Credit Tracker

Weekly Credit Report – The Ramification of Option Pricing Framework of Distressed Equities for the Debt of Those Equities

• Our Chart of the Week this week explored the application of financial valuation theory for distressed equities. We calculated an equity value as a call option on the value of the firm’s assets with a strike price of its debt.
• This theoretically sound approach requires a lot of assumptions: we first calculated a weighted average maturity of each company’s debt. We then restated the debt as a zero coupon with that maturity by estimating and including all interest expenses up to that maturity date. We then had to make a volatility assumption, and we used the same 30% that we used in our effective cost of debt calculations. Then, we had to estimate the current liquidation value of the firm’s assets, which we calculated as the maximum of 1x LTM revenues or 1x tangible assets.
• The value of the debt is easy to calculate once you have done the Black Scholes valuation of the equity: it’s simply the value of the assets – the value of the equity.
• The issue with all of that is that it hides the dynamics of how the various variables conspire to produce valuations.
• This week’s credit tracker is a thought experiment. The graphs below seek to show how the movement of each variable affects debt and equity values while holding the other variables constant.
• ChatGPT was kind enough to process the enormous spreadsheet with over 1000 rows to produce these graphs. Thank you, AI!
• First, we assumed that the liquidation value of the firm’s assets was 100% of the debt. To make things easy, we assumed the assets were worth $100 and the debt was $100. In other words, if the game were called immediately, the equity would be worthless as there would just be sufficient value to cover the debt. We also assumed a volatility of 30% and allowed the time to maturity to vary from .5 years to 5 years.

• Even if the debt maturities are pretty short, the equity stubbornly refuses to go to zero. As the term increases, the volatility of asset values produces some upside scenarios that accrue to the equity. It’s all upside for the equity because today they are worthless, but tomorrow, especially if the volatility is high, they are likely to be in the money. Fair yields on the debt start high since the option value gives some of the valuation to the equity, and the fair price of the debt is below par.

• In this scenario, we assumed a two-year maturity of the debt and 100% Asset value/Debt. The equity initially has almost $20 of value even though it is only at the money with no intrinsic value. As we increase the volatility, most of this value accrues to the equity. As we increase the volatility, there are more chances for the equity to be in the money, but there are also more opportunities for the debt to lose. This is the reason why lenders want to have control over borrowers that are skirting trouble. The borrowers rationally want to increase volatility by taking on riskier and riskier projects because they have nothing to lose. The debt holders will pick up the tab if these risky projects fail.

• Here, we vary the starting point. On the left side, we assume the assets are only worth 50% of the debt, while on the far right, the assets are worth 2x the debt.
• The graph assumes constant 30% volatility and a 2-year debt maturity.
• With only 30% volatility and 2 years to run, the equity starts virtually worthless. There isn’t enough time or volatility to make up for the deep, out-of-the-money situation the equity finds itself in. This is genuinely a “sell the office building and buy lottery tickets” position, and as crazy as it seems, that might not be an irrational move for the equity holders at the far left of this graph. Debt yields are pretty high as the debt value of 100 is only 50% of par value. As the assumed value/debt ratio increases, yields level off, and the debt becomes a safe bet.
• Option pricing gives us a unique perspective on rational equity holder and debt holder behavior. It’s often counterintuitive but grounded in sound financial theory.