(s/b 10M / 100M = 10%). He is interchanging the terms and he should have written things differently to avoid confusion. It s/b "yield = annual earnings/purchase price", not "interest rates = annual earnings/purchase price". (He does correct himself later in the paragraph.)
Just, one more thing... how did he go from the 10% yield ($100M / 10M = 10% yield) to "if interest rates are 5% instead of 10%, then you would pay $200mm for the business ($10mm/$200mm = 5%)." Is he simply interchanging the word "yield" with "interest rates" or actually talking about the central bank?