pyppr.ppr_net_fv#

pyppr.ppr_net_fv(ua_cagr, nper, pv, ppr_costr, ppr_tcr, ppr_standard_withdrawal)#

Compute the final tax-net value of a PPR.

Given:

  • the CAGR of the PPR’s underlying assets, ua_cagr, compounded once per period, of which there are

  • nper total,

  • the initial invested capital, pv, often referred to as the present value,

  • the PPR’s total costs, ppr_costr, including its management commission and others, expressed as a percentage of the invested capital,

  • the tax credit rate, ppr_tcr, the investor gets in his IRS for investing in a PPR,

  • and whether the PPR will be withdrawn in standard conditions or not, ppr_standard_withdrawal.

Return:

The tax-net value of a PPR at the end of the investment.

Parameters:
ua_cagrscalar or array_like of shape(M, )

Cumulative annual growth rate of the PPR’s underlying assets, in percentage Example: 0.05

nperscalar or array_like of shape(M, )

Number of compounding periods

pvscalar or array_like of shape(M, )

Initial invested capital, often referred to as the present value

ppr_costrscalar or array_like of shape(M, )

PPR’s total costs, including its management commission and others, expressed as a percentage of the invested capital Example: 0.0075

ppr_tcrscalar or array_like of shape(M, )

Tax credit rate the investor gets in his IRS for investing in a PPR Example: 0 or 0.2

ppr_standard_withdrawalbool

Whether the PPR will be withdrawn in standard conditions or not.

Returns:
outarray_like

Final tax-net value of a PPR. If all input is scalar, returns a scalar float. If any input is array_like, returns the annual cost rate for each input element.

Warning

ppr_net_fv considers the PPR’s tax credit is reinvested into the PPR, itself not generating any tax credit.

Notes

Returns the result of

\[V_0 + (PPR_n - V_0)\,(1 - tr_{PPR}) + TC_0 + (TC_n - TC_0)\,(1 - tr_{PPR})\]

which, according to The Math Behind the Functions, in its longest form, can be decomposed to

\[V_0\,(1 + tcp_{PPR})\,(1 + r)^n\,(1 - cr_{PPR})^n\,(1 - tr_{PPR}) + V_0\,(1 + tcp_{PPR})\,(tr_{PPR})\]

You should take care to define the PPR’s tax credit rate according to the law. We recommend you to only consider inputting 0 or the current credit rate (at the time of this writing, 0.2) in the \(ppr_{tcr}\) parameter, even if only part of the investment will generate the credit. In that case, split the investment into two parts, one with \(ppr_{tcr}\) = 0 and the other with \(ppr_{tcr} = 0.2\).

Examples

>>> import pyppr

What will be the final value of an investment in the a PPR, under the following scenario?

  • I expect the PPR’s underlying assets to grow at a CAGR of 7%.

  • I expect to hold this investment for the next 30 years.

  • I’m investing 4,000€.

  • I’m 30 years old, which means I can receive a tax credit of up to 400€.

  • This PPR charges a management commission of 0.75% per year, and no other costs.

  • I’m going to withdraw the PPR under standard conditions.

>>> fv1 = pyppr.ppr_net_fv(0.07, 20, 2000, 0.0075, 0.2, True)
>>> fv2 = pyppr.ppr_net_fv(0.07, 20, 2000, 0.0075, 0, True)
>>> print(f'{fv1 + fv2:,.2f} ({fv1:,.2f} + {fv2:,.2f})')
13,826.93 (7,541.96 + 6,284.97)

Or, alternatively,

>>> fv = pyppr.ppr_net_fv(0.07, 20, 2000, 0.0075, np.array([0.2, 0]), True)
>>> print(f'{fv.sum():,.2f} ({fv[0]:,.2f} + {fv[1]:,.2f})')
13,826.93 (7,541.96 + 6,284.97)

If we were investing 5,000€ instead,

>>> import numpy as np
>>> fv = pyppr.ppr_net_fv(0.07, 20, np.array([2000, 3000]), 0.0075, np.array([0.2, 0]), True)
>>> print(f'{fv.sum():,.2f} ({fv[0]:,.2f} + {fv[1]:,.2f})')
16,969.41 (7,541.96 + 9,427.45)