In September $2000,$ a report entitled Options to Improve Skytrain Passenger Safety &

Security to Reduce Fare Evasion was submitted by a consulting firm to the Skytrain

Authority. Two scenarios were considered for the new Skytrain Millennium Line $($see

table below$).$ Each option achieves the same level of safety and fare compliance.

Option Gates Proof of Payment

Description $$ Add turnstiles at all

stations

$$ Increase the number of

Skytrain attendants

$$ Double the number of

Skytrain attendants

$$ Increase the number of

Skytrain constables

Labour Costs $$21\mathrm{.}9$ million per year $$32\mathrm{.}8$ million per year

Capital Costs $$82\mathrm{.}3$ million $$35\mathrm{.}7$ million

The new Millennium Line was built in $2001$ and started operating in $2002.$ The

discount rate is $5\%.$

a$)$ Assuming each option lasts forever, which scenario would you financially prefer?

b$)$ How would you change your previous formulae if each scenario lasts only for $20$

years $($you do not have to calculate the new values$)?$

If any option is implemented, the increased Skytrain revenues are $$13\mathrm{.}2$ million $($in

present value terms$)$ due to better safety, and $$40\mathrm{.}8($in PV terms$)$ due to increased fare

compliance.

c$)$ What kind of additional information would you need to actually approve $($or not$)$

any of these two possible scenarios?

To combat fare evasion on buses, Translink will equip its buses with new electronic

fare boxes starting next week. The bus$-$related fare evasion that will be avoided after

the new boxes are in place is estimated at $$5$ million per year. The cost of installing

these buses is $$27$ million.

d$)$ Write down the condition that lets you determine how long it will take for these

new electronic boxes to $$break even$$ financially.In September $2000,$ a report entitled Options to Improve Skytrain Passenger Safety &

Security to Reduce Fare Evasion was submitted by a consulting firm to the Skytrain

Authority. Two scenarios were considered for the new Skytrain Millennium Line $($see

table below$).$ Each option achieves the same level of safety and fare compliance.

The new Millennium Line was built in $2001$ and started operating in $2002.$ The

discount rate is $5\%.$

a$)$ Assuming each option lasts forever, which scenario would you financially prefer?

b$)$ How would you change your previous formulae if each scenario lasts only for $20$

years $($you do not have to calculate the new values$)?$

If any option is implemented, the increased Skytrain revenues are $$13\mathrm{.}2$ million $($in

present value terms$)$ due to better safety, and $$40\mathrm{.}8($in PV terms$)$ due to increased fare

compliance.

c$)$ What kind of additional information would you need to actually approve $($or not$)$

any of these two possible scenarios?

To combat fare evasion on buses, Translink will equip its buses with new electronic

fare boxes starting next week. The bus$-$related fare evasion that will be avoided after

the new boxes are in place is estimated at $$5$ million per year. The cost of installing

these buses is $$27$ million.

d$)$ Write down the condition that lets you determine how long it will take for these

new electronic boxes to "break even" financially.