7.8 - Present value of benefits and costs
- 7.1 - Benefits and costs of transport services
- 7.2 - Transport service user benefits
- 7.3 - Congestion benefits
- 7.4 - Accident reduction benefits
- 7.5 - Disbenefits during implementation/construction
- 7.6 - Other benefits and national strategic factors
- 7.7 - Costs to government
- 7.8 - Present value of benefits and costs
7.8 - Present value of benefits and costs
Introduction
All benefits and costs must be discounted over the life of the proposal and each option to calculate their present value.
Benefits and costs may:
- occur as a single payment or benefit
- recur uniformly over the life of the proposal
- increase or decrease arithmetically over the life of the proposal.
Benefits and costs are discounted individually to take this timing into account using a present worth factor from table A1.1 in appendix A1 (volume 1).
Calculating the present value of benefits
Calculating the present value (PV) of all the benefits of the transport service proposal and each option involves the following:
| Step | Action |
|---|---|
| 1 | List all the benefits associated with each option, including the transport service proposal. Ensure that the benefits are annual amounts. Adjust them if necessary. Note: Service provider revenue (and service provider costs) are not included in this part of the evaluation. |
| 2 |
Determine if each benefit occurs:
|
| 3 | For a one-off benefit: a. State which year the benefit occurs in. b. Select the appropriate single payment present worth factor from table A1.1 in appendix A.1 (volume 1). c. Multiply the benefit by the present worth factor to find its PV. |
| 4 | For a uniformly occurring benefit: a. Determine the time stream for the benefit. For example, a benefit may start in year three and continue until year 15. b. Select the appropriate uniform series present worth factor for the first year the benefit occurs in and for the last year it occurs. c. Subtract the present worth factor for the start time of the benefit stream from the present worth factor for the end time of the benefit stream. d. Multiply the answer to step c by the annual benefit amount to determine its present value. |
| 5 | Where the benefits grow or decrease arithmetically: a. Determine the time stream for the benefit. For example, a benefit may start in year three and continue until year 15. b. Select the appropriate uniform series and arithmetic growth present worth factors (PWF) for the first year the benefit occurs in and for the last year it occurs. c. Subtract the uniform series PWF for the start time of the benefit stream from the PWF for the end time of the benefit stream. d. Repeat step c for the arithmetic growth PWF. e. Determine the appropriate traffic growth rate factor. For transport service user benefits this will be based on predicted traffic growth rates. Default rates for road-based traffic growth rates are provided in table A2.4 in appendix A2 (volume 1). The traffic growth rate factor is usually expressed as a percentage of the traffic volume at time zero. For the purposes of this calculation, the traffic growth rate should be expressed as a decimal figure. Note: The basis for the predicted future growth rate for each mode should have been detailed in developing the demand estimates. If not, do so here. f. For accident benefits only. Adjust the road traffic growth rate to take account of the downward trend in road-based accidents using one of the factors below: (i) if the posted speed limit is 50 or 60 km/h then subtract three percent from the traffic growth rate (ii) if the posted speed limit is 70 km/h or above then subtract one percent from the traffic growth rate. Note: It is possible for the adjusted accident growth rate to be negative if the predicted traffic growth rate is less than three percent (0.03) in 50 or 60 km/h areas or one percent (0.01) in 70 km/h and above areas. g. Multiply the traffic growth rate (from step e or step f, for accident benefits) by the arithmetic growth PWF determined in step d. Add this figure to the uniform series PWF calculated in step c. h. Multiply the result of step g by the value of the benefit when it first occurs to obtain the PV of the benefit. |
| 6 | Sum the present values of all of the benefits to obtain the total present value of future benefits for the transport service proposal and each option. |
| 7 | Enter the information into the reporting table at the end of this chapter. |
Calculating the present value of costs
The procedure for calculating the present value of costs is very similar to that for determining the present value of benefits. Evaluators are referred in part to the preceding table where the calculations are the same. Simply substitute the word 'cost' where 'benefit' appears.
The procedure involves the following steps:
| Step | Action |
|---|---|
| 1 |
Using the information from chapter 6 and section 7.7, for the transport service proposal and each option, list the:
|
| 2 |
Determine if each cost occurs:
|
| 3 | For a one-off cost. Follow the procedure outlined in step 3 of the table for calculating the present value of benefits. |
| 4 | For a uniformly occurring cost. Follow the procedure outlined in step 4 of the table for calculating the present value of benefits. |
| 5 | Where the costs grow or decrease arithmetically. Follow the procedure outlined in step 5 of the table for calculating the present value of benefits. |
| 6 |
Obtain the PV of the net cost to government:
|
| 7 | Enter the information into the reporting table. |
Complete benefits and costs table
All benefits and costs shall be recorded in the benefits and costs present value table at the end of this chapter.
Indicate basis of deriving benefits
All methodologies for deriving transport service user benefits and road user benefits shall be explained, along with any assumptions employment in their calculation, in the evaluator's report.
For an improved transport service, report the existing and projected patronage and the improvement, ie existing and projected service frequencies, interchanges eliminated, fare changes and other improvements.
The assumptions and calculations underlying the determination of the road capital and maintenance cost savings, as appropriate, shall also be included in the evaluator's report.
Where the road capital and/or maintenance cost savings vary from time to time, the variations and when they occur shall be entered into the table.
Suggested format for reporting
It may be useful to use the following format to present the present values of costs and benefits for transport services proposals for each option under consideration.
