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published on 20 February 2024 | reading time approx. 8 minutes
The cost of debt is generally equated with the interest rate on debt capital. However, due to the company-specific default risk, the cost of debt, relevant for company valuation, is always lower than the corresponding interest rate. The latter consist of two components that can be determined using different approaches based on rating-specific yield curves. From default risk and credit spreads to the cost of capital – a guide from the valuation practice.
The cost of debt is commonly and broadly equated with the interest rate on debt instruments plus the fees charged by banks. However, in the case of a company valuation, which rests on the foundations of capital market theory, contractual interest rates are only the first point of reference for determining the actual cost of debt.According to capital market theory, the diversification of investments implies that the assumption of unsystematic or company-specific risks and therefore diversifiable risks is not remunerated. Only systematic risks, i.e., market risks, are remunerated via the cost of equity and cost of debt. In addition, the cost of capital is determined as an expected value. Conceptually, expected values are probability weighted averages over a range of scenarios.With the exception of government bonds – particularly AAA-rated government bonds – debt instruments are subject to default risk. As a result of the company-specific default risk, future expected interest payments can range between the contractually agreed interest rate – in case of no default – and zero – in case of default of the debt instrument. As a result, the expected cost of debt is always lower than the contractually agreed interest rate. The difference is determined by the probability of default (PD) and the recovery rate (RR). The lower the PD and the higher the RR, the smaller the difference between the contractual interest rate and the corresponding cost of debt. For example, an interest rate of 10 per cent, a probability of default of 5 per cent and a recovery rate of 50 per cent result in a corresponding cost of debt of 7per cent.
When a loan is signed or a bond is issued, an interest rate is defined. The interest rate reflects the financing conditions at the point in time of the loan agreement or the bond issue. The nominal amount of the debt – i.e., the book value – remains unchanged over time, as do the interest payments, which are based on the book value and the contractually agreed interest rate.However, interest rates change over time. For example, if market interest rates rise and are higher than the contractual interest rate, the present value of future interest payments will fall and the current market value will be lower than the historical book value of the debt. The lender receives the contractually agreed interest rate, which is lower than what he could currently earn, and therefore the debt is worth less even though the book value is unchanged. Conversely, if market interest rates fall, the market value of the debt increases because the lender receives the contractually agreed interest rate, which is higher than he could currently earn. In conclusion, the market value of the debt will always differ from its original book value. The following examples are based on the following assumptions: book value of EUR 1,000; term of three years; bullet repayment; contractual interest rate of 10 per cent p.a. i.e., annual interest payment of EUR 100. In the first case, the market interest rate rises to 12 per cent p.a. In the second case, the market interest rate falls to 8 per cent p.a.Only the market values of equity and debt are considered in company valuation. As a result of interest rate fluctuations and other company-specific changes, such as changes in creditworthiness, the cost of equity and cost of debt must be recalculated for each valuation date in order to calculate representative and reliable market values of equity and debt. It should be noted that current market interest rates, similar to contractually agreed interest rates, must be adjusted for default risk when determining the expected cost of debt in order to account for both the non-default case and default case of debt.
Similar to contractual interest rates, the cost the debt is influenced by a variety of parameters such as currency, maturity, ranking, collateral, etc. However, creditworthiness plays the most important role because it is related to the risk of default. Creditworthiness is measured by credit ratings or credit scores. Credit ratings are determined by banks or rating agencies using a variety of quantitative and qualitative factors and are published in the case of sovereigns, multinational corporations or companies with traded securities. Credit scores can be estimated for small and medium-sized companies using statistical and econometric methods based on their financial data, e.g. using scoring models from financial information providers or scientific studies.The rating sclaes of Fitch, Moody’s or Standard & Poor’s are well-established in the financial world. There are two categories of ratings: so-called investment grades with a low risk of default (from AAA to BBB) and so-called non-investment grades with a higher risk of default (below BB). The latter also includes debt with a significant risk of default (below CCC). In general, the lower the rating, the higher the risk of default and the higher the interest rate charged by the lender.If the default risk is material, the expected cost of debt will deviate more from the agreed interest rate, and it is therefore necessary to derive the cost of debt separately based on the probability of default and the recovery rate, as described above.
When determining the creditworthiness of companies within a multinational group, the question arises as to whether the standalone rating or the group rating should be used. It is clear that the standalone rating is the most accurate measure of creditworthiness of a borrowing company. In this case, the company is treated as an independent and separate entity and its creditworthiness is assessed on the basis of its own financial performance. This approach ignores the influence of the parent company and other group members. Nevertheless, in most cases, even for smaller but still multinational companies, the group rating is preferred. The main argument is the implicit support of the parent company, which intervenes directly if the subsidiary gets into financial difficulties or provides guarantees to third parties. In the event of insolvency, the parent company will use all available resources within the group to prevent its troubled subsidiary from defaulting on its debts, which would then affect the creditworthiness of the entire group. As all financial resources are used to prevent a subsidiary's insolvency, the group's rating must also be taken into account.
