Uncertainty in Refurbishment Investment - Nearly Zero Energy Building Refurbishment - page 162

becomes zero or less. Thus, a slight uncertainty about the annual cost savings will
change the decision from invest to do not invest even when there are other
strategic benefits for having a NZER. If the uncertainty is represented by r v [see
Eq. ( 1 )], and we assume that r = 0.05 and d v = 0.15 (i.e., corresponds to the
building owner's MARR), then the investment decision can be analyzed for the
three scenarios in the next sections.

6.3.1 Single-Stage Investment: Option to Defer

In the single-stage NZER, the building stakeholders want to commit a fixed-
amount I to cover the costs of the sustainable refurbishment. An important aspect
of a single-stage investment in NZER for existing buildings is that once the money
is committed, the decision cannot be reversed regardless of how the building
performs in the future. This presents a challenge to the building stakeholders
especially when uncertainty about future benefits V is very high. Simply relying on
a positive NPV analysis might be misleading because of the irreversibility of the
investment which means that the selected NZER measures (e.g., new renewable
energy sources/high-performance mechanical systems) placed inside of the
building cannot be simply dismantled and moved to another building if the
required energy efficiency and building performance are not achieved. In this type
of investment, postponing the decision to invest in NZER effort is beneficial (i.e.,
can invest at anytime in the future) to allow for some of the uncertainty about
NZER benefits to unfold. For example, testing of a given technology at another
building might result in more accurate information about its effect on the building
refurbishment. Thus, the building stakeholders should evaluate the investment
with the time to wait to determine whether this alternative adds value to their
investment. This is analogous to the perpetual American option case where the
investor decides to wait and exercises the option only when market conditions are
favorable. Using this analogy, the exercise price K and stock price S correspond to
the total cost of investment I and expected benefits V of the NZER. However, as
discussed in the previous section, the option might be more valuable if left
unexercised until S [ S* even when market conditions are favorable (e.g.,
S [ K for a call option). In this case, the solution of a perpetual American option
proposed by McDonald and Siegel ( 1986 ) can be used to determine the value and
time of the investment in single-stage NZER projects as given in Eq. ( 2 ). This
value will be the modified NPV for single-refurbishment project, NPV m . When-
ever, NPV m [ NPV, the building stakeholders should wait.

NPV m ð V ; I Þ¼ð V I Þð V = V Þ b when V V

ð 2 Þ

NPV m ð V ; I Þ¼ð V I Þ when V [ V

r

r d v

þ 2 þ 2r = r v

V

Þ ; b ¼ 0 : 5 r d v
r v

where

I ¼ b = b I

ð

r v 0 : 5