It is a well-known fact that one of the most important determinants of growth is private investment. But in the developing country context of widespread poverty, the effects of initial conditions on the process of capital accumulation have seldom been investigated. This paper highlights heterogeneity in the process of capital accumulation across different countries in Sub-Saharan Africa, and derives a formal specification of investment functions in the primary, industry, and service sectors in the region using a variation of the combined Tobin's Q Theory and the neoclassical models of investment. The results highlight a more rapid accumulation of capital in the relatively high income subpanel and a widening public-private capital accumulation gap. A functional specification points to the significance of aggregate profitability shocks, the financing cost of investment, and public capital stock in estimating the growth rate of private capital accumulation. These results are supported empirically, as highlighted by the relatively small absolute deviation between actual and predicted value distributions.