The largest and most powerful automobile offered by the Fjord Motor Company in North America is the
Question:
The largest and most powerful automobile offered by the Fjord Motor Company in North America is the Coronet Elizabeth. Like Fjord's other models, the Coronet Elizabeth is sold through two different channels. Most cars are sold to the public through Fjord's nationwide network of dealers. However, the Coronet Elizabeth is also a popular model for fleet purchases, particularly by police departments and corporate fleets and Fjord maintains a separate direct channel for fleet sales.
Fjord defines fleet sales as those that include 10 or more vehicles. Most fleet sales are negotiated by Fjord's regional sales network. (A handful of very large deals involving hundreds of cars and mixed fleets are handled by a national sales team.) For the purposes of this problem, you can assume that each fleet purchase is strictly for Coronet Elizabeth's and that each bid proceeds by the buyer specifying the number of vehicles that he wishes to purchase, followed by Fjord submitting a sealed a bid for the order specifying Fjord's price for satisfying the bid. Bids are competitive but typically Fjord does not know who they are bidding against nor the size of the bids submitted by the other competitors. After evaluating all bids, a buyer will tell Fjord whether or not Fjord has won the deal1.
All fleet sales are for a "plain vanilla" (e.g. standard) version of the Coronet Elizabeth. This version costs Fjord $15,000 per vehicle to make and the Manufacturer's Suggested Retail Price (MSRP) is $25,000. However, all fleet bids are somewhere between the cost (at which Fjord makes no margin) and the MSRP (at which the buyer receives no discount). Fjord makes about 4,000 fleet bids per quarter and wins almost 70% of them. According to Fjord management about half of the bids are to police departments and half are to corporate fleet purchasing departments.
Fjord management has recently become concerned that its fleet sales staff have been "leaving money on the table" through inconsistent and capricious bidding and has hired you as a consultant to help Fjord institute a more rational pricing process for fleet sales. As part of this effort, they have given you the data on the spreadsheet. This data is the information available for all 4,000 bids made by the regional sales group during the last quarter of 2007. Unfortunately, due to difficulties reconciling the pricing database with the CRM database, this data does not include any information that would allow you to differentiate between bids to police departments and bids to corporations.
1. On the basis of the data in the spreadsheet, find a two-parameter logistic model that best estimates the probability of winning each bid as a function of the discount from list price assuming that a single price per unit will be offered for each bid. The model you are fitting is (p) = 1/(1+exp(a +bp)), where is the probability of winning the bid and a and b are the parameters to be estimated. p is the price that Fjord bid on a deal expressed as a fraction of the MSRP of $25,000 per unit - that is if Fjord bid $20,000 per unit, p would be equal to 20,000/25,000 or 8.
What are the values of a and b that maximize the sum of log likelihoods?
What is the optimum price that Fjord should offer assuming that it is going to bid at a single price for each bid?
What would the expected total contribution have been for the 4,000 bids?
How does this compare to the contribution that Fjord actually received?
International Marketing And Export Management
ISBN: 9781292016924
8th Edition
Authors: Gerald Albaum , Alexander Josiassen , Edwin Duerr