Uncertain Productivity Growth and the Choice between FDI and Export

Uncertain Productivity Growth

Finally, the net present investment values of both market entry modes associated with uncertain

productivity growth result as

For κ = 1 and σ = 0 the two net present value functions increase linearly in iï and they exactly
behave as in the deterministic scenario, because the opportunity cost rates are equal (δ_u⁰ = δ_c⁰ ).⁹
However, driven by Jensen’s inequality, both expected present investment values are higher than
in the previous scenario (Vi_u (iï) > Vi(iï)) if the cash-flows are convex in iï and if the productivity
growth is accompanied by uncertainty (σ > 0). Formally, the additional term 2κ(κ — 1)σ² ac-
counts for these additional expected gains in the investment values.

In figure 5 the two net present value functions shift to the north if productivity growth is associated
with uncertainty. Consequently, the intersection points between the horizontal axis and the
export and FDI investment value functions appear at lower productivity levels with iï⁰_E and iï⁰_F
representing the critical thresholds for positive values respectively for both market entry modes.
However, as in the previous scenario both market entry modes are associated with a timing
problem as the periodical cash-flows rise over time whereas the fixed costs Ii are unchanged and
appear only in the first investment period. Therefore, in order to assess whether there exits a
value of waiting, it is necessary to determine the option values of both investment strategies.

⁹ Equation (51) provides reasonable values if the interest rate r is strictly bigger than α.

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