If the FA increased the prize money for the FA Cup would managers/chairmen take the competition more seriously?

The prize money for the FA Cup 2013/14 is set out below:


Prize Money Run Total:
5th round – £337,500
6th round – £697,500
Semi-Final Loser – £1,147,500
Semi-Final Winner – £1,597,500

The estimated financial return for each Premier League position is set out below:


The Premier League winner of the FA Cup will accrue £3,397,500 in prize money.
The Merit Payment awards each Premier League position £1,126,750 more than the one below it.

Winning the FA Cup is the financial equivalent of finishing 3 positions higher in the Premier League based on the Merit Payment alone.