Realistic system and link level simulations require specific information about the radio channel. A key role is played by the power delay profile which is widely agreed to be a negative exponential characterized by the delay spread. Since this finding is based on empirical evidence only, the delay spread must be derived from measured data. The power delay profile is rigorously derived by combining ray optical and statistical properties of wave propagation in a single room. We show that the power delay profile is indeed a negative exponential and provide a decay constant which serves as an analytical upper bound for experimentally obtained delay spreads of indoor environments. To the best knowledge of the author, this is the first derivation of the power delay profile from first principles.