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 function fixed_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.
class cashflows.loan.Loan[source]

Bases: object

Class for representing loans

begbal()[source]

Returns the balance at the begining of each period as a Cashflow object.

endbal()[source]

Returns the balance at the ending of each period as a Cashflow object.

interest()[source]

Returns the interest paid as a Cashflow object.

ppalpmt()[source]

Returns the principal payment for each period as a Cashflow object.

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.

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.
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
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
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
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