Alright, lets take a look:
Mira AKA
Omicron Ceti is about 400 light years away, and is a variable star with a 331 day period. It's diameter is huge, being at times large enough that were it in the Sun's place, it would cover part of the asteroid belt between Mars and Jupiter. It also changes in outward brightness by a variable amount, but has been observed over nearly a factor of 10,000. At its dimmest, it is less bright than the Sun.
Let's imagine that the ESA decides to send an unmanned mission to this star, to explore close up what this star is like. An all out effort is made to try and get there as soon as possible.
They look at the energy requirements, and conclude that they need to build a fusion powerplant more of less like the ITER reactor, but larger, and in space (See
http://www.iter.org/index.htm ). This space-based reactor will be designed to generate a continuous 10 gigawatts, have a mass of one thousand tons. The spacecraft will also carry one hundred thousand tons of deuterium which it will fuse to create the power for the trip. The rest of the ship will include a hundred tons of combined structure and payload.
The plan is that this ship will get up to 0.02c, and then turn around to decelerate. The one way trip will last forty-thousand years. Plans are made to keep increasing the budget for the listening stations to detect the increasingly weak signal from the probe over the course of the 400 centuries it takes to get to the target.
Some administrators object noting that there is a risk that this star will explode before the mission can get there, while others say that would provide spectacular information, and is all the more reason to send the mission.
The budget is put together. The cost of the fuel deuterium is brought down to about $70 Euros/ kilogram because of the economies of scale, though another $1000 Euros/kilogram must be added for getting it to orbit. So, for the fuel alone we are looking at 107 billion Euros for the fuel. The reactor is expected to cost seventy billion Euros to build, but the good news is that it will only cost a billion Euros to put its parts in orbit, and another nineteen billion to assemble the parts in space. So, ninety billion Euros for that. Finally is the structure, and the payload. These parts will cost one billion to launch into space, and nineteen billion to assemble the parts in space. However, the development cost of probes and instruments that will work for forty-thousand years through all kinds of radiation and other problems. This cost is estimated at two trillion Euros.
One risk is that there is an assumption that the cost of getting to orbit will drop to $1000/kg.
So the budget to launch this mission is 2.2 trillion Euros with an expected payoff for this expense in forty-thousand, four hundred years. The econmists are ecstatic, and the taxes on the European member states are increased about a thousand Euros per person per year to cover the expense, and the new tax is passed by an overwhelming majority.
Fifty years from now, the mission launches.