capacitor
Why do you need to store the voltage for some time in a capacitor? I've always assumed circuits to work when you power it on and stop when you power it off.
Why can't the whole circuit be drawn capacitor free? If it's meant for storage why not just use a flip-flop?
Appropriate bleeder resistors are the usual solution. They aren't usually switched, although they can be.
The value depends on the time you require to discharge the capacitors. The formula is
$$ V_{t} = V_{0} \, e^{ -t / RC } $$
where \$V_{t}\$ is the voltage at time t and \$V_{0}\$ is the initial voltage at time 0. It's an exponential function, so I'd just assume 1/10 of the initial voltage.
It isn't a power function, as someone edited it!
You should find that the power taken by the bleeder resistors is negligible compared to the 120W capability of the supply.
The most likely reason why that is done is because, in real life, capacitors do not have infinite bandwidth. Generally, the higher the capacitance of the capacitor, the less it will be able to react to high frequencies, while small-valued capacitors react better to higher frequencies, as seen in the graph below. Using two different-valued capacitors together is just done to improve the response of the filtering.
Best Answer
If all you wanted to build was digital circuitry, and your voltage sources really held constant voltage no matter how much current was drawn from them, and nothing produced electrical noise, you wouldn't need capacitors.
But voltage sources sag when you draw current from them. Motor brushes (and lots of other components) produce horrendous voltage spikes that you want to filter out of your digital circuitry. Some people also deal with analog circuitry, where voltage and current signals vary continuously across a wide range. For that kind of time-varying circuitry, capacitors are needed.