Economic evaluation of scale dependent technology investments

We study the effect of financial risk on the economic evaluation of a project with capacity decisions. Capacity decisions have an important effect on the project's value through the up-front investment, the associated operating cost, and constraints on output. However, increased scale also affects the financial risk of the project through its effect on the operating leverage of the investment. Although it has long been recognized in the finance literature that operating leverage affects project risk, this result has not been incorporated in the operations management literature when evaluating projects. We study the decision problem of a firm that must choose project scale. Future cash flow uncertainty is introduced by uncertain future market prices. The firm's capacity decision affects the firm's potential sales, its expected price for output, and its costs. We study the firm's profit maximizing scale decision using the CAPM model for risk adjustment. Our results include that project risk, as measured by the required rate of return, is related to the inverse of the expected profit per unit sold. We also show that project risk is related to the scale choice. In contrast, in traditional discounted cash flow analysis (DCF), a fixed prescribed rate is used to evaluate the project and choose its scale. When a fixed rate is used with DCF, a manager will ignore the effect of scale on risk and choose suboptimal capacity that reduces project value. S/he will also misestimate project value. Use of DCF for choosing scale is studied for two special cases. It is shown that is the manager is directed to use a prescribed discount rate that induces the optimal scale decision, then the manager will greatly undervalue the project. In contrast, if the discount rate is set to the risk of the optimally-scaled project, the manager will undersize the project by a small amount, and slightly undervalue the project with the economic impact of the error being small. These results underline the importance of understanding the source of financial risk in projects where risk is endogenous to the project design.