Kelly with a Proportional Trading Cost

On an even-money coin with win probability $p$, each round you pay a proportional cost $c$ on the amount staked, regardless of the outcome. So staking fraction $f$, a win multiplies wealth by $1+f(1-c)$ and a loss by $1-f(1+c)$. Derive the growth-optimal fraction $f^*$ in terms of $p$ and $c$, evaluate it for $p=0.6,\ c=0.05$, and find the cost level at which the optimal stake drops to zero.