What is meant by 废钱？ I can't understand the reference here. Is there such a thing as 'waste money， 废钱' in China? Or is it 'abandoned， discarded money'? Who threw the money there '我们‘ or 其他人？？ Is he alluding to some story or 成语？

那还能不同意？ 这就好比我们家后院扔着一堆废钱，你要拿它给我换一辆汽车。 我不光同意，甚至还有点儿不敢相信呢！

这就好比我们家后院扔着一堆废钱，你要拿它给我换一辆汽车。

I translate:
That's like someone threw a pile of money in our backyard and then you come along and offer to give me a car in exchange for it.

(Seems a weird idea, because first you need to know how much money it is. Could be more than the value of a car.)

PS: if you have any waste money, you can throw it my way!
Your reference is very likely comes from this Japanese Chinese teaching book 1, and the character "钱" actually is a typo of "铁", this is a very common mistake when people type Chinese in Wubi Input Method (or 五笔字型输入法". 

废铁 is scrap metal (for recycling), it perfectly fits the surroundings (后院 backyard), put it in the context this sentence's meaning: 
If you can trade this this not valuable thing (废铁) to a way much more valuable thing (汽车) for me, I'll be not only happy to agree but also surprised.

You can see in the linked book, the conversation is the girl (maybe a producer) asks Mr. Wang, will he agree to let them adapt his Internet novel to a TV show, so Mr. Wang made a humble and humorous metaphor. (The context is Mr. Wang wrote more than 30 novels, only two of them got published)