The economic calculation in T*SOL® using the net present value method is based on the following formulas:
Investment Costs = Installation Costs - Subsidy
Yearly Operating Costs = Pump Performance * Operating Time * Electricity Costs
The Net Present Value (NPV) of a price-dynamic payment sequence Z, Zr, Zr², … over T years (lifespan) according to VDI 2067 is:
$ NPV = Z * b(T, q, r) $
$b(T,q,r) = \begin{cases} \frac{1 - \left(\frac{r}{q}\right)^T}{q - r} & \text{if } r \neq q, \\ \frac{T}{q} & \text{if } r = q \end{cases}$
For the Capital Value (CV) of the total investment:
$K = \sum[\text{NPV of the price-dynamic payment sequence over the lifespan}] - \text{Investments} + \text{Subsidies}$
The payback period is the time the system must operate to yield a net present value of zero. Payback periods exceeding 40 years are not displayed.
To calculate the heating price, the net present value of the costs is determined:
$\text{NPV of Costs (BW)} = \text{Investments} + \text{NPV of Operating and Maintenance Costs}$
If the NPV of the costs is converted into a constant payment sequence ($r = 1$), then the following applies to this sequence $Z$:
$Z = \frac{\text{NPV of Costs}}{b(T, q, r)}$
For $r = 1$, $\frac{1}{b(T, q, r)}$ becomes the annuity factor:
$a(q, T) = \frac{q^T \cdot (q - 1)}{q^T - 1}$ (also according to VDI 2067)
The Heating Price is then:
$\text{Heating Price} = \frac{\text{Yearly Costs Z}}{\text{Yearly Energy Yield}}$