Project evaluation must select a time horizon. Especially for projects front-loaded with significant capital investment, the longer the time horizon, the greater the prospect that the present value of project benefits exceeds the present value of project costs. This fourth post in the series on “Project Evaluation” argues that, rather than debating the choice of a fixed number for the time horizon, one should focus on the sources of project termination risk.
I have reviewed many project evaluations over the years. One practice is to select a fixed duration based on the following:
- the term of debt financing,
- the term of project contracts,
- the anticipated life of project infrastructure
Each has conceptual problems.
Term of Project Financing. A central tenet of the capital market is that the term of financing should never exceed project life. Therefore, a time horizon based on the term of financing will neglect project benefits after financing is paid off.
Term of Project Contracts. A time horizon based on the term of contracts neglects the prospect for contract renewal. Contracts come in many forms. Some will state a contract term without discussion of renewal. Others will state a term and discuss the process for renewals. Especially if the project’s existence or a party’s participation during the initial term confers an advantage during renewal, project evaluation should consider the value of renewals.
Anticipated Infrastructure Life. Anticipated infrastructure life has the most promise for selecting the time horizon. A practical problem is the all elements of project infrastructure do not have the same life. Property ownership is permanent (unless there is confiscation risk). Wells, pumps, and pipelines will have different lives. Further, when capital equipment fails or wears out, it can be replaced. Therefore, the life of infrastructure has more relevance for determining a project’s capital improvement and replacement schedule than determining the time horizon for project evaluation.
Risk Assessment and Time Horizon
The upshot of the above is that a project does not have a known time horizon. In other words, a project may or may not continue up to and past the time original project financing is repaid, through contract renewals, and through replacement and modernization of initial infrastructure. Unknown project lives does not mean that projects lives are infinite. Nothing lasts forever.
What should one do? Think about the project. What are the termination risks?
Consider the simple example of risk used in last week’s post on risk assessment—a constant annual risk of termination. Consistent with the range of risk premiums, let the annual rate of termination vary between 0.5%, 1.0%, 1.5%, 2.0% and 2.5%. The expected life for these risks are, respectively, 200 years, 100 years, 67 years, 50 years and 40 years (expected life = 1/annual probability of termination).
Should one used a time horizon equal to the expected life? No. The project life is unknown. It may terminate before or after its expected life.
See the chart below stating the probability of survival by project duration with different termination risks. A project with a 200-year expected life has a 67% probability to survive 80 years. In other words, there is a one-third chance that the project terminates before 80 years. A project with a 100-year expected life has only a 45% chance to survive 80 years. For the other projects whose expected life is less than 80 years, there is some chance that they will survive 80 years or longer.
The share of present value of expected benefits captured by a fixed horizon model depends on project termination risk and the fixed horizon (see chart below). For projects with an expected life of 50 years or less, a 100-year fixed horizon captures almost all (99%) of the project’s anticipated benefit. For projects with an expected life greater than 100 years, a fixed horizon model of 100 years severely understates the present value of expected benefits.
Project evaluations depend on time horizons. Especially for low-risk projects (expected life 50 years or longer), a fixed horizon model will severely understate the present value of expected benefits. As discussed above, long-lived projects have low termination risk. As discussed last week, projects with low termination risk have lower interest rates. So, long-lived projects will have low interest rates and, as such, should not be evaluated with fixed time horizon models of even 100 years.
This week’s post and last week’s post on Project Evaluation comes to the same point. Explicit consideration of project risks.