Let us also suppose that the study has 60% power to find an association with an odds ratio of 1.3 at α = 0.05. Then it can be estimated that if a statistically significant association is found with the p-value barely crossing the 0.05 threshold, the post-study probability that this is true increases about 12-fold compared with the pre-study probability, but it is still only 12 × 10−4.
http://plosmedicine.org/article/info:doi/10.1371/journal.pmed.0020124#article1.body1.sec5.boxed-text1.sec1.p1

This calculation assumes that the p-value of 0.05 is not corrected for multiple hypothesis testing. I'm not an expert in association studies, but I think it is considered a bad practice to use non-corrected p-values. If any correction for multiple hypothesis testing was applied (e.g. Bonferroni or Benjamini-Hochberg) the resulting ppv would be altered by 5 orders of magnitude...