The life cycle cost criterion is based on the selling cost to the final occupant. Most of the cost data per unit of material comes from the RS Means Residential Cost Data 2011 book (RS Means, 2010). Prices from this database are corrected for St-Jérôme (small town north of Montreal, close to the actual building location) using the location factor given in the book, which is 1.15. It
58 also includes the currency exchange rate, from US dollar to Canadian dollar. Prices obtained from RS Means Residential Cost Data 2011 include 20 percent overhead and profits. A sales tax of 13.925% (composed of a federal tax of 5%, and a provincial tax of 8.5%) is also added to all prices, as applicable. The same material quantity, waste factors and lifespan as those specified for the life cycle energy calculations apply.
A penalty cost is added for exterior wall systems that take up more space than the minimum 38 mm per 140 mm (2 in per 6 in) wood stud framing walls and 25 mm of exterior insulation. As modules have given exterior dimensions, any wall that is thicker takes up some of the living space. For each square meter of floor area lost to insulation and framing, there is an additional cost of $970 which corresponds to the selling cost per square meter of floor area that the developer is aiming at.
All prices are given in 2011 constant dollars. Since constant dollars are used, a real discount rate and a real escalation rate are used to calculate the present value of each cost, in order to combine them into a meaningful life cycle cost. The real discount rate represents the time-value of money, excluding inflation, while the real escalation rate is the increase or decrease (if negative) of the price of a good, excluding inflation (Fuller and Petersen, 1996). The real discount rate used is calculated based on a nominal discount rate equal to the average interest rate for the period between 2001 and 2011 (Bank of Canada, 2011b), and an inflation rate also equal to the average for Canada during this period (Bank of Canada, 2011a). Equation 4.3 defines the real discount rate d:
59 where the nominal discount rate D is 0.0269 (2.69%) and the inflation rate I is 0.0203 (2.03%), for a real discount rate of 0.0065.
Life cycle costs considered for the envelope are part of three main categories: investment costs, maintenance and replacement costs, and operation costs. Municipal taxes, insurance and other similar costs are not considered. The investment cost Cinvest is the cost of the initial envelope,
which occurs at the beginning of year 1, and is consequently already in constant dollars. Maintenance and replacement costs, CM&R, include repainting of interior walls (every 8 years),
replacement of vinyl siding (every 35 years), replacement of windows (every 25 years), replacement of fiber-cement siding (every 30 years) and repainting of fiber-cement every 15 years. Replacement costs are assumed to have the same cost in constant dollars, and are discounted from the end of the year at which they occur, following equation 4.4 to calculate the present value of an amount occurring a single time (Fuller and Petersen, 1996). Operation costs are the annual costs of electricity for heating and cooling Cenergy; they are discounted at the end
of each year. Electrical energy is assumed to have a real escalation rate of 2%. This value is subject to debate; the MNECH 1997 assumes a real escalation of 0% for the province of Quebec in its LCC calculation. However, in other studies, scenarios where the annual escalation rate for electricity varies from -1% to 5% are considered (Peippo et al. 1999, Keoleian et al. 2001, Hasan et al. 2008, Palonen et al. 2009). Some might argue that electricity prices in Quebec have been closely following inflation in the past decade (Leckner, 2011), but the author thinks that in a context where the electricity demand continues to rise and new hydro-electricity projects are more and more expensive due to the lack of new rivers that can easily be harnessed, it is too optimistic to think that energy prices will stay at their extremely low levels in Quebec. To take into account the effect of both escalation and discount rates of the 2011 constant dollar price of
60 energy, equation 4.5 is used, which applies to obtain the present value PVrecurring of an amount
that has to be paid annually (Fuller and Petersen, 1996).
(Eq. 4.4) (Eq. 4.5)
where Ft is the cost at the year of occurrence t (with respect to the year of reference for present
value), Ao is the cost of electricity for the first year of operation, e is the real escalation rate for
electricity and n is the period over which energy costs occur, in years. The life cycle cost for each design alternative LCCenv is then calculated using equation 4.6:
(Eq. 4.6)
where Cinvestiment is not discounted, CM&R is the sum of each maintenance and replacement,
discounted at its year of occurrence using equation 4.4, and Cenergy is calculated using the cost of
electricity for year 1 in equation 4.5. For 2010, the average cost of electricity for residential customers for a monthly consumption of 1000 kWh in the province of Québec was 6.88$/kWh (Hydro-Québec, 2010), to which are added taxes (13.925%), for a total of 7.84$/kWh. That price is used for year one of the life of the building.
Table 4.5 gives the LCC of the base case house, divided into assemblies and operation costs, as an example of the contribution of the house cost versus the operation cost.
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Table 4.5 – Life cycle cost for the base case house
Assembly Life cycle cost (constant
2011 CAD)
Percentage of LCC
Total material cost 273,321 84.0%
Roof 23,121 7.1%
Exterior walls 53,247 16.4%
Partition walls 5,293 1.6%
Floors 26,615 8.2%
Foundation 30,860 9.5%
Windows and doors 100,008 30.7%
Outside frame of modules 34,178 10.5%
Total energy cost for 50 years 51,920 16.0%
Yearly energy cost (first year) 725.75 0.2%
TOTAL LIFE CYCLE COST 325,240 100%