Cashflows: A Package for Investment Modeling and Advanced Engineering Economics using Python¶
Contents:
Time value of money models¶
This module contains functions for computing the time value of the money.
pvfv: computes the missing value in the equationfval = pval * (1 + rate) ** nper, that represents the following cashflow.
pvpmt: computes the missing value (pmt, pval, nper, nrate) in a model relating a present value and a finite sequence of payments made at the end of the period (payments in arrears, or ordinary annuities), as indicated in the following cashflow diagram:
pmtfv: computes the missing value (pmt, fval, nper, nrate) in a model relating a finite sequence of payments in advance (annuities due) and a future value, as indicated in the following diagram:
tvmm: computes the missing value (pmt, fval, pval, `nper, nrate) in a model relating a finite sequence of payments made at the beginning or at the end of the period, a present value, a future value, and an interest rate, as indicated in the following diagram:
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cashflows.tvmm.amortize(pval=None, fval=None, pmt=None, nrate=None, nper=None, due=0, pyr=1, noprint=True)[source]¶ Amortization schedule of a loan.
Parameters: - pval (float) – present value.
- fval (float) – Future value.
- pmt (float) – periodic payment per period.
- nrate (float) – nominal interest rate per year.
- nper (int) – total number of compounding periods.
- due (int) – When payments are due.
- pyr (int, list) – number of periods per year.
- noprint (bool) – prints enhanced output
Returns: (principal, interest, payment, balance)
Return type: A tuple
Examples.
>>> pmt = tvmm(pval=100, nrate=10, nper=5, fval=0) >>> amortize(pval=100, nrate=10, nper=5, fval=0, noprint=False) t Beginning Periodic Interest Principal Final Principal Payment Payment Repayment Principal Amount Amount Amount -------------------------------------------------------------------- 0 100.00 0.00 0.00 0.00 100.00 1 100.00 -26.38 10.00 -16.38 83.62 2 83.62 -26.38 8.36 -18.02 65.60 3 65.60 -26.38 6.56 -19.82 45.78 4 45.78 -26.38 4.58 -21.80 23.98 5 23.98 -26.38 2.40 -23.98 0.00
>>> amortize(pval=-100, nrate=10, nper=5, fval=0, noprint=False) t Beginning Periodic Interest Principal Final Principal Payment Payment Repayment Principal Amount Amount Amount -------------------------------------------------------------------- 0 -100.00 0.00 0.00 0.00 -100.00 1 -100.00 26.38 -10.00 16.38 -83.62 2 -83.62 26.38 -8.36 18.02 -65.60 3 -65.60 26.38 -6.56 19.82 -45.78 4 -45.78 26.38 -4.58 21.80 -23.98 5 -23.98 26.38 -2.40 23.98 -0.00
>>> amortize(pval=100, nrate=10, nper=5, fval=0, due=1, noprint=False) t Beginning Periodic Interest Principal Final Principal Payment Payment Repayment Principal Amount Amount Amount -------------------------------------------------------------------- 0 100.00 -23.98 0.00 -23.98 76.02 1 76.02 -23.98 7.60 -16.38 59.64 2 59.64 -23.98 5.96 -18.02 41.62 3 41.62 -23.98 4.16 -19.82 21.80 4 21.80 -23.98 2.18 -21.80 0.00 5 0.00 0.00 0.00 0.00 0.00
>>> amortize(pval=-100, nrate=10, nper=5, fval=0, due=1, noprint=False) t Beginning Periodic Interest Principal Final Principal Payment Payment Repayment Principal Amount Amount Amount -------------------------------------------------------------------- 0 -100.00 23.98 0.00 23.98 -76.02 1 -76.02 23.98 -7.60 16.38 -59.64 2 -59.64 23.98 -5.96 18.02 -41.62 3 -41.62 23.98 -4.16 19.82 -21.80 4 -21.80 23.98 -2.18 21.80 -0.00 5 -0.00 0.00 -0.00 -0.00 -0.00
>>> principal, interest, payment, balance = amortize(pval=100, ... nrate=10, nper=5, fval=0)
>>> principal [0, -16.37..., -18.01..., -19.81..., -21.80..., -23.98...]
>>> interest [0, 10.0, 8.36..., 6.56..., 4.57..., 2.39...]
>>> payment [0, -26.37..., -26.37..., -26.37..., -26.37..., -26.37...]
>>> balance [100, 83.62..., 65.60..., 45.78..., 23.98..., 1...]
>>> principal, interest, payment, balance = amortize(pval=100, ... nrate=10, nper=5, pmt=pmt)
>>> sum(interest) 31.89...
>>> sum(principal) -99.99...
>>> principal, interest, payment, balance = amortize(fval=0, ... nrate=10, nper=5, pmt=pmt)
>>> sum(interest) 31.89...
>>> sum(principal) -99.99...
>>> principal, interest, payment, balance = amortize(pval=100, ... fval=0, nper=5, pmt=pmt)
>>> sum(interest) 31.89...
>>> sum(principal) -99.99...
>>> amortize(pval=100, fval=0, nrate=10, pmt=pmt, noprint=False) t Beginning Periodic Interest Principal Final Principal Payment Payment Repayment Principal Amount Amount Amount -------------------------------------------------------------------- 0 100.00 0.00 0.00 0.00 100.00 1 100.00 -26.38 10.00 -16.38 83.62 2 83.62 -26.38 8.36 -18.02 65.60 3 65.60 -26.38 6.56 -19.82 45.78 4 45.78 -26.38 4.58 -21.80 23.98 5 23.98 -26.38 2.40 -23.98 0.00
>>> principal, interest, payment, balance = amortize(pval=100, ... fval=0, nrate=10, pmt=pmt)
>>> sum(interest) 31.89...
>>> sum(principal) -99.99...
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cashflows.tvmm.pmtfv(pmt=None, fval=None, nrate=None, nper=None, pyr=1, noprint=True)[source]¶ CComputes the missing argument (set to None) in the function call.
Parameters: - pmt (float, list) – Periodic payment.
- fval (float, list) – Future value.
- nrate (float, list) – Nominal rate per year.
- nper (int, list) – Number of compounding periods.
- pyr (int, list) – number of periods per year.
- noprint (bool) – prints enhanced output
Returns: The value of the parameter set to None in the function call.
Effective interest rate per period is calculated as nrate / pyr.
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cashflows.tvmm.pvfv(pval=None, fval=None, nrate=None, nper=None, pyr=1, noprint=True)[source]¶ Computes the missing argument (set to None) in the function call.
Parameters: - pval (float, list) – Present value.
- fval (float, list) – Future value.
- nrate (float, list) – Nominal interest rate per year.
- nper (int, list) – Number of compounding periods.
- pyr (int, list) – number of periods per year.
- noprint (bool) – prints enhanced output
Returns: The value of the parameter set to None in the function call.
Effective interest rate per period is calculated as nrate / pyr.
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cashflows.tvmm.pvpmt(pmt=None, pval=None, nrate=None, nper=None, pyr=1, noprint=True)[source]¶ Computes the missing argument (set to None) in the function call.
Parameters: - pmt (float, list) – Periodic payment.
- pval (float, list) – Present value.
- nrate (float, list) – Nominal interest rate per year.
- nper (int, list) – Number of compounding periods.
- pyr (int, list) – number of periods per year.
- noprint (bool) – prints enhanced output
Returns: The value of the parameter set to None in the function call.
Effective interest rate per period is calculated as nrate / pyr.
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cashflows.tvmm.tvmm(pval=None, fval=None, pmt=None, nrate=None, nper=None, due=0, pyr=1, noprint=True)[source]¶ Computes present and future values, periodic payments, nominal interest rate or number of periods.
Parameters: - pval (float, list) – Present value.
- fval (float, list) – Future value.
- pmt (float, list) – Periodic payment.
- nrate (float, list) – Nominal interest rate per year.
- nper (int, list) – Number of compounding periods.
- due (int) – When payments are due.
- pyr (int, list) – number of periods per year.
- noprint (bool) – prints enhanced output
Returns: Argument set to None in the function call.
Effective interest rate per period is calculated as nrate / pyr.
Examples.
In this example shows how to find different values for a loan of 5000, with a monthly payment of 130 at the end of the month, a life of 48 periods, and a interest rate of 0.94 per month (equivalent to 11.32% nominal)
- Periodic payment:
>>> pmt = tvmm(pval=5000, nrate=11.32/12, nper=48, fval=0) >>> pmt -130.00...
