Appendix 3: Sensitivity Analysis for Smart and Integrated Ticketing Options55
Appendix 3: Sensitivity Analysis for Smart and Integrated Ticketing Options55
Introduction
As the base case relies upon certain assumptions for which the evidence is not fully conclusive, a sensitivity analysis is particularly important for this business case. This focuses on the key drivers that affect the benefit-cost-ratios (BCRs). Mostly these BCRs were found to be high. This means that the aim of the sensitivity analysis has been to investigate under what conditions the various ticketing options would no longer represent value for money, to allow a better understanding of the potential risks involved with smart and integrated ticketing.
Sensitivity analysis
The BCRs in the base case are as follows:
- Smart ticketing – 14.6;
- Integrated ticketing – 14.7; and
- Smart Integrated ticketing – 19.7.
The table below shows the key base case assumptions for the three ticketing options which have been included in the sensitivity analysis:
Table A3.1 - Base Case Assumptions
|
|
Smart |
Integrated |
Smart Integrated |
|---|---|---|---|
|
Time savings per passenger (bus) |
2 Seconds |
3 Seconds |
2 Seconds |
|
Percentage of passengers using the new ticketing product |
100% |
100% |
100% |
|
Increase in patronage following introduction of new ticketing product |
4% |
4% |
6% |
|
Average number of people on a bus |
10 |
10 |
10 |
Benefit Sensitivity Analysis
The following sensitivities were assessed for each ticketing option:
- Lowering boarding time savings per bus passenger (to zero and -2 seconds). Some in the industry are sceptical about the likelihood of there being any boarding time savings; some go further to argue that smart cards will lead to slightly longer boarding times. This is significant because any time saving per boarder will also apply to those already on the bus;
- Lowering the percentage of passenger take up (to 75%, 50%, 25% and 10%). The model assumes 100% take-up, in line with the DfT business case, though actual take up would undoubtedly be lower. Note that this also lowers costs;
- Lowering the percentage increase in patronage (to 2%, 1% and 0% for smart ticketing and integrated ticketing, and 3%, 2% and 0% for smart integrated ticketing) ; and
- Reducing the average number of people on a bus from 10 to 5. This affects the overall time saving for the reason set out in the first bullet.
N.B. the international evidence, set out in the PTEG report56, does not link evidence of overall patronage increase with take up. This means that it cannot be said, for example, that a 6% increase in patronage would be associated with 50% take up. This has presented a problem for the sensitivity analysis: because these two factors are not connected in the evidence there is no robust way to connect them in the model. This initially had the effect that, when take up was varied, the benefits associated with patronage increase were independent and thus unchanged, while the variable costs fell, and so the BCRs for lower rates of take up were actually higher than the BCRs for higher rates of take up (though the NPVs were lower).
Because it seemed anomalous that patronage and take up would not be in some way correlated, it was decided for the sensitivity analysis, to vary the assumed patronage increase for each ticket type by the take up rate. Thus, in the sensitivity assessment of a 10% take up, the patronage increase is actually 0.6% for smart, integrated ticketing, as opposed to 6% in the base case (and 0.4% compared with 4% for the other ticket types). This is probably too restrictive an assumption, but the adoption of this highly conservative approach gives further confidence in the figures produced under the sensitivity analysis.
Cost Sensitivity Analysis
The following variations were also assessed for each ticketing option, in conjunction with the benefit sensitivities:
- Capital costs increase by 50%;
- Capital costs increase by 100%;
- Operating costs increase by 50%; and
- Operating costs increase by 100%.
Results
The results of the sensitivity analysis can be seen overleaf. Each of the individual variations was still associated with healthy BCRs and even applying different combinations did not yield a BCR below 1. This provides comfort, given the uncertainties around some of the key assumptions, that the business case for smart and integrated ticketing in Scotland stands up even under significantly more restrictive assumptions.
