Hedge with equity future- why sometimes we need to multiply (1+r)

We multiply by 1+r?

I guess you are trying to fine the future value of a futures contract using the current price. You need to multiply by (1 + r) in order to create an arbitrage free transaction. If you don’t do it that way investors will force it to that price as they structure products to create arbitrage out of it.

Are you referring to synthetic positions (e.g., synthetic cash of synthetic S&P)? If it says synthetic, then we have to raise it by 1+risk free rate.

Futures price embodies the interest cost of borrowing . so you cannot ignore the (1+r) term. Remember all things being equal ( i.e. no storage costs or convenience yield etc. ) , futures price could be approximated as spot*(1+r)^t.

I think it is because cash (either synthtic cash or cash on hand) is involed and no arbitragy shall be exploited.