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Merge pull request #183 from BioSTEAMDevelopmentGroup/npv
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Fix NPV/solve_IRR/solve_price methods consistent with cashflow table #180
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@yoelcortes
yoelcortes authored Jan 10, 2024
2 parents 5eb838c + d7c3bd5 commit 6f94939
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Showing 2 changed files with 239 additions and 19 deletions.
43 changes: 28 additions & 15 deletions biosteam/_tea.py
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Original file line number Diff line number Diff line change
Expand Up @@ -204,10 +204,11 @@ def taxable_and_nontaxable_cashflows(
loan_principal = loan_principal_with_interest(loan, interest)
else:
loan_principal = loan.sum()
LP[:start] = loan * interest
LP[start:start + years] = solve_payment(loan_principal, interest, years)
taxable_cashflow = S - C - D - LP
nontaxable_cashflow = D + Loan - C_FC - C_WC
if not accumulate_interest_during_construction:
nontaxable_cashflow[:start] -= loan * interest
else:
taxable_cashflow = S - C - D
nontaxable_cashflow = D - C_FC - C_WC
Expand All @@ -224,9 +225,13 @@ def NPV_with_sales(
):
"""Return NPV with an additional annualized sales."""
taxable_cashflow = taxable_cashflow + sales * sales_coefficients
tax = np.zeros_like(taxable_cashflow)
tax = np.zeros_like(taxable_cashflow, dtype=float)
incentives = tax.copy()
fill_tax_and_incentives(incentives, taxable_cashflow, nontaxable_cashflow, tax, depreciation)
fill_tax_and_incentives(
incentives,
taxable_earnings_with_fowarded_losses(taxable_cashflow),
nontaxable_cashflow, tax, depreciation
)
cashflow = nontaxable_cashflow + taxable_cashflow + incentives - tax
return (cashflow/discount_factors).sum()

Expand Down Expand Up @@ -790,8 +795,10 @@ def get_cashflow_table(self):
taxable_cashflow = S - C - D
nontaxable_cashflow = D - C_FC - C_WC
TE[:] = taxable_earnings_with_fowarded_losses(taxable_cashflow)
FL[:] = (taxable_cashflow - TE).cumsum()
self._fill_tax_and_incentives(I, taxable_cashflow, nontaxable_cashflow, T, D)
FL[1:] = (taxable_cashflow - TE).cumsum()[:-1]
self._fill_tax_and_incentives(
I, TE, nontaxable_cashflow, T, D
)
NE[:] = taxable_cashflow + I - T
CF[:] = NE + nontaxable_cashflow
DF[:] = 1/(1.+self.IRR)**self._get_duration_array()
Expand All @@ -808,7 +815,11 @@ def NPV(self) -> float:
taxable_cashflow, nontaxable_cashflow, depreciation = self._taxable_nontaxable_depreciation_cashflows()
tax = np.zeros_like(taxable_cashflow)
incentives = tax.copy()
self._fill_tax_and_incentives(incentives, taxable_cashflow, nontaxable_cashflow, tax, depreciation)
self._fill_tax_and_incentives(
incentives,
taxable_earnings_with_fowarded_losses(taxable_cashflow),
nontaxable_cashflow, tax, depreciation
)
cashflow = nontaxable_cashflow + taxable_cashflow + incentives - tax
return NPV_at_IRR(self.IRR, cashflow, self._get_duration_array())

Expand Down Expand Up @@ -859,14 +870,18 @@ def _taxable_nontaxable_depreciation_cashflows(self):
)

def _fill_tax_and_incentives(self, incentives, taxable_cashflow, nontaxable_cashflow, tax, depreciation):
tax[:] = self.income_tax * taxable_earnings_with_fowarded_losses(taxable_cashflow)
tax[:] = self.income_tax * taxable_cashflow

def _net_earnings_and_nontaxable_cashflow_arrays(self):
taxable_cashflow, nontaxable_cashflow, depreciation = self._taxable_nontaxable_depreciation_cashflows()
size = taxable_cashflow.size
tax = np.zeros(size)
incentives = tax.copy()
self._fill_tax_and_incentives(incentives, taxable_cashflow, nontaxable_cashflow, tax, depreciation)
self._fill_tax_and_incentives(
incentives,
taxable_earnings_with_fowarded_losses(taxable_cashflow),
nontaxable_cashflow, tax, depreciation
)
net_earnings = taxable_cashflow + incentives - tax
return net_earnings, nontaxable_cashflow

