Civil Engineering Reference
In-Depth Information
$10
$8
$6
V
3
*
$4
$2
V
2
*
V
1
*
$0
$0
$5
$10
$15
$20
V (Million)
σ
v =
0.2 ( V
2
* =
$11.9
; A
2
= $1.9)
σ
v =
0.1 ( V
1
* =
$10.5
; A
1
=
$1.7)
σ
v =
0.5 ( V
3
* =
$20.0
; A
3
=
$3.2)
Exercise Now
Fig. 3
Value of single-stage investment under uncertainty (Menassa
2011
)
The ratio V*/I is known as the critical ratio for investment to be undertaken
without waiting.
Equation (
2
) can then be used to determine whether it is optimal to invest at an
expected A = $1.65 million when there are different levels of uncertainty. Figure
3
shows the change in value of NPV
m
versus the expected benefits from the invest-
ment V, for different levels of r
v
. The results indicate that when the level of
uncertainty increases, the value of V* at which the option to NZER an existing
building increases. This in turn implies that investment should only be undertaken
in the future when A is greater than initially estimated $1.65 million even when
level of uncertainty is low at r
v
= 0.15 where the corresponding A = $1.7 million.
The solid line indicates the ''exercise now'' option if all uncertainty is resolved
about V. It is clear from Fig.
3
, than when there is uncertainty, that simply making a
decision based on a positive NPV (represented by the ''exercise now'' line) will
ignore additional value of postponing this investment to resolve uncertainty.
6.3.2 Multistage Investment with Option to Abandon
In this option, each stage of the investment provides the decision-maker with more
information that can be used to decide whether to go ahead with the subsequent
stages of the investment or not (McDonald and Siegel
1985
). In this case, I
k
(k = 2, 3, …, n) defines the amount of investment at each stage/time period, k,
during the NZER process. This provides the decision-makers with strong flexi-
bility to stop or abandon the investment at any stage when it becomes apparent that
the expected benefits V are not attainable. If the NPV approach is to be used, then
costs incurred at different stages of the investment are discounted to current time
