The LPL Inc. train company manages the passenger transport service by train on two lines in the northern suburbs of the city of Montreal (Blainville – Saint-Jérôme and Deux-Montagnes).

The LPL Inc. train company derives its revenue from the following sources.

On the one hand, users pay for the tickets. There are two modes of purchase: the monthly pass giving the right to an unlimited number of trips and the regular pass, good for one trip on the day the pass is acquired.

On the other hand, the company receives an annual subsidy of $2,500,000.00 from the Ministère des Transports and contributions from the municipalities served by the network from a portion of the gas tax. These municipal contributions total $1,500,000.00 annually.

The company must, moreover, disburse substantial amounts as expenses. Station maintenance costs an average of $35,000.00 per station per year (sanitary maintenance, repairs, painting, etc.), while track maintenance (rails) costs an average of $12,500.00 per kilometer of track per year (which includes preventive inspection of the rails, preventive maintenance, replacement of defective parts, parts and labor included). Finally, the maintenance of the trains (one per circuit) amounts to an average of $17,000.00 per kilometer of track, per year per train.

In addition, the operation of the trains requires, per train, one driver and eight security and ticket check attendants. Each driver earns $60,000.00 per year while the attendants earn, annually and individually, $50,000.00. A contingency of 16% must be added for staff remuneration to take into account social benefits.

The company accumulates annual fixed management costs in the order of $7,500,000.00 and it wishes to make a net profit after tax of the order of 10% on its sales.

Your task is to propose a price list to the company. You must offer for each fare zone an amount for annual subscriptions and for individual passages.

To perform your calculations, you will need to take into account the fact that passengers who prefer to pay each passage make an average of 12 journeys per month, while those who opt for monthly subscriptions do so on average eight months per year (taking into account holidays and the fact that a large proportion of subscribers subscribe in the winter but prefer to use the car or bicycle when the weather allows it).

The fare zones are determined according to the distance from the station at which the user takes (and leaves when returning) the train and the terminal in downtown Montreal. The further away the station, the higher the number identifying the fare zone of the station and, consequently, the higher the fare. However, regardless of the circuit, the tariff must be the same for the entire network for stations in the same tariff zone.

In addition, for your pricing proposal, the monthly fare must never exceed 10 times the monthly fare in the same fare zone because we want to encourage users to use the train frequently and want to offer pricing that makes the purchase of 'a monthly pass for anyone planning to use the train at least 10 times during the month.

 

The following table contains all the useful information for your work. Blainville-St-Jerome Two-Mountains Station Lucien L'Allier Vendome Montreal West Canora Park Chabanel Bois de Boulogne From Concord Vimont Sainte-Rose Rosemere Sainte-Therese Blainville Mirabel St. Jerome Canora Mont Royal Montpellier From the Stream Bois-Franc Sunnybrooke Roxboro-Pierrefonds lle-Bigras Sainte-Dorothee Big Mill Two-Mountains Distance (km from previous station) 2 3 4 8 2 2 2 4 7 4 3 3 5 7 11 6 1 2 3 1 8 3 5 2 5 3 Tariff zone 1 1 1 1 1 1 2 3 3 3 5 5 6 7 7 1 1 1 2 2 2 2 3 3 5 5 Population served 0 0 0 0 0 0 0 25000 35000 18000 28000 19000 22500 14000 25000 0 0 0 0 0 35000 28000 8000 38000 39000 27500 Percentage of population served Market for Market for monthly subscriptions regular passage 1.50% 2.00% 4.50% 4.00% 6.00% 5.00% 9.00% 11.00% 3.00% 4.50% 8.00% 7.50% 7.00% 11.00% 2.00% 2.00% 2.00% 3.00% 5.00% 7.00% 5.00% 6.00% 3.50% 4.00% 8.00% 6.50% 9.00% 11.00%