Net Present Value (NPV) - Examples

In [2]:
import pandas as pd

%matplotlib inline

PV Example

In [17]:
lifetime = 20 #years
discount_rate = 0.04 #0.0775 #per unit
size = 100 #kW
specific_cost = 800 #EUR/kW
fom = 20 #EUR/kW/a
fit = 0.1 #EUR/kWh
flh = 1000 #h/a
flows = pd.DataFrame(index=range(lifetime+1))
flows["investment"] = [-size*specific_cost] + [0]*lifetime
flows["FOM"] = [0] + [-size*fom]*lifetime
flows["income"] = [0] + [size*flh*fit]*lifetime
flows["total_flow"] = flows.sum(axis=1)
flows["discount_factor"] = [(1+discount_rate)**(-t) for t in range(lifetime+1)]
flows["discounted_total_flow"] = flows["total_flow"]*flows["discount_factor"]
In [18]:
flows.head()
Out[18]:
investment FOM income total_flow discount_factor discounted_total_flow
0 -80000 0 0.0 -80000.0 1.000000 -80000.000000
1 0 -2000 10000.0 8000.0 0.961538 7692.307692
2 0 -2000 10000.0 8000.0 0.924556 7396.449704
3 0 -2000 10000.0 8000.0 0.888996 7111.970869
4 0 -2000 10000.0 8000.0 0.854804 6838.433528
In [19]:
flows.sum()
Out[19]:
investment               -80000.000000
FOM                      -40000.000000
income                   200000.000000
total_flow                80000.000000
discount_factor              14.590326
discounted_total_flow     28722.610760
dtype: float64
In [9]:
(size*specific_cost/(sum(flows["discount_factor"])-1)+2500)/1e5
Out[9]:
0.6650050203417118
In [8]:
flows["discount_factor"].plot()
Out[8]:
<matplotlib.axes._subplots.AxesSubplot at 0x7f4c3e060f28>

Nuclear Example

In [23]:
lifetime = 40 #years
discount_rate = 0.10 #per unit
size = 3e6 #kW
specific_cost = 5000 #EUR/kW
decommissioning_cost = 0 #EUR/kW
fom = 20 #EUR/kW/a
fuel = 10 #EUR/MWh
market_value = 50 #EUR/MWh
flh = 8000 #h/a
flows = pd.DataFrame(index=range(lifetime+1))
flows["investment"] = [-size*specific_cost] + [0]*(lifetime-1) + [-size*decommissioning_cost]
flows["FOM"] = [0] + [-size*fom]*lifetime
flows["income"] = [0] + [size*flh*market_value/1000]*lifetime
flows["total_flow"] = flows.sum(axis=1)
flows["discount_factor"] = [(1+discount_rate)**(-t) for t in range(lifetime+1)]
flows["discounted_total_flow"] = flows["total_flow"]*flows["discount_factor"]
In [24]:
flows.head()
Out[24]:
investment FOM income total_flow discount_factor discounted_total_flow
0 -1.500000e+10 0.0 0.000000e+00 -1.500000e+10 1.000000 -1.500000e+10
1 0.000000e+00 -60000000.0 1.200000e+09 1.140000e+09 0.909091 1.036364e+09
2 0.000000e+00 -60000000.0 1.200000e+09 1.140000e+09 0.826446 9.421488e+08
3 0.000000e+00 -60000000.0 1.200000e+09 1.140000e+09 0.751315 8.564989e+08
4 0.000000e+00 -60000000.0 1.200000e+09 1.140000e+09 0.683013 7.786353e+08
In [25]:
flows.sum()
Out[25]:
investment              -1.500000e+10
FOM                     -2.400000e+09
income                   4.800000e+10
total_flow               3.060000e+10
discount_factor          1.077905e+01
discounted_total_flow   -3.851882e+09
dtype: float64
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