The group, which includes the Evans Halshaw, Stratstone and Car Store chains, has carried out a review of its estate and operational structure.
There are Evans Halshaw dealerships in Shrewsbury, Stourbridge, Walsall, Worfield and Wolverhampton, and a Stratstone site in Wolverhampton.
Pendragon is not saying which dealerships are at risk of closure at this stage or when the closures will take effect. It will be left with 150 dealerships across the country.
The impact of Covid-19 has accelerated the review of the group's future operating model, which had begun before the pandemic struck.
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The board plans to shut the 15 sites – seven freehold and eight leasehold – which are mainly loss making and no longer expected to be viable. Combined, these stores made an operating loss before tax around £2 million in the last financial year.
A total of about 400 redundancies are expected from these locations with estimated one-off cash redundancy costs of £1.2m and closure costs of approximately £1m.
The board has decided that a leaner and more sustainable operating model is necessary to safeguard the Pendragon business and position it to deliver improved results over the short to medium-term, against what is expected to remain a challenging economic environment.
This decision has been taken as a result of work undertaken pre-Covid-19 and follows efficiency gains achieved during the lockdown and in the subsequent reopening programme.
The proposed changes to the operating model are expected to result in approximately 1,400 redundancies and, subject to consultation, are expected to deliver an annual reduction in costs of £35m, with an estimated one-off cash restructuring cost of approximately £5m.
The Group is entering into 45-day redundancy consultations with a number of its employees across the business.
Chief executive Bill Berman said: "The above proposals reflect our intention to create a resilient, leaner and more profitable business across the entire group. These have been difficult decisions for the board to make and our priority now is to manage the transition to our new operating model.
"The Covid-19 pandemic is a uniquely challenging situation and we want to protect as many jobs as we can sustainably and the proposed redundancies are, of course, extremely regrettable. During the pandemic we have focused on ways to improve workflow, efficiency and our digital capabilities.
"It is paramount that we embed these behaviours into all areas of the business, as we expect the economic environment to remain challenging. The actions that we are undertaking are for the long-term health and success of the group and ensure that we emerge from the pandemic as a more competitive and stronger business with the ability to thrive in the future.
"I would like to take this opportunity to thank every one of our employees for the hard work that has been done to reopen our businesses from lockdown. I am proud of the essential work we undertook to assist key workers during lockdown and for the way we have served our customers in store and online during these difficult times."