I doubt that Germany could build a Spitfire for less then half the cost of a British built aircraft.
So do I. But then I doubt the Spitfire cost twice as much as the 109.
Olaf Groehler, I believe, quoted the price of the Bf 109E as about 86,000 RM with engine, 58,000 without. The British government paid close to £9,000 for the first batch of Spitfires, dropping to just over £5,000 in 1940, presumably without engine. There were about 11 RM to the pound at the fixed exchange rates.
German Aircraft Industry and Production 1933 - 1945 by Vajda and Dancey says the Bf 109E was offered for export in 1939 at a price of 162,000 RM each. France bought a Spitfire before the war, with spare engine the price was about £16,500. Turkey ordered Spitfires at £11,700 each, Greece paid just over £9,300 each. Estonia paid £12,604 for 12 Spitfires in early 1939.
Of course, we can't be certain what's included in those prices. They must be for completed aircraft, but what about spares, technical training and support etc? That's the problem with comparing figures from different sources. At the cheapest you can find an airframe only price, at the most expensive a complete aircraft with spares. And just about every variation in between.
That's why the German report is useful, because it compares to the same standard. It gives the price of the 109 as 15,000 RM (airframe only) and says the Spitfire, built in German factories, would cost 12,500 RM.
As to the Germans building Spitfires at half the cost of the British, that's not likely early in the war. Britain had far fewer people employed in the aircraft industry than Germany yet produced more aircraft.
Late war when the Germans were using slave labour things may have changed. According to Tooze in Wages of Destruction a factory could rent a skilled metalworker slave from the SS for about 40% of the cost of a German metalworker, and despite lower productivity, that led to lower unit costs.