Page 211 - Sustainable Cities and Communities Design Handbook

Life Cycle Analysis Chapter j 10 185

Formulas
The following are the formulas for discounted payback, NPV p , and BCR p for
the Participant Test.
NPV p ¼ B p C p
NPV avp ¼ðB p C p Þ=P

BCR p ¼ B p =C p
DPp ¼ Min j such that B j C j
where
NPV p ¼ NPV to all participants
NPV avp ¼ NPV to the average participant
BCR p ¼ BCR to participants
DP p ¼ Discounted payback in years
B p ¼ NPV of benefit to participants
C p ¼ NPV of costs to participants
B j ¼ Cumulative benefits to participants in year j
C j ¼ Cumulative costs to participants in year j
P ¼ Number of program participants
J ¼ First year in which cumulative benefits are cumulative costs
d ¼ Interest rate (discount)
The Benefit (B p ) and Cost (C p ) terms are further defined as follows:
N N
BR t þ TC t þ INC t AB at þ PAC at
X X
B p ¼ þ
t 1 t 1
t¼1 ð1 þ dÞ t¼1 ð1 þ dÞ
N
PC t þ BI t
X
C ¼
t 1
t¼1 ð1 þ dÞ
where
BR t ¼ Bill reductions in year t
BI t ¼ Bill increases in year t
TC t ¼ Tax credits in year t
INC t ¼ Incentives paid to the participant by the sponsoring utility in year t
(refer to point 3 in Notes)
PC t ¼ Participant costs in year t to include:
l initial capital costs, including sales tax (refer to point 4 of Notes)
l ongoing operation and maintenance costs including fuel cost
l removal costs, less salvage value
l value of the customer’s time in arranging for installation, if
significant
PAC at ¼ Participant-avoided costs in year t for alternative fuel devices
(costs of devices not chosen)
Ab at ¼ Avoided bill from alternative fuel in year t