"affect the cost" is a perfectly correct and usable phrase in written English.
You might use it in a sentence such as "The rise in energy costs could adversely affect the cost of production."
What variables affect the cost of product placement?
Did it affect the cost of your insurance?
But it's not like it's going to affect the cost of credit a whole lot".
How would these figures affect the cost of the surveillance system?
Williams added that he expected the outbreak would not affect the cost of Thanksgiving turkeys.
The changes do not affect the cost of making the cigarettes, industry officials say.
Training regulations directly affect the cost-benefit ratio of apprenticeship training.
Especially when vaccines confer modest direct protection, the indirect and overall effects of widespread vaccination may affect the cost-effectiveness of vaccination.
Environmental characteristics that affect the cost-benefit trade-off of grouping vary in space and time.
However, many variables will affect the cost-effectiveness analysis.
However, the changes do not affect the cost-value ratios sufficiently to change the ranking.