- Future value:
>>> tvmm(pval=5000, nrate=11.32/12, nper=48, pmt=pmt) -0.0...
- Present value:
>>> tvmm(nrate=11.32/12, nper=48, pmt=pmt, fval = 0.0) 5000...
- Rate:
>>> tvmm(pval=5000, nper=48, pmt=pmt, fval = 0.0) 0.94...
- Number of periods:
>>> tvmm(pval=5000, nrate=11.32/12, pmt=pmt, fval=0.0) 48.0...
- Periodic paymnts:
>>> tvmm(pval=5000, nrate=11.32, nper=48, fval=0, pyr=12) -130.00...
- Nominal rate:
>>> tvmm(pval=5000, nper=48, pmt=pmt, fval = 0.0, pyr=12) 11.32...
>>> tvmm(pval=5000, nrate=11.32, nper=48, fval=0, pyr=12, noprint=False) Present Value: ....... 5000.00 Future Value: ........ 0.00 Payment: ............. -130.01 Due: ................. END No. of Periods: ...... 48.00 Compoundings per Year: 12 Nominal Rate: ....... 11.32 Effective Rate: ..... 11.93 Periodic Rate: ...... 0.94
>>> tvmm(pval=[5, 500, 5], nrate=11.32, nper=48, fval=0, pyr=12, noprint=False) # pval fval pmt nper nrate erate prate due ------------------------------------------------------ 0 5.00 0.00 -0.13 48.00 11.32 11.93 0.94 END 1 500.00 0.00 -0.13 48.00 11.32 11.93 0.94 END 2 5.00 0.00 -0.13 48.00 11.32 11.93 0.94 END
Interest rate transformations¶
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cashflows.rate.equivalent_rate(nrate=None, erate=None, prate=None)[source]¶ Returns the equivalent interest rate over a time period.
Parameters: - nrate (TimeSeries) – Nominal interest rate per year.
- nrate – Effective interest rate per year.
- prate (TimeSeries) – Periodic interest rate.
Returns: float value.
Only one of the interest rate must be supplied for the computation.
>>> equivalent_rate(prate=interest_rate([10]*5)) 10.0...
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cashflows.rate.iconv(nrate=None, erate=None, prate=None, pyr=1)[source]¶ The function iconv computes the conversion among periodic, nominal and effective interest rates. Only an interest rate (periodic, nominal or effective) must be specified and the other two are computed. The periodic rate is the rate used in each compounding period. The effective rate is the equivalent rate that produces the same interest earnings that a periodic rate when there is P compounding periods in a year. The nominal rate is defined as the annual rate computed as P times the periodic rate.
Parameters: - nrate (float, list, TimeSeries) – nominal interest rate per year.
- erate (float, list, TimeSeries) – effective interest rate per year.
- prate (float, list, TimeSeries) – periodic rate
- pyr (int, list) – number of compounding periods per year
Returns: - (nrate, prate): when erate is specified.
- (erate, prate): when nrate is specified.
- (nrate, erate): when prate is specified.
Return type: A tuple
Effective rate to nominal rate compounded monthly and monthly peridic rate.
>>> iconv(erate=10, pyr=12) (9.56..., 0.79...)
>>> iconv(prate=1, pyr=12) (12, 12.68...)
>>> iconv(nrate=10, pyr=12) (10.47..., 0.83...)
iconv accepts Python vectors.
>>> iconv(erate=10, pyr=[3, 6, 12]) ([9.68..., 9.60..., 9.56...], [3.22..., 1.60..., 0.79...])
>>> iconv(prate=1, pyr=[3, 6, 12]) ([3, 6, 12], [3.03..., 6.15..., 12.68...])
>>> iconv(nrate=10, pyr=[3, 6, 12]) ([10.33..., 10.42..., 10.47...], [3.33..., 1.66..., 0.83...])
>>> iconv(erate=[10, 12, 14], pyr=12) ([9.56..., 11.38..., 13.17...], [0.79..., 0.94..., 1.09...])
>>> iconv(prate=[1, 2, 3], pyr=12) ([12, 24, 36], [12.68..., 26.82..., 42.57...])
>>> iconv(nrate=[10, 12, 14], pyr=12) ([10.47..., 12.68..., 14.93...], [0.83..., 1.0, 1.16...])
When a rate and the number of compounding periods (pyr) are vectors, they must have the same length. Computations are executed using the first rate with the first compounding and so on.
>>> iconv(erate=[10, 12, 14], pyr=[3, 6, 12]) ([9.68..., 11.44..., 13.17...], [3.22..., 1.90..., 1.09...])
>>> iconv(nrate=[10, 12, 14], pyr=[3, 6, 12]) ([10.33..., 12.61..., 14.93...], [3.33..., 2.0, 1.16...])
>>> iconv(prate=[1, 2, 3], pyr=[3, 6, 12]) ([3, 12, 36], [3.03..., 12.61..., 42.57...])
iconv accepts TimeSeries objects
>>> erate, prate = iconv(nrate = interest_rate(const_value=12, nper=12, pyr=2)) >>> prate Time Series: Start = (0, 0) End = (5, 1) pyr = 2 Data = (0, 0)-(5, 1) [12] 6.00
>>> erate Time Series: Start = (0, 0) End = (5, 1) pyr = 2 Data = (0, 0)-(5, 1) [12] 12.36
>>> erate, prate = iconv(nrate = interest_rate(const_value=12, nper=12, pyr=4)) >>> prate Qtr0 Qtr1 Qtr2 Qtr3 0 3.00 3.00 3.00 3.00 1 3.00 3.00 3.00 3.00 2 3.00 3.00 3.00 3.00
>>> erate Qtr0 Qtr1 Qtr2 Qtr3 0 12.55 12.55 12.55 12.55 1 12.55 12.55 12.55 12.55 2 12.55 12.55 12.55 12.55
>>> nrate, prate = iconv(erate = erate) >>> nrate Qtr0 Qtr1 Qtr2 Qtr3 0 12.00 12.00 12.00 12.00 1 12.00 12.00 12.00 12.00 2 12.00 12.00 12.00 12.00
>>> prate Qtr0 Qtr1 Qtr2 Qtr3 0 3.00 3.00 3.00 3.00 1 3.00 3.00 3.00 3.00 2 3.00 3.00 3.00 3.00
>>> nrate, erate = iconv(prate = prate) >>> nrate Qtr0 Qtr1 Qtr2 Qtr3 0 12.00 12.00 12.00 12.00 1 12.00 12.00 12.00 12.00 2 12.00 12.00 12.00 12.00
>>> erate Qtr0 Qtr1 Qtr2 Qtr3 0 12.55 12.55 12.55 12.55 1 12.55 12.55 12.55 12.55 2 12.55 12.55 12.55 12.55
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cashflows.rate.to_compound_factor(nrate=None, erate=None, prate=None, base_date=0)[source]¶ Returns a list of compounding factors calculated as (1 + r)^(t - t0).
Parameters: - nrate (TimeSeries) – Nominal interest rate per year.
- nrate – Effective interest rate per year.
- prate (TimeSeries) – Periodic interest rate.
- base_date (int, tuple) – basis time.
Returns: Compound factor (list)
Examples
>>> nrate = interest_rate(const_value=4,nper=10, pyr=4) >>> erate, prate = iconv(nrate=nrate) >>> to_compound_factor(prate=prate, base_date=2) [0.980..., 0.990..., 1.0, 1.01, 1.0201, 1.030..., 1.040..., 1.051..., 1.061..., 1.072...]
>>> to_compound_factor(nrate=nrate, base_date=2) [0.980..., 0.990..., 1.0, 1.01, 1.0201, 1.030..., 1.040..., 1.051..., 1.061..., 1.072...]
>>> to_compound_factor(erate=erate, base_date=2) [0.980..., 0.990..., 1.0, 1.01, 1.0201, 1.030..., 1.040..., 1.051..., 1.061..., 1.072...]
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cashflows.rate.to_discount_factor(nrate=None, erate=None, prate=None, base_date=0)[source]¶ Returns a list of discount factors calculated as 1 / (1 + r)^(t - t0).
Parameters: - nrate (TimeSeries) – Nominal interest rate per year.
- nrate – Effective interest rate per year.
- prate (TimeSeries) – Periodic interest rate.
- base_date (int, tuple) – basis time.
Returns: List of float values
Only one of the interest rates must be supplied for the computation.
