why companies do stock-split and repurchase shares almost at the same time?

Noticed that a company announced a 5-to-1 stock split and, in the same month, the same company announced a one-year share buyback program for its 1% of outstanding shares. The part that puzzles me is:

• The purpose of the stock was to increase liquidity. To this date, the stock increased ~10% (not suggesting that it is entirely because of the stock split), and given the fundamentals of the company, management must be aware that the price of the stock may benefit from the stock split.
• After two weeks of the stock split, the company announced a share repurchase program.

My question is: Let's say hypothetically that the management knows that the stock price will very likely increase. Aren't they going to repurchase shares at a higher price (than in a case of no stock split benefit)? Meaning, the company is not allocating capital efficiently?