Any debt financing involves systematic and non-systematic risks, including default risk, corresponding to its creditworthiness. These risks are priced via a risk premium above the so-called risk-free rate from capital market theory. In practice, market interest rates of government bonds, especially those with AAA ratings, are considered risk-free. The risk-free rate represents the lower limit of any interest rate for a given term. The difference between the interest rate and the risk-free rate is usually referred to as credit spread. Therefore, any interest rate consists of two components.All systematic and unsystematic risks as well as other unsystematic components such as taxes, transaction costs or profit margins of banks are priced into the credit spread. However, these non-systematic components are of secondary importance in valuation practice. The main driver of the credit spread is the unsystematic default risk. In principle, the lower the rating, the higher the credit spread and the higher the default risk. Due to the necessary adjustment for default risk when determining the cost of debt based on an interest rate, the cost of debt can also be split into two components.The expected cost of equity and expected cost of debt are relevant in the context of company valuation. The credit spread excluding unsystematic risks is therefore relevant when determining the cost of capital.
If a credit rating is available or a credit score has been calculated, the first step is to determine the appropriate interest rate. This requires taking into account the other parameters of the debt instrument. There are several approaches for determining the interest rate.One approach is the use of yield curves. Based on a set of government or corporate bonds, yield curves show the dependence of interest rates (Y-axis) on maturities (X-axis) at a given date. Yield curves can have different shapes (as maturities increase): normal (rising interest rates), flat (constant interest rates), inverted (falling interest rates), or irregular shapes such as "humped" (first rising, then falling interest rates).
Source: Deutsche Bundesbank, Analysis Rödl & PartnerYield curves based on a country's government bonds – especially those with AAA ratings – are regularly used as a reference for the risk-free rate in that country or currency. For example, the yield curve for German government bonds represents the risk-free rate in EUR, and the yield curve for US government bonds represents the risk-free rate in USD. Yield curves are aggregated by financial information providers such as Bloomberg or Capital IQ also based on corporate bonds for various combinations of parameters such as currency, industry and rating, and serve as a reference for standard market interest rates. By definition, these are higher than the corresponding maturity-specific risk-free rates. The differences represent credit spreads, including unsystematic risks, on top of the risk-free rate. Consequently, in this approach, the target market interest rate for a selected date is taken from the applicable yield curve and for the corresponding maturity. However, the target market rate can also be determined additively. If a representative credit spread from an alternative source is available, and the consistency of parameters such as currency or maturity is taken into account, it can be added to the applicable risk-free rate.A second more sophisticated approach is to create a peer group of corporate bonds. In a first step, the Bloomberg search can take into account various parameters to ensure comparability with the parameters of the debt instrument being valued: rating, industry group, rank, collateralization, repayment type, coupon type, etc. By analyzing the issuers' business models and risk profiles, the peer group can be optimally defined. In a second step, the yields can be adjusted for the currency and the maturity using yield curves to determine comparable interest rates at arm’s length for the debt instrument. This approach ensures that the market interest rates determined for the debt instrument are much more representative, as bonds from narrower industry groups or even tailor-made peer groups can be used instead of bonds selected by Bloomberg or Capital IQ for the yield curves of broad industry sectors.Another approach to determining a market interest rate for a new debt instrument is when another near-term debt financing of the same entity can be considered representative. While some parameters of the two debt instruments may be directly comparable, adjustments must be made to the interest rate of the comparable financing instrument to adequately reflect differences in the remaining parameters. Under this approach, the interest rate type, currency, maturity, ranking, collateral, etc. can be adjusted using yield curves. For example, based on a floating rate for a 7-year senior loan, the corresponding fixed rate for a 25-year subordinated loan can be calculated.Regardless of the approach used, observable market rates for a selected date are used to determine the target interest rate. However, these market rates are not the same as the cost of debt. Particularly in the case of lower ratings due to the material default risk, the cost of debt is derived in a final step based on the probability of default and the recovery rate.
Interest rates and the cost of debt should not be equated or confused. Depending on the context, either interest rates or the cost of debt are used.When a loan agreement is signed with a bank or investor, an interest rate is agreed based on prevailing market rates. Of course, the corresponding expected cost of debt is also taken into account in the financing decision, but ultimately an interest rate is agreed.In the case of intra-group financing, interest rates are also applied. However, when mezzanine instruments are granted, the internal profitability analysis and the required arm's length analysis are performed using the cost of debt and cost of equity and the equity orientation of the instrument.As a result of the introduction of IFRS 16 on lease accounting, companies are required to determine incremental borrowing rates (IBR). These are also interest rates and not the cost of debt.A company's valuation is based solely on the expected cost of debt. The cost of debt, together with the cost of equity, goes directly into the calculation of the weighted average cost of capital (WACC).However, the cost of debt also affects the cost of equity as a debt beta is considered in the unlevered beta factor. Debt beta is a risk measure of debt and is calculated as the ratio of the credit spread to the market risk premium. The credit spread to be applied is the difference between the expected cost of debt and the risk-free rate. For impairment testing, a similar present value calculation is performed using the WACC. The applicable standards explicitly state that the cost of debt and not the interest rates must be used.
The cost of debt is not the same as the interest rate. The cost of debt to be applied in forward-looking company valuations is derived from market interest rates at the valuation date – and not from contractual interest rates agreed in the past – taking into account the risk of default.Interest rates consist of two components: the risk-free rate and the credit spread. Both components can be determined using different approaches based on yield curves. Creditworthiness – expressed as a credit rating or credit score – plays a central role in determining an appropriate interest rate and selecting appropriate capital market data. The general rule is: lower default risk – higher rating – lower credit spread – lower interest rate – lower cost of debt – and vice versa.
Christian Puscasu
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