The kinematic dependences of the relative production rates, \(f_{\Lambda_b^0}/f_d\), of \(\Lambda_b^0\) baryons and \(\bar{B}^0\) mesons are measured using \(\Lambda_b^0 \rightarrow \Lambda_c^+ \pi^-\) and \(\bar{B}^0 \rightarrow D^+ \pi^-\) decays. The measurements use proton-proton collision data, corresponding to an integrated luminosity of 1 fb\(^{-1}\) at a centre-of-mass energy of 7 TeV, recorded in the forward region with the LHCb experiment. The relative production rates are observed to depend on the transverse momentum, \(p_T\), and pseudorapidity, \(\eta\), of the beauty hadron, in the studied kinematic region \(1.5 < p_T < 40\) GeV/\(c\) and \(2 < \eta < 5\). Using a previous LHCb measurement of \(f_{\Lambda_b^0}/f_d\) in semileptonic decays, the branching fraction \(\mathcal{B}(\Lambda_b^0 \rightarrow \Lambda_c^+ \pi^-) = \Big( 4.30 \pm 0.03 \,\, ^{+0.12}_{-0.11} \pm 0.26 \pm 0.21 \Big) \times 10^{-3}\) is obtained, where the first uncertainty is statistical, the second is systematic, the third is from the previous LHCb measurement of \(f_{\Lambda_b^0}/f_d\) and the fourth is due to the \(\bar{B}^0 \rightarrow D^+ \pi^-\) branching fraction. This is the most precise measurement of a \(\Lambda_b^0\) branching fraction to date.