QUESTION 1                                                                                                 

AutoSafeTech (AST) is considering marketing, at the start of next year, a new anti-theft device for motor vehicles.  Based on GPS technology, the device would be supplied free to customers. Customers would then pay an annual subscription for AST's monitoring services.  AST wants to estimate the accumulated profit at the end of the next 5 years.

Assume that

• there are 610,000 vehicles which could potentially use the device at the start of next year, and that this figure will grow each year.
• the annual percentage growth in the number of vehicles which could potentially use the device is Normally distributed with a mean of 5.4% and a standard deviation of 1.1%.
• the proportion (market share) of the 610,000 vehicles that AST will have as subscribers next year (ie, the first year) is modelled by the Triangular distribution, with a minimum of 25%, a most likely value of 40% and a maximum of 75%. If no competitors enter the market, AST expect to retain that market share.
• there are 3 potential competitors.
  • At the start of each year (including the first year), there is a 40% chance that any competitor who has not yet entered the market will enter during that year.
  • The year after it enters the market, a competitor will have impact on AST's market share.

Any competitor entering the market will capture 20% of the market share that AST had prior to that competitor's entry. eg, if AST had 60% market share, the entry of

*    1 competitor would reduce that 60% share to                                   60(1 - 0.2)        = 48%;

*    2 competitors in the same year would reduce that 60% share to        60(1 - 2*0.2)    = 36%.

o    Once a competitor has entered the market, that competitor will remain there.

o    If all 3 competitors have entered the market, no more competitors will enter.

o    The competitors behave independently.

• each annual subscription yields $220 revenue to AST.
• each subscriber costs AST $40 per year to service (including provision of the device).

(a) (i) Use simulation, with 1,000 iterations, to estimate the accumulated profit after 5 years for

AST.  (You may ignore the use of Net Present Value.)

(ii)  Provide a histogram and summary statistics for each of your output variable(s).

(b) From your simulation, report your findings on the estimated accumulated profit(loss) after 5 years for AST.Your responses do not need to be set out as a formal report, but should be succinct and directed to an imagined target audience of colleagues with a similar level of statistical knowledge to yours.  Substantiate your findings with suitable figures/tables/graphs - as appropriate.  Explain any additional assumptions that you have made.