30 min or 60 min fine. This note derives three conditions under which affine or piecewise-linear contracts emerge in the classical principal-agent model of \cite{Holmstrom1979}. Specifically, augmenting fixed pay with equity or call options is optimal when: (1) the agent has logarithmic utility, (2) the principal is risk-neutral, and (3) the agent's effort induces an exponential tilt in the output distribution. Importantly, as the baseline distribution is unrestricted, affine contracts can be optimal regardless of the shape of the output distribution. When a lower bound on compensation is required to ensure existence of an optimal contract, the optimal contract is iecewise linear, comprising a fixed wage and a call option on output.