rate for company valuation - base interest rate. In: IDW-Fachnachrichten. No. 8, 2005, pp. 555-556.
  23. ↑ Cf. Reese, Wiese: The capital market-oriented determination of the base rate for company valuation. 2006, p. 11.
  24. ↑ Cf. Reese, Wiese: The capital market-oriented determination of the base rate for company valuation. 2006, p. 11.
  25. ↑ See Deutsche Bundesbank: Estimation of interest rate structure curves. In: Deutsche Bundesbank. Monthly report. October 1997, p. 65.
  26. ↑ Cf. Nelson, Siegel: Parsimonious Modeling of Yield Curves. In: The Journal of Business. Vol. 60, No. 4, 1987, p. 487.
  27. ↑ Cf. one of the theoretically very good sources for the base rate according to the IDW Svensson method is u. A. to be found on Basiszinskurve.de . Retrieved November 28, 2011.
  28. ↑ Cf. Reese, Wiese: The capital market-oriented determination of the base rate for company valuation. 2006, p. 19.
  29. ↑ See working group on company valuation: key data for determining the capitalization rate for company valuation - base interest rate. In: IDW-Fachnachrichten. No. 8, 2005, p. 556.
  30. ^ Based on Reese, Wiese: The capital market-oriented determination of the base rate for company valuation. 2006, p. 19.
  31. ↑ See, inter alia, Reese, Wiese: The capital market-oriented determination of the base rate for company valuation. 2006, pp. 21-22; Wagner, Jonas, Ballwieser, Tschöpel: Company Valuation in Practice. In: The auditing. WPg. Vol. 59, 2006, p. 1016; and Obermaier: company valuation, base rate and interest structure. 2005, pp. 25-32.
  32. ↑ See working group on company valuation: key data for determining the capitalization rate for company valuation - base interest rate. In: IDW-Fachnachrichten. No. 8, 2005, p. 556.
  33. ↑ See Wagner, Jonas, Ballwieser, Tschöpel: Company Valuation in Practice. In: The auditing. WPg. Vol. 59, 2006, pp. 647-653, p. 651; and: Working group for company valuation: key data for determining the capitalization rate for company valuation - base rate. In: IDW-Fachnachrichten. No. 8, 2005, p. 556.
  34. ↑ See Wagner, Jonas, Ballwieser, Tschöpel: Company Valuation in Practice. In: The auditing. WPg. Vol. 59, 2006, pp. 647-653, p. 652.
  35. ↑ See Obermaier: Company Valuation, Base Rate and Interest Structure. 2005, p. 475; Knoll: Base interest rate and interest rate structure, comments on a methodical realignment of the IDW. In: Economics Studies. WiSt. 35th volume, issue 9, 2006, p. 527.
  36. ↑ BMF letter of January 2, 2015 - IV D 4 - S 3102/07/10001