Extended warranty (and common shocks)

You are a quantitative analyst for Company X, which sells cheap digital cameras at €50 in the European market at a production cost of €20. The cameras are offered with a 1-year warranty that comes with a free replacement for failures during the warranty period.

A new model (MB4) of camera with the same price as the rest of the range is going to be sold in the Christmas period in 2014 and 25,000 sales across Europe are expected.

A recent study of the probability of failure suggests that the failure rate for a similar camera model (MB2) was 5% during the first year, although some differences amongst different European territories were noticed.

You can assume that:

i. You can only get one replacement a year.

ii. The overall replacement cost is €25 (= production cost + expenses including mailing expenses).

iii. If a camera is replaced, the warranty expiry date remains the original one: it does not start again from the date when the camera is received.

i. Calculate the expected cost of providing warranty cover for the lot of MB4 models sold during Christmas. Clearly state all the assumptions you make.

ii. Describe how you would calculate the 90th percentile of the statistical distribution of the costs (you do not need to carry out the actual calculations, only to set up the methodology clearly enough for one to follow). Clearly state all the assumptions you make.

iii. What are the main uncertainties around the expected cost calculated in (i)?