Expand Down Expand Up @@ -984,12 +999,11 @@ def solve_sales(self):
"""
discount_factors = (1 + self.IRR)**self._get_duration_array()
sales_coefficients = np.ones_like(discount_factors)
sales_coefficients = np.ones_like(discount_factors, dtype=float)
start = self._start
sales_coefficients[:start] = 0
w0 = self._startup_time
sales_coefficients[self._start] = w0*self.startup_VOCfrac + (1-w0)
sales = self._sales
sales_coefficients[start] = w0*self.startup_salesfrac + (1.-w0)
taxable_cashflow, nontaxable_cashflow, depreciation = self._taxable_nontaxable_depreciation_cashflows()
if np.isnan(taxable_cashflow).any():
warn('nan encountered in cashflow array; resimulating system', category=RuntimeWarning)
Expand All @@ -1003,17 +1017,16 @@ def solve_sales(self):
sales_coefficients,
discount_factors,
self._fill_tax_and_incentives)
x0 = sales
x0 = self._sales if np.isfinite(self._sales) else 0
f = NPV_with_sales
if not np.isfinite(x0): x0 = 0.
y0 = f(x0, *args)
x1 = x0 - y0 / self._years # First estimate
try:
sales = flx.aitken_secant(f, x0, x1, xtol=10, ytol=1000.,
sales = flx.aitken_secant(f, x0, x1, xtol=10, ytol=100.,
maxiter=1000, args=args, checkiter=True)
except:
bracket = flx.find_bracket(f, x0, x1, args=args)
sales = flx.IQ_interpolation(f, *bracket, args=args, xtol=10, ytol=1000, maxiter=1000, checkiter=False)
sales = flx.IQ_interpolation(f, *bracket, args=args, xtol=10, ytol=100, maxiter=1000, checkiter=False)
self._sales = sales
return sales

Expand Down
215 changes: 211 additions & 4 deletions tests/test_tea.py
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Original file line number Diff line number Diff line change
@@ -1,16 +1,17 @@
# -*- coding: utf-8 -*-
# BioSTEAM: The Biorefinery Simulation and Techno-Economic Analysis Modules
# Copyright (C) 2021-2022, Yalin Li <zoe[email protected]>
# Copyright (C) 2021-2024, Yalin Li <mailto[email protected]>
#
# This module is under the UIUC open-source license. See
# github.com/BioSTEAMDevelopmentGroup/biosteam/blob/master/LICENSE.txt
# for license details.
"""
"""

import pytest, numpy as np
import pytest, numpy as np, biosteam as bst
from numpy.testing import assert_allclose
from biosteam import TEA, System
from biosteam import TEA, System, Stream, Unit, Chemical, settings
from biorefineries.tea import create_cellulosic_ethanol_tea

def test_depreciation_schedule():
correct_arrs = {
Expand Down Expand Up @@ -51,6 +52,212 @@ def test_depreciation_schedule():
with pytest.raises(ValueError):
tea.depreciation = 'bad'

def test_cashflow_consistency():
settings.set_thermo([
Chemical('Dummy', default=True, phase='s', MW=1, search_db=False)
])

cost = Stream(Dummy=9793.983511363867 - 1280.916880939845, price=1) # Includes co-product electricity credits
ethanol = Stream(flow=[21978.374283953395], price=0.7198608114634679)

class MockCellulosicEthanolBiorefinery(Unit):
_N_ins = _N_outs = 1

def _run(self): pass

def _cost(self):
self.baseline_purchase_costs['Biorefinery'] = 85338080.48935215

class OSBL(Unit):
N_outs = _N_ins = 0

def _run(self): pass

def _cost(self):
self.baseline_purchase_costs['Biorefinery'] = 122287135.13152598

