I suspect that many readers of this blog also follow the blog of Aswath Damodaran, and if they don’t, I would recommend doing so. Damodaran is a Professor of Finance at the Stern School of Business and he often posts how he would approach valuing high-profile stocks such as Tesla or Uber. It’s very unlikely I would ever be interested in investing one of those companies, but his valuation methodology is pretty solid and his posts are educational. I think having a good grasp on the fundamentals of valuing a company is very important, even when most of the time you revert to simple back of the napkin valuations using a P/E multiple (which I do).

However, I disagree strongly with his approach in his latest post about how to incorporate truncation risk in the valuation of Aramco. To quickly recap Damodaran point of view, a DCF valuation is only suitable for going concerns because you assume cash flows are continuing long-term and potentially indefinitely. Because of that you can’t properly model survival risk where a company might cease to exist after a certain point in time. In the case of Amerco it could be a possible regime change at some point in time to fundamentally change the value of the business going forward. But it’s also very relevant in startups that have a high probability of not making it past the first few years. His suggested solution is to value the company as a going concern in one scenario, value it with a regime change in a second scenario, put some probabilities on the two scenarios and call it a day.

I think there are two problems with his post:

- This approach doesn’t work well because it doesn’t fit reality
- A DCF is perfectly capable of incorporating truncation risk

The reason that this methodology is flawed is because it doesn’t incorporate the timing of the potential event. It matters a whole lot if the regime change is in the next year, or if it happens in 30 years time. So what does a 20% probability mean? Is that a 20% probability of regime change happening this year? the next 5 years? the next 50 years? And because that question isn’t answered, you also can’t really do a equity valuation in the regime change scenario. What he is doing I think is just taking the going concern equity valuation, and reducing it by 50% in the regime change scenario to account for higher taxes and royalties. That implicitly assumes that the regime change will happen on day one, which is of course highly unlikely and unrealistic.

A better model would be to assume that there is a small probability of a regime change every single year. That sounds complicated, but luckily, that’s exactly what we can model in a DCF by increasing the discount rate. If you would for example assume a 1% probability that there is a regime change in a given year you can simply increase your discount rate by 1%. It’s that easy! A one percent chance for 10 years in a row would imply a probability of regime change of 9.56% during that period and 39.5% during a 50 year period.

Note that by increasing the discount rate by one percent in case of a regime change we are assuming that the residual value is zero. If you think there is a 1% probability with 50% residual value we should increase the discount rate by just 0.5%. And a second small note, if you want to do things mathematically correct, you can’t simply add probabilities. In the example below you can see how that becomes especially relevant when probabilities become large.

If you want you can also easily change the model to customize probabilities of failure for each time period. Perhaps you have the view that there is in the next five years a higher chance of regime change, followed by a period of lower probabilities. But it’s probably more useful when thinking about a startup. The probability of failure is presumably very high in the first few years while lower in subsequent year.

Let’s imagine a project that will costs 10 million to start and 10 million more at the end of the first two years, and will produce 100 million at the end of year 3 and 4. In the first two years there is a 25% probability of failure. We could (and should!) model that as following:

Note that the discount rate is calculated by taking: `(1 + "equity risk") / (1 - "truncation risk") - 1`

and the NPV factor is the factor of the previous year multiplied by `1 / (1 + "discount rate")`

of the current year. That way you carry a risk of total failure that you introduced in the early years forward for the calculations of the NPV of later years^{1}.

The great thing about this model is that it matches actual reality. If you have a failure in the first year you don’t have to put more cash in the project, that’s why the net present value of the cash outlays at the end of year one and two are severely discounted. And of course, the same is true about the payoff in year 3 and 4 because there is a high probability that the project will never get to that point. If you would want to model this using Damodaran’s approach you would be in big trouble, because one single failure scenario can’t easily account for the fact that failure can occur at different times, and that the impact on the net present value depends on the timing.

# Concluding remarks

Let me know in the comments if you found this post useful, otherwise I will be back to posting the occasional merger with a contingent value right ;). And of course, perhaps you want to point out that I’m completely wrong. It’s totally possible that I don’t know things better than someone who is a professor of Finance.

# Disclosure

No intention to ever initiate a position in Aramco

1. A previous version of this post was using the wrong formula to calculate the discount factor and the combined discount rate. Thanks to a reader in the comments this has now been corrected.