September 12, 2020

How to value green investments (and eat chocolate)?

The first thing we learn in finance classes is how to value for-profit investments. An investment project is worth the present value of the cash flow it generates, which we calculate as expected cash flow discounted at the appropriate rate.

Can we adapt the method for nonprofit investments whose output is not pecuniary but environmental or social? The answer is yes!

The main idea of discounting cash flow is that money in the future is worth less than money today and uncertain cash flow is worth less than certain cash flow.

The same logic applies to investments that produce environmental benefits: future environmental gains are worth less than present ones; uncertain environmental gains are worth less than certain ones.

We can illustrate this principle with two examples, one straightforward and one more subtle.

1. Early gains are more valuable than late gains

Consider two investment projects in green technologies that aim at reducing carbon emissions. Project A leads to a 100 million tons (Mt) reduction in carbon emission at an horizon of two years. Project B generates the same reduction in carbon emission but it does so at an horizon of four years. The development cost is the same for both projects.

We naturally prefer project A over project B because its gains are earlier. This is an illustration of time discounting.

2. Certain gains are more valuable than uncertain gains — but there's a twist to it!

Project X uses a proven technology and leads to a certain 200 Mt reduction in carbon emission in ten years. Project Y uses an uncertain technology: it may work and reduce carbon emissions by 400 Mt in ten year; it may also fail and deliver no gains. Project Y's success depends on external factors out of our control; success and failure are equally likely. The development cost is the same for both projects. Which project do you prefer?

Risk discounting implies you should select project X because it generates the same expected gain as project Y (the expected emission reduction is 200 Mt for both projects) with lower risk.

There is a twist, however. Situations exist in which we should pick project Y over project X because the uncertainty over the environmental benefits of project Y is valuable. Can you see in which situation this could happen?

If you already completed the Financial Economics course, you should know the answer. If you are currently following the course, you don't know yet but can still try to guess!

Now, chocolate. Email me your answer before Monday midnight: there is a chocolate box to win. I will draw lots among the correct answers coming from students currently on campus to determine the winner. (Chocolate delivered on campus only to save carbon!)

Solution: We might prefer project Y because of diversification.

Suppose project Y relies on a technology that works only if atmospheric temperature does not rise too much. Suppose also that we already started another project Z, which generates uncertain carbon emission reduction: 400 Mt with probability one-half and 0 Mt with probability one-half. Project Z relies on a technology that works if atmospheric temperatures rise.

Therefore, project Y is successful when project Z fails, and it fails when project Z is successful. In finance language, projects Y hedges against the uncertainty of project Z because the payoff of both projects are negatively correlated. The portfolio project Y + project Z is therefore a safe portfolio. By contrast, the portfolio project X + project Z is risky. In this case, we prefer project Y over project X.

VoilĂ !

Congratulations to students who found the solution and to students who made creative suggestions and to Maxime who won and enjoyed the chocolate!

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