Color-magnitude diagrams of globular clusters usually exhibit a prominent horizontal branch (HB) and may also show features such as the red giant branch (RGB) bump and the asymptotic giant branch (AGB) bump. Stellar evolution theory predicts that the luminosities of these features will depend on the metallicity and age of the cluster. We calculate theoretical lines of 2-12 Gyr constant age RGB bumps and AGB bumps in the ΔV-[Fe/H] diagram, which shows the brightness difference between the bump and the HB as a function of metallicity. In order to test the predictions, we identify giant branch bumps in new Hubble Space Telescope color-magnitude diagrams for eight SMC clusters. First, we conclude that the SMC cluster bumps are RGB bumps. The data for clusters younger than ~6 Gyr are in fair agreement with our predictions for the relative age-dependent luminosities of the HB and RGB bump. The ΔV data for clusters older than ~6 Gyr demonstrate a less satisfactory agreement with our calculations. We conclude that ~6 Gyr is the lower bound to the age of clusters for which the Galactic globular cluster, age-independent ΔV-[Fe/H] calibration is valid. Application of the ΔV-[Fe/H] diagram to stellar population studies is discussed.