>>> nrate = interest_rate(const_value=4,nper=10, pyr=4) >>> erate, prate = iconv(nrate=nrate) >>> to_discount_factor(nrate=nrate, base_date=2) [1.0201, 1.01, 1.0, 0.990..., 0.980..., 0.970..., 0.960..., 0.951..., 0.942..., 0.932...]
>>> to_discount_factor(erate=erate, base_date=2) [1.0201, 1.01, 1.0, 0.990..., 0.980..., 0.970..., 0.960..., 0.951..., 0.942..., 0.932...]
>>> to_discount_factor(prate=prate, base_date=2) [1.0201, 1.01, 1.0, 0.990..., 0.980..., 0.970..., 0.960..., 0.951..., 0.942..., 0.932...]
Time series objects¶
This module implements a TimeSeries object that is used to represent generic cashflows and interest rate.
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class
cashflows.gtimeseries.TimeSeries(start=None, end=None, nper=None, pyr=1)[source]¶ Bases:
objectTime series object for representing generic cashflows and interest rates.
Examples.
>>> TimeSeries(start=(2000, 0), end=(2002, 3), nper=12, pyr=4) Qtr0 Qtr1 Qtr2 Qtr3 2000 0.00 0.00 0.00 0.00 2001 0.00 0.00 0.00 0.00 2002 0.00 0.00 0.00 0.00
>>> TimeSeries(start=(2000, 0), end=(2002, 3), pyr=4) Qtr0 Qtr1 Qtr2 Qtr3 2000 0.00 0.00 0.00 0.00 2001 0.00 0.00 0.00 0.00 2002 0.00 0.00 0.00 0.00
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cashflows.gtimeseries.cashflow(const_value=0, start=None, end=None, nper=None, pyr=1, spec=None)[source]¶ Returns a time series as a generic cashflow.
>>> spec = ((2000, 3), 10) >>> cashflow(const_value=1, start=(2000, 0), nper=8, pyr=4, spec=spec) Qtr0 Qtr1 Qtr2 Qtr3 2000 1.00 1.00 1.00 10.00 2001 1.00 1.00 1.00 1.00
>>> spec = [((2000, 3), 10), ((2001, 3), 10)] >>> cashflow(const_value=1, start=(2000, 0), nper=8, pyr=4, spec=spec) Qtr0 Qtr1 Qtr2 Qtr3 2000 1.00 1.00 1.00 10.00 2001 1.00 1.00 1.00 10.00
>>> spec = (3, 10) >>> cashflow(const_value=1, start=(2000, 0), nper=8, pyr=4, spec=spec) Qtr0 Qtr1 Qtr2 Qtr3 2000 1.00 1.00 1.00 10.00 2001 1.00 1.00 1.00 1.00
>>> spec = [(3, 10), (7, 10)] >>> cashflow(const_value=1, start=(2000, 0), nper=8, pyr=4, spec=spec) Qtr0 Qtr1 Qtr2 Qtr3 2000 1.00 1.00 1.00 10.00 2001 1.00 1.00 1.00 10.00
>>> cashflow(const_value=[10]*10, pyr=4) Qtr0 Qtr1 Qtr2 Qtr3 0 10.00 10.00 10.00 10.00 1 10.00 10.00 10.00 10.00 2 10.00 10.00
>>> cashflow(const_value=[-10]*4) Time Series: Start = (0,) End = (3,) pyr = 1 Data = (0,)-(3,) [4] -10.00
>>> x = cashflow(const_value=[0, 1, 2, 3], pyr=4) >>> x[3] = 10 >>> x Qtr0 Qtr1 Qtr2 Qtr3 0 0.00 1.00 2.00 10.00
>>> x[3] 10
>>> x[(0, 3)] = 0 >>> x Qtr0 Qtr1 Qtr2 Qtr3 0 0.00 1.00 2.00 0.00
>>> x[(0,2)] 2
>>> cashflow(const_value=[0, 1, 2, 2, 4, 5, 6, 7, 8]) Time Series: Start = (0,) End = (8,) pyr = 1 Data = (0,) 0.00 (1,) 1.00 (2,)-(3,) [2] 2.00 (4,) 4.00 (5,) 5.00 (6,) 6.00 (7,) 7.00 (8,) 8.00
>>> cashflow(const_value=0, nper=15, pyr=1, spec=[(t,100) for t in range(5,10)]) Time Series: Start = (0,) End = (14,) pyr = 1 Data = (0,)-(4,) [5] 0.00 (5,)-(9,) [5] 100.00 (10,)-(14,) [5] 0.00
>>> cashflow(const_value=[0, 1, 2, 3, 4, 5]).cumsum() Time Series: Start = (0,) End = (5,) pyr = 1 Data = (0,) 0.00 (1,) 1.00 (2,) 3.00 (3,) 6.00 (4,) 10.00 (5,) 15.00
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cashflows.gtimeseries.cfloplot(cflo)[source]¶ Text plot of a cashflow.
>>> cflo = cashflow(const_value=[-10, 5, 0, 20] * 3, pyr=4) >>> cfloplot(cflo) time value +------------------+------------------+ (0, 0) -10.00 ********** (0, 1) 5.00 ***** (0, 2) 0.00 * (0, 3) 20.00 ******************** (1, 0) -10.00 ********** (1, 1) 5.00 ***** (1, 2) 0.00 * (1, 3) 20.00 ******************** (2, 0) -10.00 ********** (2, 1) 5.00 ***** (2, 2) 0.00 * (2, 3) 20.00 ********************
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cashflows.gtimeseries.interest_rate(const_value=0, start=None, end=None, nper=None, pyr=1, spec=None)[source]¶ Creates a time series object specified as a interest rate.
>>> spec = ((2000, 3), 10) >>> interest_rate(const_value=1, start=(2000, 0), nper=8, pyr=4, spec=spec) Qtr0 Qtr1 Qtr2 Qtr3 2000 1.00 1.00 1.00 10.00 2001 10.00 10.00 10.00 10.00
>>> spec = [((2000, 3), 10), ((2001, 1), 20)] >>> interest_rate(const_value=1, start=(2000, 0), nper=8, pyr=4, spec=spec) Qtr0 Qtr1 Qtr2 Qtr3 2000 1.00 1.00 1.00 10.00 2001 10.00 20.00 20.00 20.00
>>> spec = (3, 10) >>> interest_rate(const_value=1, start=(2000, 0), nper=8, pyr=4, spec=spec) Qtr0 Qtr1 Qtr2 Qtr3 2000 1.00 1.00 1.00 10.00 2001 10.00 10.00 10.00 10.00
>>> spec = [(3, 10), (6, 20)] >>> interest_rate(const_value=1, start=(2000, 0), nper=8, pyr=4, spec=spec) Qtr0 Qtr1 Qtr2 Qtr3 2000 1.00 1.00 1.00 10.00 2001 10.00 10.00 20.00 20.00
>>> interest_rate(const_value=[10]*10, pyr=4) Qtr0 Qtr1 Qtr2 Qtr3 0 10.00 10.00 10.00 10.00 1 10.00 10.00 10.00 10.00 2 10.00 10.00
After tax cashflow calculation.¶
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cashflows.taxing.after_tax_cashflow(cflo, tax_rate)[source]¶ The function after_tax_cashflow returns a new cashflow object for which the values are taxed. The specified tax rate is only appled to positive values in the cashflow. Negative values are reemplazed by a zero value. cflo and tax_rate must have the same length and time specification.
Computes the after cashflow for a tax rate. Taxes are not computed for negative values in the cashflow.
Parameters: - cflo (TimeSeries) – generic cashflow.
- tax_rate (TimeSeries) – periodic income tax rate.
Returns: TimeSeries objects with taxed values
Example*
>>> cflo = cashflow(const_value=[100] * 5, spec=(0, -100)) >>> tax_rate = interest_rate(const_value=[10] * 5) >>> after_tax_cashflow(cflo=cflo, tax_rate=tax_rate) Time Series: Start = (0,) End = (4,) pyr = 1 Data = (0,) 0.00 (1,)-(4,) [4] 10.00
Currency conversion¶
The function currency_conversion allows the user to convert an cashflow in a currency to the equivalent flow in other currency using the specified exchange_rate. In addition, it is possible to include the devaluation of the foreign exchange rate.
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cashflows.currency.currency_conversion(cflo, exchange_rate=1, devaluation=None, base_date=0)[source]¶ Converts a cashflow of dollars to another currency.
Parameters: - cflo (TimeSeries) – A cashflow.
- exchange_rate (float) – Exchange rate at time base_date.
- devaluation (TimeSeries) – Devaluation rate per compounding period.
