Investment timing with fixed and proportional costs of external financing

We develop a dynamic model in which a firm exercises an option to expand production with cash balance and costly external funds. While related papers explain their results only by numerical examples, we analytically prove the following results. In the presence of only a proportional cost of external financing, the firm with more cash balance invests earlier; however, the presence of both proportional and fixed costs leads to a non-monotonic relation between the investment time and cash balance. The firm with more cash balance invests later to save a fixed cost, particularly when the cash balance is close to the investment cost. Our results can potentially account for a variety of empirical results concerning the relation between investment volume and financing constraints.Real options; investment timing; costly external financing; growth option; optimal stopping.