# Net Present Value (NPV)

In order to compare schemes, we have converted capital and operating costs and revenues into Net Present Values. This is a normal step in project evaluation: future benefits are worth less to us than benefits received today. Net Present Value (NPV) is a way of representing the current value of future benefits and costs.

We found some discrepancies in the existing analyses that hinder straightforward comparisons and may confuse some readers. For example, the Benefits Case Analyses prepared by Metrolinx provide estimates of NPVs for many costs and benefits, and for many - but not all - of the schemes. In some cases they present annual data as well. By contrast, TTC generally presents estimates of capital costs in current dollars, including allowance for inflation. This means that a scheme estimated to cost, say, \$1 billion in current (2013) dollars over several years, might be shown by Metrolinx to have a cost of about \$850 million NPV, while TTC might show the scheme as estimated to cost \$1.1 billion. The two figures are not necessarily inconsistent; the difference is in the approach. Metrolinx is in effect saying that if you put \$850 million in the bank, in an account earning 5% per year interest, plus inflation, you would be able to build the scheme over time, because the money would grow before you spent it. TTC on the other hand is saying that they would actually spend \$1.1 billion on the project, over time, because the costs of the work would increase with inflation.

The best way to estimate NPVs is to build a financial model, with projections of year-by-year cash flows and benefits. Metrolinx seems to have done this, although they have not released the detailed projections, only the final NPVs. We do not have sufficient information to prepare year-by-year cash flow projections. However, we can estimate the NPVs for each scheme from data provided by TTC and Metrolinx, using consistent, somewhat simplified, heuristic methods.

For the GO Rail and TTC schemes, the NPV of revenue, passenger and road traffic benefits, and O&M costs is assumed to be 23 times the 2023 annual figure. Capital costs are converted to NPVs in 2010 (the base year for most Metrolinx analyses) by taking 70% of the estimated cost. The factors of 23 and 70% are broadly consistent with the figures presented in Metrolinx and GO reports, and with Metrolinx's 5% real discount rate.

For the 905 region BRT schemes, we used Metrolinx BCA figures, which are in most cases already presented as NPVs.