- base_date (int) – Time index for the exchange_rate in current dollars.
Returns: A TimeSeries object.
Examples.
>>> cflo = cashflow(const_value=[100] * 5) >>> currency_conversion(cflo=cflo, exchange_rate=2) Time Series: Start = (0,) End = (4,) pyr = 1 Data = (0,)-(4,) [5] 200.00
>>> currency_conversion(cflo=cflo, exchange_rate=2, ... devaluation=interest_rate(const_value=[5]*5), base_date=(2,)) Time Series: Start = (0,) End = (4,) pyr = 1 Data = (0,) 181.41 (1,) 190.48 (2,) 200.00 (3,) 210.00 (4,) 220.50
>>> cflo = cashflow(const_value=[100] * 8, pyr=4) >>> currency_conversion(cflo=cflo, ... exchange_rate=2, ... devaluation=interest_rate([1]*8, pyr=4)) Qtr0 Qtr1 Qtr2 Qtr3 0 200.00 202.00 204.02 206.06 1 208.12 210.20 212.30 214.43
>>> cflo = cashflow(const_value=[100] * 5) >>> currency_conversion(cflo=[cflo, cflo], exchange_rate=2) [Time Series: Start = (0,) End = (4,) pyr = 1 Data = (0,)-(4,) [5] 200.00 , Time Series: Start = (0,) End = (4,) pyr = 1 Data = (0,)-(4,) [5] 200.00 ]
Constant dollar transformations¶
The function const2curr computes the equivalent generic cashflow in current dollars from a generic cashflow in constant dollars of the date given by base_date. inflation is the inflation rate per compounding period. curr2const computes the inverse transformation.
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cashflows.inflation.const2curr(cflo, inflation, base_date=0)[source]¶ Converts a cashflow of constant dollars to current dollars of the time base_date.
Parameters: - cflo (TimeSeries) – A cashflow.
- inflation (TimeSeries) – Inflation rate per compounding period.
- base_date (int, tuple) – base date.
Returns: A cashflow in current money (TimeSeries)
Examples.
>>> const2curr(cflo=cashflow(const_value=[100] * 5), ... inflation=interest_rate(const_value=[10, 10, 20, 20, 20])) Time Series: Start = (0,) End = (4,) pyr = 1 Data = (0,) 100.00 (1,) 110.00 (2,) 132.00 (3,) 158.40 (4,) 190.08
>>> const2curr(cflo=cashflow(const_value=[100] * 5), ... inflation=interest_rate(const_value=[10, 10, 20, 20, 20]), base_date=4) Time Series: Start = (0,) End = (4,) pyr = 1 Data = (0,) 52.61 (1,) 57.87 (2,) 69.44 (3,) 83.33 (4,) 100.00
>>> const2curr(cflo=cashflow(const_value=[100] * 8, pyr=4), ... inflation=interest_rate(const_value=1, nper=8, pyr=4)) Qtr0 Qtr1 Qtr2 Qtr3 0 100.00 101.00 102.01 103.03 1 104.06 105.10 106.15 107.21
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cashflows.inflation.curr2const(cflo, inflation, base_date=0)[source]¶ Converts a cashflow of current dollars to constant dollars of the date base_date.
Parameters: - cflo (list, Cashflow) – A cashflow.
- inflation_rate (float, Rate) – Inflation rate per compounding period.
- base_date (int) – base time..
Returns: A cashflow in constant dollars
>>> curr2const(cflo=cashflow(const_value=[100] * 5), ... inflation=interest_rate(const_value=[10, 10, 20, 20, 20])) Time Series: Start = (0,) End = (4,) pyr = 1 Data = (0,) 100.00 (1,) 90.91 (2,) 75.76 (3,) 63.13 (4,) 52.61
>>> curr2const(cflo=cashflow(const_value=[100] * 5), ... inflation=interest_rate(const_value=[10, 10, 20, 20, 20]), base_date=4) Time Series: Start = (0,) End = (4,) pyr = 1 Data = (0,) 190.08 (1,) 172.80 (2,) 144.00 (3,) 120.00 (4,) 100.00
>>> curr2const(cflo=cashflow(const_value=[100] * 8, pyr=4), ... inflation=interest_rate(const_value=1, nper=8, pyr=4)) Qtr0 Qtr1 Qtr2 Qtr3 0 100.00 99.01 98.03 97.06 1 96.10 95.15 94.20 93.27
Analysis of cashflows¶
This module implements the following functions for financial analysis of cashflows:
timevalue: computes the equivalent net value of a cashflow in a specified time moment.net_uniform_series: computes the periodic equivalent net value of a cashflow for a specified number of payments.benefit_cost_ratio: computes the benefit cost ratio of a cashflow using a periodic interest rate for discounting the cashflow.irr: calculates the periodic internal rate of return of a cashflow.mirr: calculates the periodic modified internal rate of return of a cashflow.list_as_table: prints a list as a table. This function is useful for comparing financial indicators for different alternatives.
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cashflows.analysis.benefit_cost_ratio(cflo, prate, base_date=0)[source]¶ Computes a benefit cost ratio at time base_date of a discounted cashflow using the periodic interest rate prate.
Parameters: - prate (int float, Rate) – Periodic interest rate.
- cflo (cashflow, list) – Generic cashflow.
- base_date (int, list) – Time.
Returns: Float or list of floats.
Examples.
>>> prate = interest_rate([2]*9, pyr=4) >>> cflo = cashflow([-717.01] + [100]*8, pyr=4) >>> benefit_cost_ratio(cflo, prate) 1.02...
>>> prate = interest_rate([12]*5) >>> cflo = cashflow([-200] + [100]*4) >>> benefit_cost_ratio(cflo, prate) 1.518...
>>> benefit_cost_ratio([cflo, cflo], prate) [1.518..., 1.518...]
>>> benefit_cost_ratio(cflo, [prate, prate]) [1.518..., 1.518...]
>>> benefit_cost_ratio([cflo, cflo], [prate, prate]) [1.518..., 1.518...]
>>> benefit_cost_ratio([cflo, cflo], [prate, prate], [0, 0]) [1.518..., 1.518...]
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cashflows.analysis.irr(cflo)[source]¶ Computes the internal rate of return of a generic cashflow as a periodic interest rate.
Parameters: cflo (TimeSeries) – Generic cashflow. Returns: Float or list of floats. Examples.
>>> cflo = cashflow([-717.01] + [100]*8, pyr=4) >>> irr(cflo) 2.50...
>>> cflo = cashflow([-200] + [100]*4) >>> irr(cflo) 34.90...
>>> irr([cflo, cflo]) [34.90..., 34.90...]
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cashflows.analysis.list_as_table(data)[source]¶ Prints the list data as a table. This function is used to produce a human-readable format of a table for comparing financial indicators.
Parameters: data (list) – List of numeric values. Returns: None Example.
>>> list_as_table(data=[1, 2, 3, 4]) # Value ------------------------ 0 1.0000 1 2.0000 2 3.0000 3 4.0000
>>> prate = interest_rate([12]*5) >>> cflo = cashflow([-200] + [100]*4) >>> list_as_table(timevalue(cflo=[cflo, cflo, cflo], prate=prate)) # Value ------------------------ 0 103.7349 1 103.7349 2 103.7349
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cashflows.analysis.mirr(cflo, finance_rate=0, reinvest_rate=0)[source]¶ Computes the modified internal rate of return of a generic cashflow as a periodic interest rate.
Parameters: - cflo (list, cashflow) – Generic cashflow.
- finance_rate (float) – Periodic interest rate applied to negative values of the cashflow.
- reinvest_rate (float) – Periodic interest rate applied to positive values of the cashflow.
Returns: Float or list of floats.
Examples.
>>> cflo = cashflow([-200] + [100]*4) >>> mirr(cflo) 18.92...
>>> mirr([cflo, cflo]) [18.92..., 18.92...]
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cashflows.analysis.net_uniform_series(cflo, prate, nper=1)[source]¶ Computes a net uniform series equivalent of a cashflow. This is, a fixed periodic payment during nper periods that is equivalent to the cashflow cflo at the periodic interest rate prate.
Parameters: - cflo (cashflow) – Generic cashflow.
- prate (TimeSeries) – Periodic interest rate.
- nper (int, list) – Number of equivalent payment periods.
Returns: Float or list of floats.
Examples.
>>> prate = interest_rate([2]*9, pyr=4) >>> cflo = cashflow([-732.54] + [100]*8, pyr=4) >>> net_uniform_series(cflo, prate) 0.00...