Results Tables
Table A3.2 – Sensitivity Analysis
|
|
SMART TICKETING SENSITIVITY ANALYSIS |
Core |
Capital Costs + 50% |
Capital Costs + 100% |
Operating Costs + 50% |
Operating Costs + 100% |
|||||
|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
|
NPV |
BCR |
NPV |
BCR |
NPV |
BCR |
NPV |
BCR |
NPV |
BCR |
|
0 |
Base case |
414 |
14.6 |
410 |
13.0 |
406 |
11.7 |
402 |
10.6 |
391 |
8.3 |
|
1 |
Bus boarding time: no time saving |
269 |
9.8 |
265 |
8.7 |
261 |
7.9 |
257 |
7.1 |
246 |
5.6 |
|
2 |
Bus boarding time: two seconds slower |
124 |
5.1 |
120 |
4.5 |
116 |
4.1 |
113 |
3.7 |
101 |
2.9 |
|
3 |
Passenger take up of smartcards is 75% |
308 |
13.4 |
304 |
11.8 |
301 |
10.5 |
299 |
9.9 |
290 |
7.8 |
|
4 |
Passenger take up of smartcards is 50% |
202 |
11.7 |
199 |
10.0 |
196 |
8.7 |
196 |
8.7 |
189 |
7.0 |
|
5 |
Passenger take up of smartcards is 25% |
97 |
8.3 |
94 |
6.9 |
91 |
5.8 |
93 |
6.5 |
89 |
5.3 |
|
6 |
Passenger take up of smartcards is 10% |
34 |
4.5 |
32 |
3.5 |
29 |
2.9 |
32 |
3.7 |
30 |
3.1 |
|
7 |
Patronage increases by 2% (base case = 4%) |
333 |
11.9 |
329 |
10.6 |
325 |
9.6 |
321 |
8.7 |
310 |
6.8 |
|
8 |
Patronage increases by 1% (base case = 4%) |
292 |
10.6 |
289 |
9.4 |
285 |
8.5 |
281 |
7.7 |
270 |
6.1 |
|
9 |
Patronage increases by 0% (base case = 4%) |
252 |
9.3 |
248 |
8.2 |
244 |
7.4 |
241 |
6.7 |
229 |
5.3 |
|
10 |
Reduce number of people on a bus to 5 |
340 |
12.2 |
336 |
10.8 |
333 |
9.7 |
329 |
8.8 |
317 |
6.9 |
|
11 |
Combination of sensitivities: no time saving and 10% take up |
20 |
3.0 |
17 |
2.4 |
15 |
2.0 |
18 |
2.5 |
15 |
2.1 |
|
12 |
Combination of sensitivities: 2 seconds slower to board and 10% take up |
6 |
1.6 |
3 |
1.2 |
0.4 |
1.0 |
3 |
1.3 |
1 |
1.1 |
NPVs are expressed in £millions.
Table A3.2 – Sensitivity Analysis Continued
|
|
INTEGRATED TICKETING SENSITIVITY ANALYSIS |
Core |
Capital Costs + 50% |
Capital Costs + 100% |
Operating Costs + 50% |
Operating Costs + 100% |
|||||
|
|
|
NPV |
BCR |
NPV |
BCR |
NPV |
BCR |
NPV |
BCR |
NPV |
BCR |
|---|---|---|---|---|---|---|---|---|---|---|---|
|
0 |
Base case |
403 |
14.7 |
402 |
14.2 |
401 |
13.8 |
390 |
10.0 |
376 |
7.6 |
|
1 |
Bus boarding time: no time saving |
186 |
7.3 |
185 |
7.1 |
184 |
6.8 |
172 |
5.0 |
159 |
3.8 |
|
2 |
Passenger take up of smartcards is 75% |
299 |
13.5 |
299 |
13.0 |
298 |
12.7 |
288 |
9.2 |
277 |
7.0 |
|
3 |
Passenger take up of smartcards is 50% |
196 |
11.5 |
196 |
11.2 |
195 |
10.9 |
187 |
7.8 |
179 |
5.9 |
|
4 |
Passenger take up of smartcards is 25% |
94 |
8.1 |
94 |
7.9 |
93 |
7.8 |
87 |
5.5 |
81 |
4.1 |
|
5 |
Passenger take up of smartcards is 10% |
33 |
4.3 |
33 |
4.2 |
32 |
4.2 |
28 |
2.9 |
23 |
2.2 |
|
6 |
Patronage increases by 2% (base case = 4%) |
322 |
11.9 |
321 |
11.5 |
320 |
11.2 |
308 |
8.2 |
294 |
6.2 |
|
7 |
Patronage increases by 1% (base case = 4%) |
281 |
10.6 |
280 |
10.2 |
279 |
9.9 |
267 |
7.2 |
254 |
5.5 |
|
8 |
Patronage increases by 0% (base case = 4%) |
240 |
9.2 |
239 |
8.9 |
238 |
8.6 |
227 |
6.3 |
213 |
4.8 |
|
9 |
Reduce number of people on a bus from 10 to 5 |
293 |
11.0 |
292 |
10.6 |
291 |
10.2 |
279 |
7.5 |
265 |
5.7 |
|
10 |
Combination of sensitivities: no time saving and 10% take up |
11 |
2.1 |
11 |
2.1 |
11 |
2.1 |
6 |
1.4 |
1 |
1.1 |
NPVs are expressed in £millions.
