Entropy of Microwave Background Radiation in Observable Universe

We show that the cosmological constant at late time places a bound on the entropy of microwave background radiation deposited in the future event horizon of a given observer, $S\le S_{{\mathrm{\Lambda }}_0}^{3\mathrm{/}4}$. This bound is independent of the energy scale of reheating and the FRW evolution after reheating. We also discuss why the entropy of microwave background in our observable universe has its present value.