>>> prate = interest_rate([12]*5) >>> cflo = cashflow([-200] + [100]*4) >>> net_uniform_series(cflo, prate) 116.18...
>>> net_uniform_series([cflo, cflo], prate) [116.18..., 116.18...]
>>> net_uniform_series(cflo, [prate, prate]) [116.18..., 116.18...]
>>> net_uniform_series([cflo, cflo], [prate, prate]) [116.18..., 116.18...]
>>> net_uniform_series([cflo, cflo], [prate, prate], nper=5) [28.77..., 28.77...]
>>> net_uniform_series([cflo, cflo], [prate, prate], nper=[5, 5]) [28.77..., 28.77...]
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cashflows.analysis.timevalue(cflo, prate, base_date=0, utility=None)[source]¶ Computes the equivalent net value of a generic cashflow at time base_date using the periodic interest rate prate. If base_date is 0, timevalue computes the net present value of the cashflow. If base_date is the index of the last element of cflo, this function computes the equivalent future value.
Parameters: - cflo (TimeSeries, list of TimeSeries) – Generic cashflow.
- prate (TimeSeries) – Periodic interest rate.
- base_date (int, tuple) – Time.
- utility (function) – Utility function.
Returns: Float or list of floats.
Examples.
>>> cflo = cashflow([-732.54] + [100]*8, pyr=4) >>> prate = interest_rate([2]*9, pyr=4) >>> timevalue(cflo, prate) 0.00...
>>> prate = interest_rate([12]*5) >>> cflo = cashflow([100]*5, spec = (0, -200)) >>> timevalue(cflo, prate) 103.73...
>>> timevalue(cflo, prate, 4) 163.22...
>>> timevalue(cflo, prate, base_date=0, utility=exp_utility_fun(200)) -84.15...
>>> timevalue(cflo, prate, base_date=0, utility=log_utility_fun(210)) 369092793...
>>> timevalue(cflo, prate, base_date=0, utility=sqrt_utility_fun(210)) 2998.12...
>>> prate = interest_rate([12]*5) >>> cflo = cashflow([-200] + [100]*4) >>> timevalue(cflo=cflo, prate=prate) 103.73...
>>> timevalue(cflo=[cflo, cflo], prate=prate) [103.73..., 103.73...]
>>> timevalue(cflo=cflo, prate=[prate, prate]) [103.73..., 103.73...]
>>> timevalue(cflo=[cflo, cflo], prate=[prate, prate]) [103.73..., 103.73...]
>>> timevalue(cflo=[cflo, cflo], prate=[prate, prate], base_date=[4, 4]) [163.22..., 163.22...]
Bond Valuation¶
This module computes the present value or the yield-to-maturity of of the expected cashflow of a bond. Also,it is possible to make a sensibility analysis for different values for the yield-to-maturity and one present value of the bond.
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cashflows.bond.bond(face_value=None, coupon_rate=None, coupon_value=None, num_coupons=None, value=None, ytm=None)[source]¶ Evaluation of bond investments.
Parameters: - face_value (float) – the bond’s value-at-maturity.
- coupon_rate (float) – rate for calculate the coupon payment.
- coupon_value (float) – periodic payment.
- num_coupons (int) – number of couont payments before maturity.
- value (float, list) – present value of the bond
- ytm (float, list) – yield-to-maturity.
Returns: - value: when ytm is specified.
- ytm: when value is specified.
- None: when ytm and value are specified. Prints a sensibility table.
Return type: None, a float value, or a list of float values
When coupon_rate is defined, coupon_value is calculated automaticly.
Examples:
>>> bond(face_value=1000, coupon_value=56, num_coupons=10, ytm=5.6) 1000.0...
>>> bond(face_value=1000, coupon_rate=5.6, num_coupons=10, value=1000) 5.6...
Also, it is possible to make sensibility analysis for bond’s data. In the following case, the present value of the bond is calculated for various values of the yield-to-maturity.
>>> bond(face_value=1000, coupon_rate=5.6, num_coupons=10, ... ytm=[4.0, 5.0, 5.6, 6.0, 7.0]) [1129.77..., 1046.33..., 1000.0..., 970.55..., 901.66...]
And for different values:
>>> bond(face_value=1000, coupon_rate=5.6, num_coupons=10, ... value=[900, 1000, 1100]) [7.0..., 5.6..., 4.3...]
When values for the yield-to-maturity and one value for present value of the bond are supplied, the function prints a report.
>>> bond(face_value=1000, coupon_rate=5.6, num_coupons=10, ... ytm=[4.0, 5.0, 5.6, 6.0, 7.0], value=1000) Bond valuation analysis Reference price: 1000 Analysis: Yield Value Change (%) ($) (%) ------------------------ 4.00 1129.77 12.98 5.00 1046.33 4.63 5.60 1000.00 0.00 6.00 970.56 -2.94 7.00 901.67 -9.83
Asset depreciation¶
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cashflows.depreciation.depreciation_db(costs, life, salvalue=None, factor=1, convert_to_sl=True, delay=None, noprint=True)[source]¶ Computes the depreciation of an asset using the declining balance method.
Parameters: - cost (TimeSeries) – the cost per period of the assets.
- life (TimeSeries) – number of depreciation periods for the asset.
- salvalue (TimeSeries) – salvage value as a percentage of cost.
- factor (float) – acelerating factor for depreciation.
- convert_to_sl (bool) – converts to straight line method?
- noprint (bool) – when True, the procedure prints a depreciation table.
Returns: depreciation per period and accumulated depreciation per period
Return type: A tuple (dep, accum) of lists (tuple)
Examples.
>>> costs1 = cashflow(const_value=0, nper=16, spec=(0, 1000), pyr=4) >>> costs2 = cashflow(const_value=0, nper=16, spec=[(0, 1000), (8, 1000)], pyr=4) >>> life1 = cashflow(const_value=0, nper=16, spec=(0, 4), pyr=4) >>> life2 = cashflow(const_value=0, nper=16, spec=[(0, 4), (8, 4)], pyr=4) >>> delay12 = cashflow(const_value=0, nper=16, spec=(0, 2), pyr=4) >>> delay22 = cashflow(const_value=0, nper=16, spec=[(0, 2), (8, 2)], pyr=4) >>> depreciation_db(costs=costs1, life=life1, factor=1.5, convert_to_sl=False) Qtr0 Qtr1 Qtr2 Qtr3 0 0.00 375.00 234.38 146.48 1 91.55 0.00 0.00 0.00 2 0.00 0.00 0.00 0.00 3 0.00 0.00 0.00 0.00
>>> depreciation_db(costs=costs1, life=life1, factor=1.5, convert_to_sl=False, noprint=False) t Beg. Cost Depre. Accum. End. Book Depre. Book Value Value ---------------------------------------------- (0, 0) 0.00 1000.00 0.00 0.00 1000.00 (0, 1) 1000.00 0.00 375.00 375.00 625.00 (0, 2) 625.00 0.00 234.38 609.38 390.62 (0, 3) 390.62 0.00 146.48 755.86 244.14 (1, 0) 244.14 0.00 91.55 847.41 152.59 (1, 1) 152.59 0.00 0.00 847.41 152.59 (1, 2) 152.59 0.00 0.00 847.41 152.59 (1, 3) 152.59 0.00 0.00 847.41 152.59 (2, 0) 152.59 0.00 0.00 847.41 152.59 (2, 1) 152.59 0.00 0.00 847.41 152.59 (2, 2) 152.59 0.00 0.00 847.41 152.59 (2, 3) 152.59 0.00 0.00 847.41 152.59 (3, 0) 152.59 0.00 0.00 847.41 152.59 (3, 1) 152.59 0.00 0.00 847.41 152.59 (3, 2) 152.59 0.00 0.00 847.41 152.59 (3, 3) 152.59 0.00 0.00 847.41 152.59
>>> depreciation_db(costs=costs1, life=life1, delay=delay12, factor=1.5, convert_to_sl=False) Qtr0 Qtr1 Qtr2 Qtr3 0 0.00 0.00 0.00 375.00 1 234.38 146.48 91.55 0.00 2 0.00 0.00 0.00 0.00 3 0.00 0.00 0.00 0.00
>>> depreciation_db(costs=costs2, life=life2, factor=1.5, convert_to_sl=False) Qtr0 Qtr1 Qtr2 Qtr3 0 0.00 375.00 234.38 146.48 1 91.55 0.00 0.00 0.00 2 0.00 375.00 234.38 146.48 3 91.55 0.00 0.00 0.00
>>> depreciation_db(costs=costs2, life=life2, delay=delay22, factor=1.5, convert_to_sl=False) Qtr0 Qtr1 Qtr2 Qtr3 0 0.00 0.00 0.00 375.00 1 234.38 146.48 91.55 0.00 2 0.00 0.00 0.00 375.00 3 234.38 146.48 91.55 0.00
>>> depreciation_db(costs=costs2, life=life2, delay=delay22, factor=1.5, convert_to_sl=False, noprint=False) t Beg. Cost Depre. Accum. End. Book Depre. Book Value Value ---------------------------------------------- (0, 0) 0.00 1000.00 0.00 0.00 1000.00 (0, 1) 1000.00 0.00 0.00 0.00 1000.00 (0, 2) 1000.00 0.00 0.00 0.00 1000.00 (0, 3) 1000.00 0.00 375.00 375.00 625.00 (1, 0) 625.00 0.00 234.38 609.38 390.62 (1, 1) 390.62 0.00 146.48 755.86 244.14 (1, 2) 244.14 0.00 91.55 847.41 152.59 (1, 3) 152.59 0.00 0.00 847.41 152.59 (2, 0) 152.59 1000.00 0.00 847.41 1152.59 (2, 1) 1152.59 0.00 0.00 847.41 1152.59 (2, 2) 1152.59 0.00 0.00 847.41 1152.59 (2, 3) 1152.59 0.00 375.00 1222.41 777.59 (3, 0) 777.59 0.00 234.38 1456.79 543.21 (3, 1) 543.21 0.00 146.48 1603.27 396.73 (3, 2) 396.73 0.00 91.55 1694.82 305.18 (3, 3) 305.18 0.00 0.00 1694.82 305.18
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cashflows.depreciation.depreciation_sl(costs, life, salvalue=None, delay=None, noprint=True)[source]¶ Computes the depreciation of an asset using straight line depreciation method.
