To resolve the issue with not all data across measures’ lifetime being available, the tool’s CBA facility should be based on weighted average annuities. This requires a number of changes, compared to the previous version of the CBA (#493).
Calculation of intermediate results
The calculation of annuity relies on new annual savings and total investments. The relevant calculcation for new annual savings is described in #339.
Constant indicators
First of all, all constant indicators need to be scaled:
\(\Delta MI_{m,i} = \sum_{k} MI_{m,i,k} / \Delta E_{m,i} \cdot N \Delta E_{m,i}\)
\(\Delta MI_{m,i}\) = scaled indicators for measure \(`m`\) in stated year \(`i`\)
\(`MI_{m,i,k}`\) = result of indicator \(`k`\) for measure \(`m`\) in stated year (Stützjahr) \(`i`\)
\(`\Delta E_{m,i}`\) = total annual savings for measure \(`m`\) in stated year (Stützjahr) \(`i`\), as input in the front end
\(`N \Delta E_{m,y}`\) = new annual savings for measure \(`m`\) in year \(`y`\) (after interpolation, #521), as input in the front end
Relevant constant indicators are the following ones:
Energy cost savings
Premature deaths due to air pollution
Avoided lost working days
Reduction of greenhouse gas emissions
Impact on RES targets
Avoided asthma cases
Avoided cold winter mortality
One-time impacts
In contrast, one-time impacts such as new annual investments (as calculated in #339) or GDP need to be discounted, using the capital recovery factor \(`CRF_m`\):
\(`dI_{m,i} = I_m \cdot CRF_m = I_m \cdot \frac{DR (1 + DR)^{LT_m}}{(1 + DR)^{LT_m} - 1}`\)
\(`dI_{m,i}`\) = discounted annual new investments
\(`I_{m,i}`\) = annual new investments, as calculated in #339
\(`DR`\) = discount rate, as implemented in slider in CBA
\(`LT`\) = measure lifetime, coming from id_parameter 36 or advanced parameters
Annuity calculation
Annuity
The annuity \(`A_{m,i}`\) describes the revenue or cost of a measure in stated year \(`i`\):
\(`A_{m,i} = dI_{m,i} - dGDP_{m,i} - \Delta MI_{m,i}`\)
\(`dGDP_{m,i}`\) = discounted effect on GDP, calculation analogous to \(`dI_m`\)
\(`MI_{m,i}`\) = monetised impacts of constant indicators
Weighted annuity
In order to combine the calculated annuity for every stated year, a weighting using the energy savings implemented since the last stated year is carried out, resulting in a weighted annuity \(`A_m`\):
\(`A_m = [\sum_i (A_{m,i} \cdot \sum_{y = y(i-1)+1}^{y(i)} N \Delta E_{m,y})] / \sum_y N \Delta E_{m,y}`\)
\(`\sum_{y = y(i-1)+1}^{y(i)} N \Delta E_{m,y}`\) = sum of all new annual savings implemented between one year after the last stated year \(`y(i-1)+1`\) and this stated year \(`y(i)`\)
\(`\sum_y N \Delta E_{m,y}`\) = total sum of all new annual savings of the measure
Other CBA aspects
As was the case before, the slider for discount rate adjusts the discount rate (relevant for the discounting of one-time impacts). The sliders for energy price and investment sensitivity are multipliers for energy costs and discounted investments, respectively.