The optimal capacity expansion time is an essential problem especially in capital intensive industries, and capacity expansion decisions have a great influence on the firm's operations and profitability. It can be said that the timing question is quite complex, and in practice the experience and intuition of the decision-makers have a central role. We can, however, use theoretical models to explain many essential relations and deepen our understanding of the nature of capacity changes. The actual object of this study is to develop a unit cost minimization model for the timing of capacity expansion. The model is based on the costs and capacities of old and new machines, and the arithmetic growth rate of demand. The analytical solution of the model shows that the relative timing of expansion can be presented with cost advantage and capacity change ratios. It is also shown that the analogical model can be used for capacity replacement and cutting. Finally, the model is extended, and it is shown that such timing can be found which minimizes unit costs and maximizes the profit of the planning period. The original contribution of the study is to suggest an alternative evaluation method for the timing of capacity changes and to present an analytical solution to the formulated problem. The presented model is applied to an illustrative case where capacity addition is planned either through expansion or replacement. The suggestion of the model to the case company is that it is preferable to replace the old machine with a bigger one rather than to acquire a totally new machine.