Parameters: - cost (TimeSeries) – the cost per period of the assets.
- life (TimeSeries) – number of depreciation periods for the asset.
- salvalue (TimeSeries) – salvage value as a percentage of cost.
- noprint (bool) – when True, the procedure prints a depreciation table.
Returns: depreciation, accum_depreciation (TimeSeries, TimeSeries).
Examples.
>>> costs1 = cashflow(const_value=0, nper=16, spec=(0, 1000), pyr=4) >>> costs2 = cashflow(const_value=0, nper=16, spec=[(0, 1000), (8, 1000)], pyr=4) >>> life1 = cashflow(const_value=0, nper=16, spec=(0, 4), pyr=4) >>> life2 = cashflow(const_value=0, nper=16, spec=[(0, 4), (8, 4)], pyr=4) >>> delay12 = cashflow(const_value=0, nper=16, spec=(0, 2), pyr=4) >>> delay22 = cashflow(const_value=0, nper=16, spec=[(0, 2), (8, 2)], pyr=4) >>> depreciation_sl(costs=costs1, life=life1) Qtr0 Qtr1 Qtr2 Qtr3 0 0.00 250.00 250.00 250.00 1 250.00 0.00 0.00 0.00 2 0.00 0.00 0.00 0.00 3 0.00 0.00 0.00 0.00
>>> depreciation_sl(costs=costs1, life=life1, delay=delay12) Qtr0 Qtr1 Qtr2 Qtr3 0 0.00 0.00 0.00 250.00 1 250.00 250.00 250.00 0.00 2 0.00 0.00 0.00 0.00 3 0.00 0.00 0.00 0.00
>>> depreciation_sl(costs=costs2, life=life2) Qtr0 Qtr1 Qtr2 Qtr3 0 0.00 250.00 250.00 250.00 1 250.00 0.00 0.00 0.00 2 0.00 250.00 250.00 250.00 3 250.00 0.00 0.00 0.00
>>> depreciation_sl(costs=costs2, life=life2, delay=delay22) Qtr0 Qtr1 Qtr2 Qtr3 0 0.00 0.00 0.00 250.00 1 250.00 250.00 250.00 0.00 2 0.00 0.00 0.00 250.00 3 250.00 250.00 250.00 0.00
>>> depreciation_sl(costs=costs2, life=life2, delay=delay22, noprint=False) t Beg. Cost Depre. Accum. End. Book Depre. Book Value Value ---------------------------------------------- (0, 0) 0.00 1000.00 0.00 0.00 1000.00 (0, 1) 1000.00 0.00 0.00 0.00 1000.00 (0, 2) 1000.00 0.00 0.00 0.00 1000.00 (0, 3) 1000.00 0.00 250.00 250.00 750.00 (1, 0) 750.00 0.00 250.00 500.00 500.00 (1, 1) 500.00 0.00 250.00 750.00 250.00 (1, 2) 250.00 0.00 250.00 1000.00 0.00 (1, 3) 0.00 0.00 0.00 1000.00 0.00 (2, 0) 0.00 1000.00 0.00 1000.00 1000.00 (2, 1) 1000.00 0.00 0.00 1000.00 1000.00 (2, 2) 1000.00 0.00 0.00 1000.00 1000.00 (2, 3) 1000.00 0.00 250.00 1250.00 750.00 (3, 0) 750.00 0.00 250.00 1500.00 500.00 (3, 1) 500.00 0.00 250.00 1750.00 250.00 (3, 2) 250.00 0.00 250.00 2000.00 0.00 (3, 3) 0.00 0.00 0.00 2000.00 0.00
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cashflows.depreciation.depreciation_soyd(costs, life, salvalue=None, delay=None, noprint=True)[source]¶ Computes the depreciation of an asset using the sum-of-year’s-digits method.
Parameters: - cost (TimeSeries) – the cost per period of the assets.
- life (TimeSeries) – number of depreciation periods for the asset.
- salvalue (TimeSeries) – salvage value as a percentage of cost.
- noprint (bool) – when True, the procedure prints a depreciation table.
Returns: depreciation per period and accumulated depreciation per period
Return type: A tuple (dep, accum) of lists (tuple)
Examples.
>>> costs1 = cashflow(const_value=0, nper=16, spec=(0, 1000), pyr=4) >>> costs2 = cashflow(const_value=0, nper=16, spec=[(0, 1000), (8, 1000)], pyr=4) >>> life1 = cashflow(const_value=0, nper=16, spec=(0, 4), pyr=4) >>> life2 = cashflow(const_value=0, nper=16, spec=[(0, 4), (8, 4)], pyr=4) >>> delay12 = cashflow(const_value=0, nper=16, spec=(0, 2), pyr=4) >>> delay22 = cashflow(const_value=0, nper=16, spec=[(0, 2), (8, 2)], pyr=4) >>> depreciation_soyd(costs=costs1, life=life1) Qtr0 Qtr1 Qtr2 Qtr3 0 0.00 400.00 300.00 200.00 1 100.00 0.00 0.00 0.00 2 0.00 0.00 0.00 0.00 3 0.00 0.00 0.00 0.00
>>> depreciation_soyd(costs=costs1, life=life1, delay=delay12) Qtr0 Qtr1 Qtr2 Qtr3 0 0.00 0.00 0.00 400.00 1 300.00 200.00 100.00 0.00 2 0.00 0.00 0.00 0.00 3 0.00 0.00 0.00 0.00
>>> depreciation_soyd(costs=costs2, life=life2) Qtr0 Qtr1 Qtr2 Qtr3 0 0.00 400.00 300.00 200.00 1 100.00 0.00 0.00 0.00 2 0.00 400.00 300.00 200.00 3 100.00 0.00 0.00 0.00
>>> depreciation_soyd(costs=costs2, life=life2, delay=delay22) Qtr0 Qtr1 Qtr2 Qtr3 0 0.00 0.00 0.00 400.00 1 300.00 200.00 100.00 0.00 2 0.00 0.00 0.00 400.00 3 300.00 200.00 100.00 0.00
>>> depreciation_soyd(costs=costs2, life=life2, delay=delay22, noprint=False) t Beg. Cost Depre. Accum. End. Book Depre. Book Value Value ---------------------------------------------- (0, 0) 0.00 1000.00 0.00 0.00 1000.00 (0, 1) 1000.00 0.00 0.00 0.00 1000.00 (0, 2) 1000.00 0.00 0.00 0.00 1000.00 (0, 3) 1000.00 0.00 400.00 400.00 600.00 (1, 0) 600.00 0.00 300.00 700.00 300.00 (1, 1) 300.00 0.00 200.00 900.00 100.00 (1, 2) 100.00 0.00 100.00 1000.00 0.00 (1, 3) 0.00 0.00 0.00 1000.00 0.00 (2, 0) 0.00 1000.00 0.00 1000.00 1000.00 (2, 1) 1000.00 0.00 0.00 1000.00 1000.00 (2, 2) 1000.00 0.00 0.00 1000.00 1000.00 (2, 3) 1000.00 0.00 400.00 1400.00 600.00 (3, 0) 600.00 0.00 300.00 1700.00 300.00 (3, 1) 300.00 0.00 200.00 1900.00 100.00 (3, 2) 100.00 0.00 100.00 2000.00 0.00 (3, 3) 0.00 0.00 0.00 2000.00 0.00
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cashflows.depreciation.print_depr(depr, adepr, costs, begbook, endbook)[source]¶ Prints a depreciation table
Parameters: - cost (int, float) – Initial cost of the asset
- depr (list) – Depreciation per period
- adepr (list) – Accumulated depreciation per period
- begbook (list) – Beginning book value
- endbook (list) – Ending book value
Returns: None
Loan analysis¶
Computes the amorization schedule for the followint types of loans:
fixed_rate_loan: In this loan, the interest rate is fixed and the total payments are equal during the life of the loan.buydown_loan: the interest rate changes during the life of the loan; the value of the payments are calculated using the current value of the interest rate. When the interest rate is constant during the life of the loan, the results are equals to the functionfixed_rate_loan.fixed_ppal_loan: the payments to the principal are constant during the life of loan.bullet_loan: the principal is payed at the end of the life of the loan.
