Fractional Triplets

Consider this puzzle. Three brothers – Youngest, Middle and Oldest – each receive some money in the form of some inheritance. Youngest keeps half the amount he receives and divides the balance equally among Middle and Oldest. After Middle receives his share, he too keeps half the amount and distributes the balance equally among Youngest and Oldest. Oldest in turn keeps half of the amount he now has (after receiving the shares from his brothers) and divides the remaining equally among Youngest and Middle. At the end, if all three of them have equal amounts, can we determine how much each of them had at the start? If so, how do we do so? If not, why not?

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