In the decumulation phase of a pension plan, consumption depends on the level of annuitization. We measure the welfare loss of an individual with a demand for annuitization if he has no access to annuitization or, equivalently, does not use such access. Unlike earlier studies of the value of the annuity option, both individuals with and without access to annuitization, respectively, are offered complete flexibility in the consumption/payout profile. In that sense, we assume that the financial institutions (are allowed to) design the best possible products in the two regimes, with and without annuitization. We find for realistic parameters that a patient individual with time-additive preferences loses 22% of wealth upon retirement if not annuitizing. Sensitivity studies show that the relative loss decreases with a higher interest rate, a higher market price of financial risk, a higher market price of mortality risk, more certainty in the lifetime distribution, and a lower elasticity of intertemporal substitution. Further, we analyze a suboptimal bank product based on conditional expected residual lifetime.