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class
cashflows.loan.Loan[source]¶ Bases:
objectClass for representing loans
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to_cashflow(tax_rate=0)[source]¶ Converts the loan to the equivalent cashflow.
For the conversion, origination points are considered as exogenous costs and they are not taking in to account in the computation. In oposition, discount points are considered as prepaid interest and included in the cashflow.
When tax_rate is different from zero, tax benefits are considered.
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true_rate(tax_rate=0)[source]¶ Computes the true interest rate for the loan.
For the computation, the loan is converted to the equivalent cashflow, taking in to account the following aspects:
- Origination points are considered as non deducible costs and they are ignored in the computation.
- Discount points are prepaid interest and they are considered as deducibles in the computation.
- When tax_rate is different from zero, the After-Tax true interest rate is calculated. This is, only the (1 - tax_rate) of paid interests (including discount points) are used in the computation.
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cashflows.loan.bullet_loan(amount, nrate, dispoints=0, orgpoints=0, prepmt=None)[source]¶ In this type of loan, the principal is payed at the end for the life of the loan. Periodic payments correspond only to interests.
Parameters: - amount (float) – Loan amount.
- nrate (float, TimeSeries) – nominal interest rate per year.
- dispoints (float) – Discount points of the loan.
- orgpoints (float) – Origination points of the loan.
- prepmt (TimeSeries) – generic cashflow representing prepayments.
Returns: A object of the class
Loan.>>> nrate = interest_rate(const_value=10, nper=11, pyr=4) >>> bullet_loan(amount=1000, nrate=nrate, dispoints=0, orgpoints=0, prepmt=None) t Beg. Per. Total Int. Ppal Ending Ppal Rate Pmt Pmt Pmt Ppal ------------------------------------------------------ (0, 0) 0.00 10.00 0.00 0.00 0.00 1000.00 (0, 1) 1000.00 10.00 25.00 25.00 0.00 1000.00 (0, 2) 1000.00 10.00 25.00 25.00 0.00 1000.00 (0, 3) 1000.00 10.00 25.00 25.00 0.00 1000.00 (1, 0) 1000.00 10.00 25.00 25.00 0.00 1000.00 (1, 1) 1000.00 10.00 25.00 25.00 0.00 1000.00 (1, 2) 1000.00 10.00 25.00 25.00 0.00 1000.00 (1, 3) 1000.00 10.00 25.00 25.00 0.00 1000.00 (2, 0) 1000.00 10.00 25.00 25.00 0.00 1000.00 (2, 1) 1000.00 10.00 25.00 25.00 0.00 1000.00 (2, 2) 1000.00 10.00 1025.00 25.00 1000.00 0.00
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cashflows.loan.buydown_loan(amount, nrate, grace=0, dispoints=0, orgpoints=0, prepmt=None)[source]¶ In this loan, the periodic payments are recalculated when there are changes in the value of the interest rate.
Parameters: - amount (float) – Loan amount.
- nrate (float, TimeSeries) – nominal interest rate per year.
- grace (int) – numner of grace periods without paying the principal.
- dispoints (float) – Discount points of the loan.
- orgpoints (float) – Origination points of the loan.
- prepmt (TimeSeries) – generic cashflow representing prepayments.
Returns: A object of the class
Loan.>>> nrate = interest_rate(const_value=10, nper=11, pyr=4, spec=(5, 20)) >>> buydown_loan(amount=1000, nrate=nrate, dispoints=0, orgpoints=0, prepmt=None) t Beg. Per. Total Int. Ppal Ending Ppal Rate Pmt Pmt Pmt Ppal ------------------------------------------------------ (0, 0) 1000.00 10.00 0.00 0.00 0.00 1000.00 (0, 1) 1000.00 10.00 114.26 25.00 89.26 910.74 (0, 2) 910.74 10.00 114.26 22.77 91.49 819.25 (0, 3) 819.25 10.00 114.26 20.48 93.78 725.47 (1, 0) 725.47 10.00 114.26 18.14 96.12 629.35 (1, 1) 629.35 20.00 123.99 31.47 92.53 536.83 (1, 2) 536.83 20.00 123.99 26.84 97.15 439.67 (1, 3) 439.67 20.00 123.99 21.98 102.01 337.66 (2, 0) 337.66 20.00 123.99 16.88 107.11 230.55 (2, 1) 230.55 20.00 123.99 11.53 112.47 118.09 (2, 2) 118.09 20.00 123.99 5.90 118.09 0.00
>>> pmt = cashflow(const_value=0, nper = 11, pyr=4, spec=((1, 3), 200)) >>> buydown_loan(amount=1000, nrate=nrate, dispoints=0, orgpoints=0, prepmt=pmt) t Beg. Per. Total Int. Ppal Ending Ppal Rate Pmt Pmt Pmt Ppal ------------------------------------------------------ (0, 0) 1000.00 10.00 0.00 0.00 0.00 1000.00 (0, 1) 1000.00 10.00 114.26 25.00 89.26 910.74 (0, 2) 910.74 10.00 114.26 22.77 91.49 819.25 (0, 3) 819.25 10.00 114.26 20.48 93.78 725.47 (1, 0) 725.47 10.00 114.26 18.14 96.12 629.35 (1, 1) 629.35 20.00 123.99 31.47 92.53 536.83 (1, 2) 536.83 20.00 123.99 26.84 97.15 439.67 (1, 3) 439.67 20.00 323.99 21.98 302.01 137.66 (2, 0) 137.66 20.00 50.55 6.88 43.67 94.00 (2, 1) 94.00 20.00 50.55 4.70 45.85 48.14 (2, 2) 48.14 20.00 50.55 2.41 48.14 0.00
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cashflows.loan.fixed_ppal_loan(amount, nrate, grace=0, dispoints=0, orgpoints=0, prepmt=None, balloonpmt=None)[source]¶ Loan with fixed principal payment.
Parameters: - amount (float) – Loan amount.
- nrate (float, TimeSeries) – nominal interest rate per year.
- grace (int) – number of grace periiods without paying principal.
- dispoints (float) – Discount points of the loan.
- orgpoints (float) – Origination points of the loan.
- prepmt (TimeSeries) – generic cashflow representing prepayments.
- balloonpmt (TimeSeries) – generic cashflow representing balloon payments.
