import numpy as np
import pandas as pd
from ccc.constants import TAX_METHODS
[docs]
def update_depr_methods(df, p, dp):
"""
Updates depreciation methods per changes from defaults that are
specified by user.
Args:
df (Pandas DataFrame): assets by type and tax treatment
p (CCC Specifications object): CCC parameters
dp (CCC DepreciationParams object): asset-specific depreciation
parameters
Returns:
df (Pandas DataFrame): assets by type and tax treatment with
updated tax depreciation methods
"""
# update tax_deprec_rates based on user defined parameters
# create dataframe with depreciation policy parameters
deprec_df = pd.DataFrame(dp.asset)
# split out value into two columns
deprec_df = deprec_df.join(
pd.DataFrame(deprec_df.pop("value").values.tolist())
)
# drop information duplicated in asset dataframe
deprec_df.drop(
columns=["asset_name", "minor_asset_group", "major_asset_group"],
inplace=True,
)
# merge depreciation policy parameters to asset dataframe
df.drop(columns=deprec_df.keys(), inplace=True, errors="ignore")
df = df.merge(
deprec_df, how="left", left_on="bea_asset_code", right_on="BEA_code"
)
# add bonus depreciation to tax deprec parameters dataframe
df["bonus"] = df["GDS_life"]
# update tax_deprec_rates based on user defined parameters
df.replace({"bonus": p.bonus_deprec}, inplace=True)
# Compute b
df["b"] = df["method"]
df.replace({"b": TAX_METHODS}, regex=True, inplace=True)
# use b value of 1 if method is not in TAX_METHODS
# NOTE: not sure why the replae method doesn't work for this method
# Related: had to comment this out in TAX_METHODS
df.loc[df["b"] == "Income Forecast", "b"] = 1.0
# cast b as float
df["b"] = df["b"].astype(float)
df.loc[df["system"] == "ADS", "Y"] = df.loc[
df["system"] == "ADS", "ADS_life"
]
df.loc[df["system"] == "GDS", "Y"] = df.loc[
df["system"] == "GDS", "GDS_life"
]
return df
[docs]
def dbsl(Y, b, bonus, r):
r"""
Makes the calculation for the declining balance with a switch to
straight line (DBSL) method of depreciation.
.. math::
z = \frac{\beta}{\beta+r}\left[1-e^{-(\beta+r)Y^{*}}\right]+
\frac{e^{-\beta Y^{*}}}{(Y-Y^{*})r}
\left[e^{-rY^{*}}-e^{-rY}\right]
Args:
Y (array_like): asset life in years
b (array_like): scale of declining balance (e.g., b=2 means
double declining balance)
bonus (array_like): rate of bonus depreciation
r (scalar): discount rate
Returns:
z (array_like): net present value of depreciation deductions for
$1 of investment
"""
beta = b / Y
Y_star = Y * (1 - (1 / b))
z = bonus + (
(1 - bonus)
* (
((beta / (beta + r)) * (1 - np.exp(-1 * (beta + r) * Y_star)))
+ (
(np.exp(-1 * beta * Y_star) / ((Y - Y_star) * r))
* (np.exp(-1 * r * Y_star) - np.exp(-1 * r * Y))
)
)
)
return z
[docs]
def sl(Y, bonus, r):
r"""
Makes the calculation for straight line (SL) method of depreciation.
.. math::
z = \frac{1 - e^{-rY}}{Yr}
Args:
Y (array_like): asset life in years
bonus (array_like): rate of bonus depreciation
r (scalar): discount rate
Returns:
z (array_like): net present value of depreciation deductions for
$1 of investment
"""
z = bonus + ((1 - bonus) * ((1 - np.exp(-1 * r * Y)) / (r * Y)))
return z
[docs]
def econ(delta, bonus, r, pi):
r"""
Makes the calculation for the NPV of depreciation deductions using
economic depreciation rates.
.. math::
z = \frac{\delta}{(\delta + r - \pi)}
Args:
delta (array_like): rate of economic depreciation
bonus (array_like): rate of bonus depreciation
r (scalar): discount rate
pi (scalar): inflation rate
Returns:
z (array_like): net present value of depreciation deductions for
$1 of investment
"""
z = bonus + ((1 - bonus) * (delta / (delta + r - pi)))
return z
def income_forecast(Y, delta, bonus, r):
r"""
Makes the calculation for the Income Forecast method.
