Congressional Budget Office Cost Estimate: H.R. 1924, Kenneth P. Thompson Begin Again Act [open pdf - 161KB]
From the Document: "H.R. 1924 would increase the number of first-time offenders who could have their records expunged following a conviction for simple drug possession. Under current law, people who are found guilty of a simple drug possession offense under federal law can be ordered by a judge to undergo a period of probation, rather than being charged with a crime, if they have not previously been convicted of a drug offense under federal or state law. Offenders who successfully complete the probation program, and who were under the age of 21 at the time the offense was committed, can then apply for expungement of their federal record."
Congressional Budget Office: http://www.cbo.gov/