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Genomic selection has the potential to revolutionize dairy cattle breeding because young animals can be accurately selected as parents, leading to a much shorter generation interval and higher rates of genetic gain. The aims of this study were to assess the effects of genomic selection and reduction of the generation interval on the rate of genetic gain and rate of inbreeding. Furthermore, the merit of proven bulls relative to young bulls was studied. This is important for breeding organizations as it determines the relative importance of progeny testing. A closed nucleus breeding scheme was simulated in which 1,000 males and 1,000 females were born annually, 200 bulls were progeny tested, and 20 sires and 200 dams were selected to produce the next generation. In the "proven" (PROV) scenario, only cows with own performance records and progeny-tested bulls were selected as parents. The proportion of the genetic variance that was explained by simulated marker information (M) was varied from 0 to 100%. When M increased from 0 to 100%, the rate of genetic gain increased from 0.238 to 0.309 genetic standard deviations (σ) per year (+30%), whereas the rate of inbreeding reduced from 1.00 to 0.42% per generation. Alternatively, when young cows and bulls were selected as parents (YNG scenario), the rate of genetic gain for M=0% was 0.292 σ/yr but the corresponding rate of inbreeding increased substantially to 3.15% per generation. A realistic genomic selection scheme (YNG with M=40%) gave 108% higher rate of genetic gain (0.495 σ/yr) and approximately the same rate of inbreeding per generation as the conventional system without genomic selection (PROV with M=0%). The rate of inbreeding per year, however, increased from 0.18 to 0.52% because the generation interval in the YNG scheme was much shorter. Progeny-testing fewer bulls reduced the rate of genetic gain and increased the rate of inbreeding for PROV, but had negligible effects for YNG because almost all sires were young bulls. In scenario YNG with M=40%, the best young bulls were superior to the best proven bulls by 1.27 σ difference in genomic estimated breeding value. This superiority increased even further when fewer bulls were progeny tested. This stochastic simulation study shows that genomic selection in combination with a severe reduction in the generation interval can double the rate of genetic gain at the same rate of inbreeding per generation, but with a higher rate of inbreeding per year. The number of progeny-tested bulls can be greatly reduced, although this will slightly affect the quality of the proven bull team. Therefore, it is important for breeding organizations to predict the future demand for proven bull semen in light of the increasing superiority of young bulls.