Uncertain Productivity Growth
3 THE OPTIMAL MARKET ENTRY MODE
3.2 FDI or Export with Productivity Growth
A more realistic scenario for productivity development can be modeled as
d$t = a$tdt
(23)
with α representing the productivity growth rate. Given the initial exponential cash-flows in
equation (16) and (17) it is necessary to adjust the growth rate for cases in which κ > 1. The
adjusted growth rate for convex profit flows results as
0 d$K
α = —— = ακ.
$к
(24)
Still, without any risk, the appropriate discount rate is equal to the riskless interest rate r.
Consequently, for both strategies the gross value of their periodical cash-flows is determined by
Z∞
Mi0κ(s)e-r^ds
(25)
with $K(s) = ^Keα0s and i ∈ {E, F}. (26)
T represents the time at which periodical profits start to flow and t the time at which the cash-
flows are evaluated, with $0 representing the current productivity state. Therefore, the gross
present value of growing periodical cash-flows (t=0) is given by7
Vi(0, T) = Mrκe-(r-α0)τ with δ,c = r - α0.
δc0
(27)
In contrast to the previous scenario an investor is not only confronted with the choice problem
between exporting and FDI. Additionally, a timing problem arises where the following net pay-offs
Fi ($) are optimized.
Fi(V) = max (M$-e r α T - ∕√ 'ʃ'ʌ , with $ = $0, i ∈ {E, F}. (28)
T r - α0
Equation (28) clearly illustrates the unequal total discount rates of the cash-flows and the fixed
costs. For α = 0 which represent the previous scenario, there is no reason to postpone or delay
7 A meaningful economic interpretation for the investment values result for r - α0 > 0. Under this condition it is
necessary that βc > κ > 1 with βc = α.
15
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