Lisø PhD Dissertation Manuscript - NTNU

772 Nordvik and Lisø
0
Â
Â
= p dV ( M) + p dV ( M)
2s 2 2s 2s 2 2s
CM
s∈S TM
s∈S 2s 2 2s
2s − ( Â p dV ( M)
+ Â p
2 2s
CM
s∈S TM
s∈S dV ( M))
is inserted into Equation 10a and the expression is
rearranged:
1 1 1 1 1
NV( M) = v ( Wˆ, z ) −c( Wˆ,
z ) −m
2s 2 2s
+ p dV ( M)
Â
s∈S Â
2s 2 2s 2s
+ p d { V ( C) −V
( M)}
CM
s∈S Â
+ −
2s 2 2s p { dT
2s
V ( M)}
(12)
TM
s∈S Into this expression, some definitions are inserted:
C
C =
2s 2 2s 2s
p d { V ( C) −V
( M)}
C
Â
s∈S CM
Â
= p { dT −V(
M)}
T 2s 2 2s 2s
s∈S TM
The symbols CC and CT are the expected values of the
possibility to choose the strategy in period 2 whenever
this is advantageous. Hence, they are real option values.
The definitions of SCM and STM ensure that these are
positively signed. Their size depends, among other
things, on the level of effort put into maintenance.
V
1 1 1 1 1
N ( M) = v ( Wˆ, z ) −c ( Wˆ,
z ) −m
2s 2 2s
C T
+ p dV ( M)
+ C + C
(12b)
Â
s∈S Using these definitions, one find that the (expected)
value of a building, which in period 1 is optimally
maintained, can be expressed as the sum of four
components:
• the net value of the building in use in the first
period;
• the expected value of the building in period
2, aggregated over all possible states, if it is
optimally maintained;
• the value of the real option to convert the building
if this is profitable when the future climate
conditions are observed; and
• the value of the real option to scrap the building
if this is profitable when the future climate
conditions are observed.
The normal action taken by an owner of a building is to
maintain it in a suitable way. The decision to convert or
to scrap is a more drastic, and less frequent, decision.
In the remaining parts of the paper, the choice of
the maintenance strategy will be termed ‘continued
ordinary use’.
This apparatus can be used for an informal characterization
of the result on the mutual dependency between
the maintenance efforts made in period 1 and the
conversion and scrapping probabilities, referred above:
Up to a certain point the net value of the building in use
in the first period is increasing in m 1 . The period 2 value
of the building if it is not scrapped or converted is
increasing in m 1 , because this, in every state, increases
the state of the building as measured by z. The value of
the real options, and the probability that they will be
exercised, will however be decreasing in m 1 . Hence,
there is a trade-off between actions that enhance the
value of the building in continued ordinary use and
actions that enhance the value of the possibility to adapt
the building to changed future weather conditions.
The uncertain risks of future climate change can be
interpreted as a situation where probabilities of states
where conversion activities and scrapping take place are
higher than they are under a steady state. Under this
interpretation, one can say that increased climate uncertainty
implies that owners will give more weight to
actions that increase the value of the possibilities to
utilize future climate information. From the arguments
above, it is seen that this means that effort put into
maintenance prior to the realization of a given climate
change scenario is decreasing due to the uncertainty
related to the likely range and nature of future weather
scenarios.
The conversion strategy
The value of an optimally designed conversion strategy
in period 1 can be written as the sum of the value of the
building in ‘continued ordinary use’ and the value of
the real options associated with conversion or scrapping.
The reformulation of the expression for NV(C) is
done the same way that NV(M) was reformulated in
Equation 12:
1 1 1 1
NV( C) = v ( W, z ) −c( W, z ) −C(
W,W ˆ )
2s 2 2s
C T
+ p dV ( M)
+ V + V
(13)
Â
s∈S Where the real options are:
V C
2s 2 2s 2s
= p d { V ( C) −V
( M)}
Â
CC
s∈S Â
V T 2s 2 2s 2s
= p d { T −V
( M)}
TC
s∈S Some remarks on the conversion technology can be
given. At the start of period 1, the clay-factor has a value
Wˆ . Then consider two alternative values Wˆ < W a < W b .
Define
C(Wˆ ,Wb ) = C(Wˆ,W a ) + d2C(Wa ,Wb ) + K (14)
where K < 0, as a normal conversion cost structure.
Hence, it is more expensive to make a two-step
conversion than to do all the conversions in one single