# Convertible Notes Valuation

## High-level Thoughts on a Complex Analysis

Convertible notes are a common and popular form of financing for private company issuers in the development stages that are looking to delay or avoid valuation discussions inherent in pure equity financing, as well as the additional dilution to the existing equity base. They can also be quicker to arrange and close. Investors are attracted to the protection that the seniority of debt provides, as well as the opportunity to share in appreciation if the issuer is performing well and seeing increased value in the equity base. Because they contain elements of debt and equity, as well as embedded optionality, the valuation of convertibles should consider varied and uncertain future cash flows and apply an appropriate discount factor.

Convertible notes feature traditional debt cash flows that include interest payments and the repayment of principal on a maturity date.1 They also provide the holder with the option to convert the principal and accrued interest to equity at a specified conversion ratio that identifies the number of shares to be received per $1,000 of par value. The conversion ratio is usually fixed and implies a conversion price; for example, a conversion ratio of 50 implies a$20 conversion price. Thus, when issuing a convertible note, the issuer is also effectively selling (and the investor is effectively buying) a call option on the issuer’s stock, with the conversion price equivalent to a strike price.

#### Hybrid Instrument & Valuation Frameworks

From a financial reporting and valuation perspective, this exchange of both a debt security and an equity option in a single instrument is referred to as a hybrid security. The valuation challenge is to consider both the equity and debt components in a combined framework, and this challenge is not without its tradeoffs. The simplest approach is to strip the equity component from the convertible note and treat the value as a sum-of-the-parts. The equity is most commonly valued in straight Black-Scholes option pricing model, and this value is deducted from the convertible note’s notional amount to imply the “value” of the straight-debt.2 The tradeoff with this bifurcated framework is the benefit of general simplicity at the expense of a more comprehensive consideration of the value interplay between the equity and debt cash flows.

A feature-rich instrument amplifies the tradeoff between simplicity and depth of approach. At any moment in time, the outstanding notes could be simultaneously subject to a “hold, convert, or redeem” position at the discretion of the holder and a “call or redemption” position at the discretion of the issuer. Other aspects such as a dividend yield on the underlying stock, soft call features, declining call premiums, etc. can further complicate the valuation and muddy the use of a bifurcated valuation approach.

The generally accepted alternative to a bifurcated valuation approach is the use of an income approach in the form of a lattice framework. The lattice is most commonly applied as a binomial representation of future cash flows. The note’s debt cash flows are “mixed” with an equity overlay that presumes optimal cash flows as determined by the holder, subject to any features that may allow the issuer to influence the timing or magnitude of the cash flows.

Modeling future expected cash flows to debt and equity requires the application of a cash flow-specific discount rate. Debt and equity cash flows have distinct pay-offs and risk-profiles that necessitate separate discounting to their present value equivalents. A risk-adjusted cost of debt or yield is estimated in order to discount debt cash flows into their present value estimate. For equity cash flows, the pay-off profile suggests a risk-neutral or risk-free rate is more appropriate than a cost of equity for calculating present value equivalents. This important insight recognizes that any future equity cash flows stem from the embedded conversion option rather than the direct investment into such equity at the time the convertible note is issued.

#### Further Considerations

Tradeoffs in model selection and approach begin with moving from the simpler to the more complex choosing to live with or eliminate certain limitations given the facts and circumstances. Once a more or less complex modeling approach is settled, there may still be further tradeoffs to assess as inputs may have a differing impact given the model selection. Both the simpler bifurcated sum-of-the-parts and the more comprehensive lattice framework share in the impact that the expected volatility assumption plays in the valuation. Generally, the volatility input – not the notes’ yield – takes the leading role when valuing the notes’ component parts on the issuance date. Volatility is estimated from market data and applied directly as an input, while the yield is implied such that the valuation is consistent with the issuance price.  In this regard, model selection and the lead role of the volatility estimate shape the straight-debt yield which is a desired output of the valuation exercise at issuance.  It is this understanding that enables the valuation process to be fully informed by the tradeoffs associated with the valuation of a hybrid security, as well as the impact of key model inputs.

The ideal situation is one where the selected volatility at issuance implies a straight-debt yield that looks consistent with market yields on other credit instruments issued as straight debt with comparable credit quality and terms (i.e., maturity). Conversely, should a market yield determination be made, the implied volatility from the model would corroborate or be consistent with market data used to support an expected volatility input. Such consistency and completeness of a modeling approach lead to a reasonable and supportable valuation process at the time of issuance and future valuation dates.

#### Volatility Haircut

When the volatility input takes the lead, it is important to consider the source of the market data used to estimate volatility. Using historical stock prices and traded options leads to an equity volatility that is generally considered by holders of convertible notes to be in excess of the volatility that they would deem appropriate to the conversion option. In other words, the higher equity volatility would price the convertible notes higher than a market participant would value or overstate the straight debt yield measured at the issuance date.

One reason could be the disparate nature of the equity position. Holding a stock or acquiring a call option entails direct exposure to the stock performance that could be economically different from the conversion option held in a convertible note where the convertible noteholder has other forms of return, including the interest payments and principal cash flows, should the conversion option be out-of-the-money. Another reason could be the volatility skew at issuance when the conversion price is higher than the stock price and implied volatilities tend to decrease as the strike price increases.  In addition, volatility mean reversion could cause the volatility to revert (generally decrease) to a mean value over longer periods typical of maturity hold periods.  Finally, another source of decrease in volatility could be attributed to model selection.  A lattice model offers the ability to capture features important to the valuation, but also generally treats the equity cash flow as the full conversion of the note which overestimates the conversion value.  Therefore, when the convertible note is valued in a lattice framework that captures the hybrid security’s cash flows in a comprehensive framework, a haircut is applied to the market-based equity volatility so that the straight debt yield is not overstated, and the conversion option is not overvalued.

#### Summary

Convertible notes introduce a mix of complexities that lead to tradeoffs in model selection and use of unobservable inputs for valuation. Structural details of the security often guide the valuation toward the optimal approach for capturing the relevant terms of the instrument while mitigating the difficulty in working with key valuation inputs that are unobservable or obtained from market data that is like in character but contains some fundamental differences leading to adjustments. The balance is driven by the recognition of each model’s strengths and weaknesses, as well as the relative importance of the valuation inputs and their sourcing.

Tags: