The Merton Model

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What is the Merton Model?

The Merton model is a common credit risk model used for evaluating a firm and determining if it will remain solvent.  This simple model is specifically useful in situations where traditional DCF and relative valuation models are ineffective, such as distressed firms, natural resource firms, and startups/high growth firms whose value is primarily based on their rights to a product, service, or innovative technology.  The Merton model is most appropriate for firms with longer liquidity event timelines and multiple liquidity options.

Model Framework

While a firm is a going concern, its equity is a claim by the shareholders to all cash flows after all debts and other claims have been fulfilled.  In a liquidity event, equity is a claim to excess value after all debts and other claims have been fulfilled.  Therefore, equity resembles a call option where exercising requires liquidation of firm assets and repayment of all debt at face value.  Debt holders, on the other hand, have a payoff akin to a portfolio that is long riskless debt and short a put on the firm value with a strike price equal to the face value of the debt.

Key Model Assumptions

  • Underlying asset is continuously traded.
  • Markets are perfect (no tax, transaction costs, etc.), meaning value of the firm equals the value of debt plus the value of equity.
  • All options are European and can only be exercised at expiry.
  • There are only two stakeholders: shareholders and creditors.
  • Firm debt is represented by only a single, zero-coupon issue that is non-convertible with no embedded options or other features.
  • Asset pricing is continuous (no gap ups, etc.)
  • Variance is known and constant.
  • Risk-free rate is known and constant.
  • The exercise process is instantaneous.
  • No dividends are paid.

As with all models, the Merton model in its simplest form is an unrealistic view of reality.   That said, the model still has value in that it provides a basic understanding of the concept. In addition, there are numerous adaptations of this basic version out there that are tailored for more realistic situations and can provide analysts with more accurate equity and debt valuations.

Takeaways from the Merton Model

Impact of time value

Using the option approach, the value of firm equity can be divided into intrinsic value (PV of all capital and debt outstanding) and time value (based on time to debt maturity). While the impact of intrinsic value is an obvious one, the effect of time value may be less so without the Merton model.  By quantifying the time value component of equity, it becomes clear why even a bankrupt firm (whose debts exceed current firm value) can have a positive equity value when the time to maturity (liquidity event) is distant.  Equity value and intrinsic value converge as the time to maturity nears.

Potential stakeholder conflicts (agency problem).

In situations where equity investors are protected by limited liability (not always the case if they are required to personally guarantee the firm’s debt), shareholders would likely elect to default on the debt when the firm value is less than the value of the outstanding debt. If the firm value is greater than the debt value, the shareholders would likely exercise their option to repay the debt and maintain the firm as a going concern.

Activities such as investing in high-risk projects or financing dividend payouts with asset liquidation can increase creditor risk (reducing value of debt) and simultaneously increase equity value for shareholders.

Equity holders may be incentivized to accept risky, negative NPV projects that increase the volatility of the firm value since increased volatility increases equity value (at the expense of creditors who lose value as the implied market interest rate on the firm debt will increase).