Civil Engineering Reference
In-Depth Information
NZER is assumed to follow the GBM process given in Eq. (
1
); (l
v
d
v
) and r
v
represent the deterministic and stochastic change in the value of the benefits from
the NZER project over time, respectively.
dV
=
V
¼ð
l
v
d
v
Þ
dt
þ
r
v
dz
ð
1
Þ
where l
v
is the market equilibrium rate of return of the completed NZER project;
d
v
is the rate of return shortfall or opportunity cost of delaying the refurbishment;
and r
v
is the volatility of future benefits from the NZER project.
The main advantage of this assumption is that it allows the decision-maker the
flexibility to align the dynamics of V, a non-market traded security, with those of
securities traded in the capital market. This assumption simply means that there
exists a traded financial asset (e.g., a stock) that has the same risk characteristics
(i.e., r
v
dz)asV. Thus, l
v
can be obtained similar to that of the traded financial
asset by using the capital asset pricing model (CAPM) (French
2003
; Mossin
1966
; Lintner
1965
; Sharpe
1964
), which states that that the expected return of an
asset equals the risk-free rate of return, r, plus a risk premium required by investors
due to the correlation of the asset with the market, and accounts for the systematic
non-diversifiable risk (Brealey et al.
2010
).
Finally, d
v
is obtained as the difference between l
v
(i.e., rate of return on traded
financial asset) and l
v
r, the rate of return for the real non-financial traded asset. In
this case, the non-traded asset is V if the NZER program is implemented (Ho and
Liu
2003
and Dixit and Pindyck
1994
). Since V is realized only if the NZER is
undertaken in the future, then d
v
represents the opportunity cost of delaying the
investment (Dixit and Pindyck
1994
).
Given this assumption about V, the subsequent section will present a case study
example using a new approach to project evaluation based on the option pricing
theory.
6.3 Case Study
Suppose that an existing building requires $10 million in energy upgrades
investment. This includes installing new PV panels, installing high-performance
windows and replacing all light fixtures with more efficient LED lights. Pre-
liminary energy analysis for the building indicates that these changes will result in
an expected $1.65 million reduction in annual costs (A) of operating and main-
taining the building for the next 20 years. If the minimum attractive rate of return
(MARR) for the building owner is 15 %, then the NPV for this investment will be
($10.33-$10) $0.33 million. Therefore, the building owner should invest imme-
diately in NZER to reduce the costs of operation.
However, if the expected annual operation cost reduction slightly fluctuates to
$1.60 million or less due to changes in energy prices and inability to accurately
evaluate building performance when the new systems are installed, then the NPV
