Uncertain Productivity Growth and the Choice between FDI and Export

Uncertain Productivity Growth
difference between the risk-adjusted return μ and the deterministic growth rate α represents the
rate of opportunity costs with

δu = μ — α.                                    (46)

For a positive δ_u , an investment exhibits an expected capital gain rate α which is lower than
the risk-adjusted rate of return μ. Therefore, by delaying the investment the investor incurs
an opportunity cost rate of δu. Consequently, for a high opportunity cost rate the immediate
execution of the respective investment is more likely because the corresponding option value will
be low, due to a low α.

Since in the underlying framework the cash-flows Miiïi increase exponentially in iï for κ > 1, it
is necessary to determine the corresponding risk-adjusted growth rate α⁰_u , which is derived as

α⁰_u = ακ + 2 κ(κ — 1)σ².                                (47)

Therefore, for both market entry modes the expected value of the cash-flows at time t can be
calculated by

E(M_i<) = M_i^^κκe^ακ+1 ^κ(^κ-1)^σ2    with i ∈{E,F}.                 (48)

Equation (48) shows that for linear periodical cash-cash flows (κ = 1) in iï, the expected value
is independent of the parameter σ. The investor expects the same profits as in the previous
deterministic case. However, for κ > 1 the expected profit-flows increase and are bigger the higher
the uncertainty in the productivity development becomes. This disproportionate expectation is
driven by Jensen’s inequality and has a positive impact on the current gross investment value in
both market entry modes. Given the risk-adjusted growth rate α_u⁰ the risk-adjusted total rate of
return results as

μU =^r + ^κ(μ ^— r)

and the risk-adjusted discount rate can be derived as

δU = r — (r — δu)κ — 2 κ(κ — 1)σ².

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