Question: I'm working with a client whose sole selling point is affordability. They sell at low margins and aim for the cheapest of demographics. 

What are some UX or design decisions I can make to make their visitors feel like they are making a bargain?

Some obvious ones are large text for prices. Perhaps strike through list prices and show discounted prices in red and so on. But are there other ways to achieve "affordability"?

Answer: 
With this request I feel like you're starting to enter into the overlap of Marketing/UX - which can maybe explain why this might be a little different of a request.

Humans are strange creatures when it comes to purchasing - they want to feel like they got a good value (generally - not talking about purchasers that purchase due to high price - aka the very expensive Apple Watch - they purchase it because they can.) However, a good bargain does not always mean the lowest price; it has more to do with the value of the product vs the cost of the product. People want to feel like they paid less than they should've.

Some things that might help that (which again, this isn't entirely UX - this is more marketing/manipulative to the user)

1. Showing a "retail price" and then showing the price they want to sell it at.
2. Showing pictures of the demographic happily using the product.
3. Show reviews/testimonials of other people that have purchased the product. These should be real people.
4. Demonstrate that the company itself is trustworthy - this could be by things they do to give back to the community or even showing that they regularly post to social media.

Hope this helps. Encourage the company to be HONEST with everything - otherwise it will hurt them in the long run.
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> Perhaps strike through list prices and show discounted prices in red
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I think most people realize there's a level of bullshit involved with that. Test, obviously, but in general, I'd avoid that altogether. If you want to show that your prices are especially low, consider showing competitors prices along side. 

In general, the best way to show affordability is just as you suggest: focus on prices and have the business make sure they are good, affordable prices to begin with. 

Beyond that, there's likely a level of marketing and branding that needs to accompany this.