Debt securities provide many challenges not present in traditional equity valuation. There are a variety of valuation approaches and selecting the right methodology requires a careful assessment of what information is available to be used as inputs to the valuation model. Relevant information used in the process can include historical market and financial data for a subject company.
Approaches to debt valuation can be separated into two broad categories: those based on traditional financial analysis and those based on arbitrage pricing. For companies with a clear operating history, it may be possible to perform a traditional financial analysis based on the fundamentals of the debt issuer. Such an approach typically entails evaluating an issuer’s credit risk, then discounting the promised coupon and principal payments at a risk adjusted discount rate. In other cases when firms have limited representative operating history and difficult-to-estimate financial projections, such approaches may not be feasible.
When prices of other investments in a company—whether debt or equity—are observable, it may be highly desirable to incorporate the observed price into the valuation process for a debt instrument. This can sometimes be accomplished by invoking arbitrage-based models to yield fair value estimates.
Two approaches to valuing debt that take the value of other securities in the capital structure as inputs are so-called structural and reduced-form models. Structural models are based on option pricing theory and typically take as an input the value of the company’s equity or the entire enterprise to yield a debt value directly or a probability that the company will default on its debt.
On the other hand, reduced form models do not usually incorporate the equity value and instead aim to value debt through estimates of the default probability and recovery rate. Unlike in structural models, it is not usually necessary to incorporate every aspect of the issuer’s capital structure into the reduced form model, making it sometimes preferable for companies with very complex capital structures. Reduced form models can be simpler than structural models and require fewer subjective assumptions, which can often lead to more realistic fair value estimates.
An Illustration of Relative Debt Valuation
Imagine that we are tasked with valuing junior notes issued by ABC Company. ABC is a public company with actively traded senior notes priced at $97. We would like to find what value for the junior notes is implied by the observed price for the more senior debt. When a firm has multiple debt issues, some of which have observable market prices, we may be able to implement a reduced form model to derive a fair value estimate.
We proceed by setting up a reduced form model that incorporates the material features of the senior debt (coupon rate, maturity, redemption features, etc.) and also takes as inputs the recovery rate of the debt and the default probability. We must make estimates for the recovery rate of both debt issues in the event of default. This can be done by evaluating the placement of the debt in the capital structure as well as the quality of any security interests. While it can be difficult to develop these assumptions, historical data on recovery rates by level of seniority and security is available from rating agencies.
In the next step, we use the valuation model, as well as the observed market price for the senior debt to determine what annual default probability is implied. We use this implied default probability as a valuation input into a separate valuation model for the junior debt. By proceeding in this fashion, we assume that various classes of debt for a given issuer have the same default probability but differ in their recovery rates.
Models of this type typically rely on the same risk neutral probability dynamics seen in option pricing models. This suggests that the default probabilities derived as an intermediate step in this approach are so-called risk neutral probabilities and thus should not be interpreted as the actual probability that a company will default on its debt obligations.