The Income Forecast method involved deducting expenses in relation
to forecasted income over the next 10 years. CCC follows the CBO
methodology (CBO, 2018:
https://www.cbo.gov/system/files/2018-11/54648-Intangible_Assets.pdf)
and approximate this method with the DBSL method, but with a the "b"
factor determined by economic depreciation rates.
.. math::
z = \frac{\beta}{\beta+r}\left[1-e^{-(\beta+r)Y^{*}}\right]+
\frac{e^{-\beta Y^{*}}}{(Y-Y^{*})r}
\left[e^{-rY^{*}}-e^{-rY}\right]
Args:
Y (array_like): asset life in years
delta (array_like): rate of economic depreciation
bonus (array_like): rate of bonus depreciation
r (scalar): discount rate
Returns:
z (array_like): net present value of depreciation deductions for
$1 of investment
"""
b = 10 * delta
beta = b / Y
Y_star = Y * (1 - (1 / b))
z = bonus + (
(1 - bonus)
* (
((beta / (beta + r)) * (1 - np.exp(-1 * (beta + r) * Y_star)))
+ (
(np.exp(-1 * beta * Y_star) / ((Y - Y_star) * r))
* (np.exp(-1 * r * Y_star) - np.exp(-1 * r * Y))
)
)
)
return z
[docs]
def npv_tax_depr(df, r, pi, land_expensing):
"""
Depending on the method of depreciation, makes calls to either
the straight line or declining balance calculations.
Args:
df (Pandas DataFrame): assets by type and tax treatment
r (scalar): discount rate
pi (scalar): inflation rate
land_expensing (scalar): rate of expensing on land
Returns:
z (Pandas series): NPV of depreciation deductions for all asset
types and tax treatments
"""
idx = (df["method"] == "DB 200%") | (df["method"] == "DB 150%")
df.loc[idx, "z"] = dbsl(
df.loc[idx, "Y"], df.loc[idx, "b"], df.loc[idx, "bonus"], r
)
idx = df["method"] == "SL"
df.loc[idx, "z"] = sl(df.loc[idx, "Y"], df.loc[idx, "bonus"], r)
idx = df["method"] == "Economic"
df.loc[idx, "z"] = econ(df.loc[idx, "delta"], df.loc[idx, "bonus"], r, pi)
idx = df["method"] == "Income Forecast"
df.loc[idx, "z"] = income_forecast(
df.loc[idx, "Y"], df.loc[idx, "delta"], df.loc[idx, "bonus"], r
)
idx = df["method"] == "Expensing"
df.loc[idx, "z"] = 1.0
idx = df["asset_name"] == "Land"
df.loc[idx, "z"] = np.squeeze(land_expensing)
idx = df["asset_name"] == "Inventories"
df.loc[idx, "z"] = 0.0 # not sure why I have to do this with changes
z = df["z"]
return z
[docs]
def eq_coc(
delta,
z,
w,
u,
u_d,
inv_tax_credit,
psi,
nu,
pi,
r,
re_credit=None,
asset_code=None,
ind_code=None,
):
r"""
Compute the cost of capital
.. math::
\rho = \frac{(r-\pi+\delta)}{1-u}(1-u_dz(1-\psi k) - k\nu)+w-\delta
Args:
delta (array_like): rate of economic depreciation
z (array_like): net present value of depreciation deductions for
$1 of investment
w (scalar): property tax rate
u (scalar): marginal tax rate for the first layer of
income taxes
u_d (scalar): marginal tax rate on deductions
inv_tax_credit (scalar): investment tax credit rate
psi (scalar): fraction investment tax credit that affects
depreciable basis of the investment
nu (scalar): NPV of the investment tax credit
pi (scalar): inflation rate
r (scalar): discount rate
re_credit (dict): rate of R&E credit by asset or industry
asset_code (array_like): asset code
ind_code (array_like): industry code
Returns:
rho (array_like): the cost of capital
"""
# Initialize re_credit_rate (only needed if arrays are passed in --
# if not, can include the R&E credit in the inv_tax_credit object)
if isinstance(delta, np.ndarray):
