Valuation models for derivative assets hold the same significance in finance as relativity theories do in physics…
In this entry, I want to address the method of discounting with the certainty equivalent at a risk-free rate, which is used when calculating the NPV of cash flows using the usual method is impossible due to highly variable risk.
What Does the Method Entail?
The discount rate consists of two components: time (risk-free rate) and risk (market risk premium). If we can convert the project’s cash flows into a certainty equivalent, we can remove the risk component.
For example, consider a typical construction development project where the general contractor has assumed the risks associated with cost variability, and part of the revenues is fixed through pre-sale contracts. This means that both revenues and costs are fixed regardless of market conditions. In this case, the cash flows can be discounted at the risk-free rate.
Now, let’s look at a scenario where the usual discounting technique leads to errors:
For instance, a pharmaceutical company is conducting a test with a 50/50 chance of success. The risk is very high, but if successful, there is an opportunity for additional investment, bringing the project within the bounds of typical risk. If we discount all the project’s cash flows at a high rate due to the testing phase, we get a distorted picture. If this approach were used, pharmaceutical companies would never invest in research.
Note that the situation resembles a typical trade option. You pay the option price (investment in testing) and purchase a 50% probability of making a profit in the next phase. The expected profit from this 50% chance is then discounted at the risk-free rate (I won’t complicate it further for now).
It is based on this concept of the risk-free assumption that models for valuing options and other derivative assets were developed.
Source of the photo and insights:
Principles of Corporate Finance,
By Richard Brealey, Stewart Myers and Franklin Allen