unit = MockCellulosicEthanolBiorefinery(ins=cost, outs=ethanol)
osbl = OSBL()
sys = System.from_units(units=[unit, osbl])
sys.simulate()
tea = create_cellulosic_ethanol_tea(sys, OSBL_units=[osbl])
table = tea.get_cashflow_table()
assert_allclose(tea.NPV, 32131936.781448975)
assert_allclose(tea.NPV, table['Cumulative NPV [MM$]'].iloc[-1]*1e6)
tea.IRR = tea.solve_IRR()
assert_allclose(tea.NPV, 0, atol=100)
assert_allclose(tea.IRR, 0.11246761316144724)
tea.IRR = 0.10
ethanol.price = tea.solve_price(ethanol)
assert_allclose(ethanol.price, 0.6952016482242149)
assert_allclose(tea.NPV, 0, atol=100)

def test_tea():
cost = bst.decorators.cost
# Total installed equipment cost to be $1 MM
bst.CE = CE = bst.design_tools.CEPCI_by_year[2013]
@cost('Fake scaler', 'Lumped cost', CE=CE, cost=1e6, S=1, n=1, BM=1)
class LumpedCost(bst.Unit):
'''Does nothing but adding given costs.'''
_units = {'Fake scaler': ''}

def _design(self):
self.design_results['Fake scaler'] = 1

class TEA(bst.TEA):
def __init__(
self,
system,
FOC_over_installed=0.5, # annual O&M
DPI_over_installed=(1+1),
TDC_over_DPI=(1+0.2)*(1+0.4), # 20% non-installed & 40% indirect
FCI_over_TDC=1,
**kwargs,
):
self.FOC_over_installed = FOC_over_installed
self.DPI_over_installed = DPI_over_installed
self.TDC_over_DPI = TDC_over_DPI
self.FCI_over_TDC = FCI_over_TDC
bst.TEA.__init__(self, system, **kwargs)

def _FOC(self, installed_equipment_cost): # fixed operating cost
return installed_equipment_cost*self.FOC_over_installed

def _DPI(self, installed_equipment_cost): # direct permanent investment
return installed_equipment_cost*self.DPI_over_installed

def _TDC(self, DPI): # total depreciable cost
return DPI*self.TDC_over_DPI

def _FCI(self, TDC): # fixed capital investment
return TDC*self.FCI_over_TDC

bst.settings.set_thermo([bst.Chemical('Water')])
reactant = bst.Stream('reactant', Water=1, units='kg/hr')
# Total annual sales to be $2.5 MM
product = bst.Stream('product', Water=1, price=2.5e6/365/24, units='kg/hr')

U101 = LumpedCost('U101', ins=reactant, outs=product)
sys = bst.System('sys', path=(U101,))
sys.simulate()

tea = TEA(
system=sys,
IRR=0.1,
duration=(2013, 2013+15), # 15 years
income_tax=0.21+0.1,
construction_schedule=(1,),
depreciation='MACRS7',
operating_days=365,
startup_months=0,
startup_FOCfrac=1,
startup_VOCfrac=1,
startup_salesfrac=1,
lang_factor=None,
WC_over_FCI=0.05,
finance_interest=0.08,
finance_years=10,
finance_fraction =0.6,
accumulate_interest_during_construction=False,
)