re_credit_rate_ind = np.zeros_like(delta)
re_credit_rate_asset = np.zeros_like(delta)
# Update by R&E credit rate amounts by industry
if (ind_code is not None) and (re_credit is not None):
idx = [
index
for index, element in enumerate(ind_code)
if element in re_credit["By industry"].keys()
]
ind_code_idx = [ind_code[i] for i in idx]
re_credit_rate_ind[idx] = [
re_credit["By industry"][ic] for ic in ind_code_idx
]
# Update by R&E credit rate amounts by asset
if (asset_code is not None) and (re_credit is not None):
idx = [
index
for index, element in enumerate(asset_code)
if element in re_credit["By asset"].keys()
]
asset_code_idx = [asset_code[i] for i in idx]
re_credit_rate_asset[idx] = [
re_credit["By asset"][ac] for ac in asset_code_idx
]
# take the larger of the two R&E credit rates
inv_tax_credit += np.maximum(re_credit_rate_asset, re_credit_rate_ind)
rho = (
((r - pi + delta) / (1 - u))
* (1 - inv_tax_credit * nu - u_d * z * (1 - psi * inv_tax_credit))
+ w
- delta
)
return rho
[docs]
def eq_coc_inventory(u, phi, Y_v, pi, r):
r"""
Compute the cost of capital for inventories
.. math::
\rho = \phi \rho_{FIFO} + (1-\phi)\rho_{LIFO}
Args:
u (scalar): statutory marginal tax rate for the first layer of
income taxes
phi (scalar): fraction of inventories that use FIFO accounting
Y_v (scalar): average number of year inventories are held
pi (scalar): inflation rate
r (scalar): discount rate
Returns:
rho (scalar): cost of capital for inventories
"""
rho_FIFO = ((1 / Y_v) * np.log((np.exp(r * Y_v) - u) / (1 - u))) - pi
rho_LIFO = (1 / Y_v) * np.log((np.exp((r - pi) * Y_v) - u) / (1 - u))
rho = phi * rho_FIFO + (1 - phi) * rho_LIFO
return rho
[docs]
def eq_ucc(rho, delta):
r"""
Compute the user cost of capital
.. math::
ucc = \rho + \delta
Args:
rho (array_like): cost of capital
delta (array_like): rate of economic depreciation
Returns:
ucc (array_like): the user cost of capital
"""
ucc = rho + delta
return ucc
[docs]
def eq_metr(rho, r_prime, pi):
r"""
Compute the marginal effective tax rate (METR)
.. math::
metr = \frac{\rho - (r^{'}-\pi)}{\rho}
Args:
rho (array_like): cost of capital
r_prime (array_like): after-tax rate of return
pi (scalar): inflation rate
Returns:
metr (array_like): METR
"""
metr = (rho - (r_prime - pi)) / rho
return metr
[docs]
def eq_mettr(rho, s):
r"""
Compute the marginal effective total tax rate (METTR)
.. math::
mettr = \frac{\rho - s}{\rho}
Args:
rho (array_like): cost of capital
s (array_like): after-tax return on savings
Returns:
mettr (array_like): METTR
"""
mettr = (rho - s) / rho
return mettr
[docs]
def eq_tax_wedge(rho, s):
r"""
Compute the tax wedge
.. math::
wedge = \rho - s
Args:
rho (array_like): cost of capital
s (array_like): after-tax return on savings
Returns:
wedge (array_like): tax wedge
"""
wedge = rho - s
return wedge
[docs]
def eq_eatr(rho, metr, p, u):
r"""
Compute the effective average tax rate (EATR).
.. math::
eatr = \left(\frac{p - rho}{p}\right)u +
\left(\frac{\rho}{p}\right)metr
Args:
rho (array_like): cost of capital
metr (array_like): marginal effective tax rate
p (scalar): profit rate
u (scalar): statutory marginal tax rate for the first layer of
income taxes
Returns:
eatr (array_like): EATR
"""
eatr = ((p - rho) / p) * u + (rho / p) * metr
return eatr
