Why is President paid more than PM?

I BELIEVE a person should be paid according to the value he contributes to an organisation vis-a-vis the market. Thus, our Prime Minister should be compensated adequately as he is steering the future of Singapore. However, what baffles me is that the President's salary exceeds the Prime Minister's. With due respect to our elected President who acts as an additional custodian of our national reserves and as ceremonial head of state, I find it hard to align the values of the two roles. An analogy will illustrate what I mean: The auditors or independent directors of a public company are never paid more than the CEO of the company.