# Below test NPV and discounted cashflow calculation
table = tea.get_cashflow_table()
data = np.array([
# Depreciable capital [MM$]
# Fixed capital investment [MM$]
# Working capital [MM$]
# Depreciation [MM$]
# Loan [MM$]
[ 3.36 , 3.36 , 0.168 , 0. , 2.016 ,
# Loan interest payment [MM$]
# Loan payment [MM$]
# Loan principal [MM$]
# Annual operating cost (excluding depreciation) [MM$]
# Sales [MM$]
0.16128 , 0. , 2.016 , 0. , 0. ,
# Tax [MM$]
# Incentives [MM$]
# Taxed earnings [MM$]
# Forwarded losses [MM$]
# Net earnings [MM$]
0. , 0. , 0. , 0. , 0. ,
# Cash flow [MM$]
# Discount factor
# Net present value (NPV) [MM$]
# Cumulative NPV [MM$]
-1.67328 , 1. , -1.67328 , -1.67328 ],
[ 0. , 0. , 0. , 0.480144 , 0. ,
0.16128 , 0.30044345, 1.87683655, 1.68 , 2.5 ,
0.01221789, 0. , 0.03941255, 0. , 0.02719466,
0.50733866, 0.90909091, 0.46121696, -1.21206304],
[ 0. , 0. , 0. , 0.822864 , 0. ,
0.15014692, 0.30044345, 1.72654003, 1.68 , 2.5 ,
0. , 0. , 0. , 0. , -0.30330745,
0.51955655, 0.82644628, 0.42938558, -0.78267746],
[ 0. , 0. , 0. , 0.587664 , 0. ,
0.1381232 , 0.30044345, 1.56421978, 1.68 , 2.5 ,
0. , 0. , 0. , -0.30330745, -0.06810745,
0.51955655, 0.7513148 , 0.39035053, -0.39232693],
[ 0. , 0. , 0. , 0.419664 , 0. ,
0.12513758, 0.30044345, 1.38891391, 1.68 , 2.5 ,
0. , 0. , 0. , -0.3714149 , 0.09989255,
0.51955655, 0.68301346, 0.35486412, -0.03746282],
[ 0. , 0. , 0. , 0.300048 , 0. ,
0.11111311, 0.30044345, 1.19958358, 1.68 , 2.5 ,
0. , 0. , 0. , -0.27152235, 0.21950855,
0.51955655, 0.62092132, 0.32260374, 0.28514093],
[ 0. , 0. , 0. , 0.299712 , 0. ,
0.09596669, 0.30044345, 0.99510681, 1.68 , 2.5 ,
0.05202753, 0. , 0.16783075, -0.0520138 , 0.16781702,
0.46752902, 0.56447393, 0.26390794, 0.54904887],
[ 0. , 0. , 0. , 0.300048 , 0. ,
0.07960854, 0.30044345, 0.77427191, 1.68 , 2.5 ,
0.06804765, 0. , 0.21950855, 0. , 0.1514609 ,
0.4515089 , 0.51315812, 0.23169546, 0.78074432],
[ 0. , 0. , 0. , 0.149856 , 0. ,
0.06194175, 0.30044345, 0.53577021, 1.68 , 2.5 ,
0.11460717, 0. , 0.36970055, 0. , 0.25509338,
0.40494938, 0.46650738, 0.18891187, 0.9696562 ],
[ 0. , 0. , 0. , 0. , 0. ,
0.04286162, 0.30044345, 0.27818838, 1.68 , 2.5 ,
0.16106253, 0. , 0.51955655, 0. , 0.35849402,
0.35849402, 0.42409762, 0.15203646, 1.12169266],
[ 0. , 0. , 0. , 0. , 0. ,
0.02225507, 0.30044345, 0. , 1.68 , 2.5 ,
0.16106253, 0. , 0.51955655, 0. , 0.35849402,
0.35849402, 0.38554329, 0.13821496, 1.25990762],
[ 0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 1.68 , 2.5 ,
0.2542 , 0. , 0.82 , 0. , 0.5658 ,
0.5658 , 0.3504939 , 0.19830945, 1.45821707],
[ 0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 1.68 , 2.5 ,
0.2542 , 0. , 0.82 , 0. , 0.5658 ,
0.5658 , 0.31863082, 0.18028132, 1.63849839],
[ 0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 1.68 , 2.5 ,
0.2542 , 0. , 0.82 , 0. , 0.5658 ,
0.5658 , 0.28966438, 0.16389211, 1.80239049],
[ 0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 1.68 , 2.5 ,
0.2542 , 0. , 0.82 , 0. , 0.5658 ,
0.5658 , 0.26333125, 0.14899282, 1.95138332],
[ 0. , 0. , -0.168 , 0. , 0. ,
0. , 0. , 0. , 1.68 , 2.5 ,
0.2542 , 0. , 0.82 , 0. , 0.5658 ,
0.7338 , 0.23939205, 0.17566589, 2.1270492 ]])

assert_allclose(table.values, data, atol=1e-4)
assert_allclose(tea.NPV, table.iloc[-1,-1]*1e6, atol=1e-4)
total_interest_payment1 = table['Loan payment [MM$]'].sum()
total_interest_payment2 = (
table['Loan interest payment [MM$]'].iloc[1:].sum() + # payment during construction (year 0) is equity/cash
table['Loan principal [MM$]'].iloc[0])
assert_allclose(total_interest_payment1, total_interest_payment2, atol=1e-4)


if __name__ == '__main__':
test_depreciation_schedule()
test_depreciation_schedule()
test_cashflow_consistency()
test_tea()

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