Investment timing with fixed and proportional costs of external financing

Abstract

We develop a dynamic model in which a firm exercises an option to expand production with a cash balance and costly external funds. By proving the properties of the option exercise regions, we reveal how the firm's financing and investment policy depends on its cash flow and balance. 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 the 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 and internal funds.

The effects of external financing costs on investment timing and sizing decisions

“…When I 2 /I 1 (or (A 1 −1)/(A 2 −1)) is sufficiently low, i.e., in the first column, the financing and investment policy is the same as that of the case with only the large-scale project (fixed-scale investment model). This case is studied in details by Nishihara and Shibata (2011), and, hence, we omit the explanation. The second and third columns present more interesting panels, in which the firm optimizes the investment size as well as investment timing.…”

“…Recall 5 The term r(1 + C)I 2 dt is negligible when X(t) is high. 6 In all figures in this paper, we set the axes in the same way as Boyle and Guthrie ( 2003), Hirth and Uhrig-Homburg (2010b), and Nishihara and Shibata (2011) for comparison. This figure illustrates the cases in which…”

“…For comparison, we set the parameter values for the large-scale expansion at the same values as Nishihara and Shibata (2011). These parameter values are also similar to those of the standard real options literature.…”

“…Then, the firm never invests when Y (t) reach nearly I 1 = 50 or I 2 = 100, which leads to disconnected exercise regions. This fixed cost effect is documented in Nishihara and Shibata (2011) who examined the fixed cost effects in a fixed-scale investment model. Furthermore, we can see from Figure 5 that the fixed cost effect is strong particularly in the small-scale project.…”

“…2 Regarding the relation between the investment timing and cash holdings, Hirth and Uhrig-Homburg (2010b), who extended Boyle and Guthrie (2003) to a case with financing costs, pointed out the possibility of various non-monotonic relations, and Nishihara and Shibata (2011) proved that a fixed cost of external financing leads to a non-monotonic relation.…”