Hertz’s plan to acquire rival car hire company Dollar Thrifty is already being questioned by some shareholders.

Hertz announced it will buy the company for $41 per share in a mix of cash and Hertz shares based on Friday’s closing stock market prices.

However, Dollar Thrifty shareholders have paid to have the deal investigated by US law firm Finkelstein Thompson. They are concerned their shares have been undervalued and could be worth as much as $44 a share.

Hertz chairman and chief executive Mark Frissora said: “Combining Hertz and Dollar Thrifty is an excellent strategic fit.

“Dollar Thrifty is a $1.6 billion business with more than 1,550 corporate and franchise rental locations worldwide which, when combined with our global network, will serve rental customers on six continents from approximately 9,800 locations.

“Together we will be able to compete even more effectively and efficiently against other multi-brand car rental companies, offering customers a full range of rental options in the US between the Hertz, Dollar, Thrifty and Advantage brands.

“Dollar Thrifty also has a strong international presence, complementing our global footprint, which enables us to utilize a recognized brand to accelerate our leisure rental strategy in Europe and other markets.”

Dollar Thrifty president and chief executive Scott Thompson added: “The combination of Dollar Thrifty with a larger company like Hertz will provide Dollar Thrifty with greater resources and the technology needed to expand our value focused leisure brands.”