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Valuing distress

The requirement is for investors to see shares in a distressed company for what they really are – a call option on the company’s survival. And the way in which plausible guesstimates of underlying equity value are teased out is to use an adapted version of the famous Black-Scholes option pricing formula, arguably the most influential pricing model the financial world has seen.

As a neat example of this conjunction of distress and opportunity, take last week’s full-year results from FirstGroup (FGP), the operator of Greyhound buses in the US and several rail franchises in the UK. FirstGroup’s finances are such that the company’s bosses needed to include a ‘going concern assessment’ and, on a “reasonable downside scenario”, they acknowledge that FirstGroup could fail to meet all the covenants attaching to its debt.

Small wonder, perhaps, that FirstGroup’s share price lurched down 26 per cent on the day. True, encountering turbulence like that has been familiar enough during a decline lasting 12 years, during which the share price has dropped 94 per cent. That has left the equity valued at £450m compared with about £1.5bn for the underlying level of the group’s net debt.

That sort of ratio between the value of equity and of debt is ideal for an adaption of the Black-Scholes model to suggest underlying value for a company’s shares. To explain, let’s start with first principles. It is axiomatic that the pay-off from a call option – the right but not the obligation to buy an asset at a pre-set price – will be the difference between the asset’s value and the price at which the option is exercised. If a security has a market value of 30p and the exercise price of the option to buy the security is 25p, the option must be worth at least 5p.


FirstGroup shares as a call option
Market value of equity£451m
Value of debt£1,508m
Security price (enterprise value)£1,959m
Exercise price (value of debt)£1,508m
Term of the debt3.3 years
Equity value as a call£563m
Per share value46.2p
Market price per share37p
Source: Company accounts 


Adapt that logic to the valuation of a distressed company and the value of its debt and equity combined – or enterprise value – proxies as the security’s value, while the exercise price is the value of the debt alone. Thus the difference between those two – the call – is the underlying value of what could be left over for holders of the equity in a worst-case scenario. The table shows the bare-bones data. Click on the link below to access a spreadsheet showing the workings and a generic Black-Scholes model that can be applied to any distressed company.

For FirstGroup, the model suggests an underlying value of £563m compared with a market value for the equity of £451m. That comes to 46p per share compared with 37p in the market. That might sound promising, but it comes with caveats. First, there is the question of how much debt FirstGroup actually employs. That is not as straightforward as it sounds now that quoted companies are obliged to calculate the obligations on their operating leases as if they were debt. The £1.5bn in the table is FirstGroup’s own figure, excluding both operating leases and ring-fenced cash in the group’s rail division.

Similarly, the model needs an estimate of the weighted-average term of the group’s debt since that, theoretically, is when the call option expires. This matters, since the longer the term, the more time given to an option holder to exercise the call at a profit and, therefore, the more valuable the option. The figure in the table – 3.3 years – comes from FirstGroup’s results and seems to include most, perhaps all, of the group’s debt.

Maybe most important is the figure for the average volatility of the value of the group’s debt and equity. The more that prices bounce around, the more valuable the call because the better the chance that it can be exercised profitably. While this logic stacks up for an option traded on an exchange, it has less relevance to the notional value of what might be left for equity investors after, say, liquidation. Thus it makes sense to minimise the volatility input since that restrains the value of the call and so reduces the gap between theoretical value and market price. In other words, it stops punters getting carried away. Play around with the volatility input in the online spreadsheet, and you’ll see.

Besides, applying the model is the easy bit. It is an adjunct to conventional analysis, not a substitute for it. But the model does encourage the thought that, if FirstGroup’s bosses manage to sell the US operations, they will be left with a UK-focused debt-free rump that is in the current share price for less than nothing.