How many valuations have you done that involved situations like these as of the valuation date:
● Client is bidding on big job, but does not know how likely he is to obtain it.
● Client may lose a big customer in financial trouble, but does not know how probable the customer’s survival (ability to pay him) might be.
● Client’s business is involved in a lawsuit (as either plaintiff or defendant) that might result in a big payoff or cost, but again, the probabilities are not ascertainable.
I can think of many other examples of similar situations that have the following common characteristics:
● The uncertainties are discrete: either something will or will not happen
● We can quantify (with reasonable certainty) the cash flows to equity for the entire business under both scenarios (“will happen” or “won’t happen”)
● We can therefore quantify the differences in cash flow between the scenarios
● Except for the discrete uncertainty, we could come up with a reasonable estimate of the cost of equity capital (cash flow discount rate) for the business
● But there is no way to confidently quantify either the probabilities of the two scenarios or the incremental or comparative risks
That last point is critical. If we could quantify (with appropriate support) the probabilities or the incremental risks, we could incorporate them into a DCF analysis. But in these cases we cannot, and, for that matter, nobody can!
I also want to emphasize that this post applies to discrete uncertainties that have a major valuation impact. As a contrasting example, consider a physician buying another doctor’s practice. The existing practice has a patient list of hundreds of names, and none of them are significant percentages of total revenue. Now, there is going to be patient attrition, but we handle this via some assumption about retention; such as that each year, 5% of the patients will be lost. (Sophisticated analysts use survivor curve analysis to do this.) This is not the same as the situations I mentioned above, in which an individual job / customer / lawsuit has a huge valuation impact.
In a real transaction, the buyer and seller could share the discrete uncertainty via an earn-out such as payments contingent on getting / keeping the job or customer. At closing, nobody knows what the ultimate payments might be, but they have agreed on how to share in whatever they are. They do not need to know the “amount certain” of the earn-out.
In tax valuations, however, the earn-out or lawsuit contingency might have to be quantified into an amount certain if a gift or estate tax return has to be filed. To put it simply, you have to put one number into a box on the tax form that indicates “tax due”!
Revenue Ruling 59-60 Section 3 helps us a little bit with this, stating that only information known or reasonably knowable as of the valuation date is relevant. The problem is, as of the valuation date the probabilities are NOT KNOWN OR REASONABLY KNOWABLE by the client or by us.
So, as a practical matter, we have to consider and reflect the discrete outcomes (will happen or won’t happen) in our appraisal. It would be wrong to ignore them: to assume (with 100% certainty) that either the “will happen” or “won’t happen” scenario will hold. That would be lying. Instead, we have to accept the unknowable probabilities and work with what we have, do the best job possible of reflecting them in our analysis and in explaining why we did what we did. Just as nobody can know the probabilities, if we do our job right and state the limitations we were under, nobody can do any better given the same information. In my experience, as long as we do the best we can, there will not be a problem with an IRS audit. (Revenue Ruling 59-60 Section 3 also implies that hindsight is not cricket!)
So with all that said, how do we deal with the unknown probabilities? To restate what we know:
● The uncertainties are discrete: either something will or will not happen
● We can quantify (with reasonable certainty) the cash flows to equity for the entire business under both scenarios (“will happen” or “won’t happen”)
● We can therefore quantify the differences in cash flow between the scenarios
● Except for the discrete uncertainty, we could come up with a reasonable estimate of the cost of equity capital (cash flow discount rate) for the business
For purposes of this discussion let’s assume that “will happen” is a favorable outcome: the job is obtained, the customer is kept, and the lawsuit is won. “Will happen” has greater value than “won’t happen” (do not get the job, lose customer, lose lawsuit).
From the above, we can compute the DCF value of “won’t happen”, because we know the cash flows and the cost of capital. We can compute the cash flows of “will happen”, but are stuck on what probability to assign to it and / or what discount rate to apply to the INCREMENTAL “will happen” cash flows.
Do we use probabilities or a higher discount rate for the incremental cash flows? (I am averse to doing both; either one is tough enough, doing both introduces the possibility that we would double-count risk, and makes things very messy.) My simple answer is to do whatever feels most comfortable based on the data available. In other words, estimate the probabilities or the incremental discount rate as best you can, clearly communicating why you selected the values, but also mentioning your subjective judgment. I do not mean to be glib about this: there is a way to double-check using the other method!
Let’s say we use subjective probabilities to weight “will happen” 50% and “won’t happen” 50%. Will happen has a DCF value of $150 and won’t happen $100. (The incremental value of will happen is $50. Remember, because we are using probabilities, we use the same discount rate for both scenarios.) The weighted average value is $125, an increase of $25. Now, by iterating (trial and error), calculate the discount rate applicable just to the incremental will happen cash flows that yield a net present value of $25. That is the discount rate implicit in the probability assessments. Working it the other way, if you use different discount rates to reflect the risks, you can reverse this procedure and determine the implied probabilities. Either way, consider the results you get; if the implied discount rates or probabilities do not make sense to you, then reconsider the initial assumptions!