Returns: A object of the class
Loan.>>> nrate = interest_rate(const_value=10, nper=11, pyr=4) >>> fixed_ppal_loan(amount=1000, nrate=nrate, grace=0, dispoints=0, orgpoints=0, ... prepmt=None, balloonpmt=None) t Beg. Per. Total Int. Ppal Ending Ppal Rate Pmt Pmt Pmt Ppal ------------------------------------------------------ (0, 0) 0.00 10.00 0.00 0.00 0.00 1000.00 (0, 1) 1000.00 10.00 125.00 25.00 100.00 900.00 (0, 2) 900.00 10.00 122.50 22.50 100.00 800.00 (0, 3) 800.00 10.00 120.00 20.00 100.00 700.00 (1, 0) 700.00 10.00 117.50 17.50 100.00 600.00 (1, 1) 600.00 10.00 115.00 15.00 100.00 500.00 (1, 2) 500.00 10.00 112.50 12.50 100.00 400.00 (1, 3) 400.00 10.00 110.00 10.00 100.00 300.00 (2, 0) 300.00 10.00 107.50 7.50 100.00 200.00 (2, 1) 200.00 10.00 105.00 5.00 100.00 100.00 (2, 2) 100.00 10.00 102.50 2.50 100.00 0.00
>>> fixed_ppal_loan(amount=1000, nrate=nrate, grace=2, dispoints=0, orgpoints=0, ... prepmt=None, balloonpmt=None) t Beg. Per. Total Int. Ppal Ending Ppal Rate Pmt Pmt Pmt Ppal ------------------------------------------------------ (0, 0) 0.00 10.00 0.00 0.00 0.00 1000.00 (0, 1) 1000.00 10.00 25.00 25.00 0.00 1000.00 (0, 2) 1000.00 10.00 25.00 25.00 0.00 1000.00 (0, 3) 1000.00 10.00 150.00 25.00 125.00 875.00 (1, 0) 875.00 10.00 146.88 21.88 125.00 750.00 (1, 1) 750.00 10.00 143.75 18.75 125.00 625.00 (1, 2) 625.00 10.00 140.62 15.62 125.00 500.00 (1, 3) 500.00 10.00 137.50 12.50 125.00 375.00 (2, 0) 375.00 10.00 134.38 9.38 125.00 250.00 (2, 1) 250.00 10.00 131.25 6.25 125.00 125.00 (2, 2) 125.00 10.00 128.12 3.12 125.00 0.00
>>> pmt = cashflow(const_value=0, nper = 11, pyr=4, spec=((1, 3), 200)) >>> fixed_ppal_loan(amount=1000, nrate=nrate, grace=2, dispoints=0, orgpoints=0, ... prepmt=pmt, balloonpmt=None) t Beg. Per. Total Int. Ppal Ending Ppal Rate Pmt Pmt Pmt Ppal ------------------------------------------------------ (0, 0) 0.00 10.00 0.00 0.00 0.00 1000.00 (0, 1) 1000.00 10.00 25.00 25.00 0.00 1000.00 (0, 2) 1000.00 10.00 25.00 25.00 0.00 1000.00 (0, 3) 1000.00 10.00 150.00 25.00 125.00 875.00 (1, 0) 875.00 10.00 146.88 21.88 125.00 750.00 (1, 1) 750.00 10.00 143.75 18.75 125.00 625.00 (1, 2) 625.00 10.00 140.62 15.62 125.00 500.00 (1, 3) 500.00 10.00 337.50 12.50 325.00 175.00 (2, 0) 175.00 10.00 129.38 4.38 125.00 50.00 (2, 1) 50.00 10.00 51.25 1.25 50.00 0.00 (2, 2) 0.00 10.00 0.00 0.00 0.00 0.00
>>> pmt = cashflow(const_value=0, nper = 11, pyr=4, spec=((1, 3), 200)) >>> fixed_ppal_loan(amount=1000, nrate=nrate, grace=2, dispoints=0, orgpoints=0, ... prepmt=None, balloonpmt=pmt) t Beg. Per. Total Int. Ppal Ending Ppal Rate Pmt Pmt Pmt Ppal ------------------------------------------------------ (0, 0) 0.00 10.00 0.00 0.00 0.00 1000.00 (0, 1) 1000.00 10.00 25.00 25.00 0.00 1000.00 (0, 2) 1000.00 10.00 25.00 25.00 0.00 1000.00 (0, 3) 1000.00 10.00 125.00 25.00 100.00 900.00 (1, 0) 900.00 10.00 122.50 22.50 100.00 800.00 (1, 1) 800.00 10.00 120.00 20.00 100.00 700.00 (1, 2) 700.00 10.00 117.50 17.50 100.00 600.00 (1, 3) 600.00 10.00 315.00 15.00 300.00 300.00 (2, 0) 300.00 10.00 107.50 7.50 100.00 200.00 (2, 1) 200.00 10.00 105.00 5.00 100.00 100.00 (2, 2) 100.00 10.00 102.50 2.50 100.00 0.00
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cashflows.loan.fixed_rate_loan(amount, nrate, life, start, pyr=1, grace=0, dispoints=0, orgpoints=0, prepmt=None, balloonpmt=None)[source]¶ Fixed rate loan.
Parameters: - amount (float) – Loan amount.
- nrate (float) – nominal interest rate per year.
- life (float) – life of the loan.
- start (int, tuple) – init period for the loan.
- pyr (int) – number of compounding periods per year.
- grace (int) – number of periods of grace (without payment of the principal)
- dispoints (float) – Discount points of the loan.
- orgpoints (float) – Origination points of the loan.
- prepmt (TimeSeries) – generic cashflow representing prepayments.
- balloonpmt (TimeSeries) – generic cashflow representing balloon payments.
Returns: A object of the class
Loan.>>> pmt = cashflow(const_value=0, nper = 11, pyr=4, spec=((1, 3), 200)) >>> fixed_rate_loan(amount=1000, nrate=10, life=10, start=None, pyr=4, grace=0, dispoints=0, ... orgpoints=0, prepmt=pmt, balloonpmt=None) t Beg. Per. Total Int. Ppal Ending Ppal Rate Pmt Pmt Pmt Ppal ------------------------------------------------------ (0, 0) 1000.00 10.00 0.00 0.00 0.00 1000.00 (0, 1) 1000.00 10.00 114.26 25.00 89.26 910.74 (0, 2) 910.74 10.00 114.26 22.77 91.49 819.25 (0, 3) 819.25 10.00 114.26 20.48 93.78 725.47 (1, 0) 725.47 10.00 114.26 18.14 96.12 629.35 (1, 1) 629.35 10.00 114.26 15.73 98.52 530.83 (1, 2) 530.83 10.00 114.26 13.27 100.99 429.84 (1, 3) 429.84 10.00 314.26 10.75 303.51 126.33 (2, 0) 126.33 10.00 114.26 3.16 111.10 15.23 (2, 1) 15.23 10.00 15.61 0.38 15.23 0.00 (2, 2) 0.00 10.00 0.00 0.00 0.00 0.00
Savings¶
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cashflows.savings.savings(deposits, nrate, initbal=0, noprint=True)[source]¶ Computes the final balance for a savings account with arbitrary deposits and withdrawls and variable interset rate.
Parameters: - deposits (TimeSeries) – deposits to the account.
- nrate (TimeSeries) – nominal interest rate paid by the account.
- initbal (float) – initial balance of the account.
- noprint (bool) – prints summary report?
Returns: interest, end_balance (TimeSeries, TimeSeries)
Examples
>>> cflo = cashflow(const_value=[100] * 12, pyr=4) >>> nrate = interest_rate([10] * 12, pyr=4) >>> savings(deposits=cflo, nrate=nrate, initbal=0, noprint=False) t Beginning Deposit Earned Ending Balance Interest Balance ----------------------------------------------- (0, 0) 0.00 100.00 0.00 100.00 (0, 1) 100.00 100.00 2.50 202.50 (0, 2) 202.50 100.00 5.06 307.56 (0, 3) 307.56 100.00 7.69 415.25 (1, 0) 415.25 100.00 10.38 525.63 (1, 1) 525.63 100.00 13.14 638.77 (1, 2) 638.77 100.00 15.97 754.74 (1, 3) 754.74 100.00 18.87 873.61 (2, 0) 873.61 100.00 21.84 995.45 (2, 1) 995.45 100.00 24.89 1120.34 (2, 2) 1120.34 100.00 28.01 1248.35 (2, 3) 1248.35 100.00 31.21 1379.56
>>> cflo = cashflow(const_value=[100] * 5, spec=[(0, 0), (2, 0)]) >>> nrate = interest_rate([0, 1, 2, 3, 4]) >>> savings(deposits=cflo, nrate=nrate, initbal=1000, noprint=False) t Beginning Deposit Earned Ending Balance Interest Balance --------------------------------------------- (0,) 1000.00 0.00 0.00 1000.00 (1,) 1000.00 100.00 10.00 1110.00 (2,) 1110.00 0.00 22.20 1132.20 (3,) 1132.20 100.00 33.97 1266.17 (4,) 1266.17 100.00 50.65 1416.81