The potential negative time saving applied to the other ticket types as sensitivity is associated with the time taken for electronic readers to read smart cards so is not applied to (non-smart) integrated ticketing.
Table A3.2 – Sensitivity Analysis Continued
|
|
SMART INTEGRATED TICKETING SENSITIVITY ANALYSIS |
Core Case |
Capital Costs + 50% | Capital Costs + 100% | Operating Costs + 50% | Operating Costs + 100% | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
|
NPV |
BCR |
NPV |
BCR |
NPV |
BCR |
NPV |
BCR |
NPV |
BCR |
|
0 |
Base case |
543 |
19.7 |
539 |
17.6 |
540 |
17.9 |
532 |
14.3 |
521 |
11.2 |
|
1 |
Bus boarding time: no time saving |
397 |
14.7 |
393 |
13.1 |
390 |
11.8 |
386 |
10.7 |
375 |
8.4 |
|
2 |
Bus boarding time: two seconds slower |
251 |
9.7 |
247 |
8.6 |
244 |
7.8 |
240 |
7.0 |
229 |
5.5 |
|
3 |
Passenger take up of smartcards is 75% |
404 |
18.1 |
400 |
15.9 |
397 |
14.2 |
395 |
13.3 |
387 |
10.5 |
|
4 |
Passenger take up of smartcards is 50% |
265 |
15.6 |
262 |
13.4 |
259 |
11.7 |
259 |
11.7 |
253 |
9.3 |
|
5 |
Passenger take up of smartcards is 25% |
128 |
11.0 |
126 |
9.1 |
123 |
7.7 |
125 |
8.6 |
121 |
7.0 |
|
6 |
Passenger take up of smartcards is 10% |
47 |
5.9 |
44 |
4.6 |
42 |
3.8 |
45 |
4.8 |
42 |
4.0 |
|
7 |
Patronage increases by 3% (base case = 6%) |
421 |
15.5 |
417 |
13.8 |
414 |
12.5 |
410 |
11.3 |
399 |
8.8 |
|
8 |
Patronage increases by 2% (base case = 6%) |
380 |
14.1 |
376 |
12.6 |
373 |
11.3 |
369 |
10.2 |
358 |
8.0 |
|
9 |
Patronage increases by 0% (base case = 6%) |
298 |
11.3 |
295 |
10.1 |
291 |
9.1 |
287 |
8.2 |
276 |
6.4 |
|
10 |
Reduce number of people on a bus to 5 |
469 |
17.2 |
465 |
15.3 |
462 |
13.8 |
458 |
12.5 |
447 |
9.8 |
|
11 |
Combination of sensitivities: no time saving and 10% take up |
32 |
4.4 |
30 |
3.4 |
27 |
2.8 |
30 |
3.6 |
28 |
3.0 |
|
12 |
Combination of sensitivities: 2 seconds slower to board and 10% take up |
18 |
2.9 |
16 |
2.3 |
13 |
1.9 |
16 |
2.4 |
14 |
2.0 |
NPVs are expressed in £millions.