.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/time_value/present_value/plot_01_fibonacci_present_value.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_time_value_present_value_plot_01_fibonacci_present_value.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_time_value_present_value_plot_01_fibonacci_present_value.py:


Fibonacci's present value: comparing payment schedules
======================================================

Chapter 12 of Fibonacci's *Liber Abaci* (1202) contains problems in
which a sum is repaid in instalments at a fixed rate per period, and
Fibonacci values each schedule by discounting every instalment back to
the start (Goetzmann, 2005). The same idea in modern form: a lender is
offered three ways to be repaid a loan of 100 bezants, and the one worth
most today depends on the rate. Present value turns each schedule into
a single number that can be compared.

.. GENERATED FROM PYTHON SOURCE LINES 15-20

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from financialkit.time_value import plot_cash_flows, present_value








.. GENERATED FROM PYTHON SOURCE LINES 21-24

Three schedules
---------------
Payments in bezants at the end of each year.

.. GENERATED FROM PYTHON SOURCE LINES 24-34

.. code-block:: Python


    schedules = {
        "lump sum at year 5": ([0, 0, 0, 0, 160.0], np.arange(1, 6)),
        "level, 5 years": ([36.0] * 5, np.arange(1, 6)),
        "front-loaded": ([60.0, 45.0, 30.0, 20.0, 10.0], np.arange(1, 6)),
    }
    for name, (cf, t) in schedules.items():
        pv = present_value(cf, t, 0.10, compounding=1)
        print(f"{name:20s} total {sum(cf):6.1f}  PV at 10% = {pv:6.2f}")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    lump sum at year 5   total  160.0  PV at 10% =  99.35
    level, 5 years       total  180.0  PV at 10% = 136.47
    front-loaded         total  165.0  PV at 10% = 134.14




.. GENERATED FROM PYTHON SOURCE LINES 35-38

Which schedule wins depends on the rate
---------------------------------------
At low rates the larger total wins; at high rates the earlier money wins.

.. GENERATED FROM PYTHON SOURCE LINES 38-52

.. code-block:: Python


    rates = np.linspace(0.0, 0.25, 101)
    fig, axes = plt.subplots(1, 2, figsize=(11, 4))
    for name, (cf, t) in schedules.items():
        axes[1].plot(100 * rates, present_value(cf, t, rates, compounding=1), label=name)
    axes[1].axhline(100.0, color="k", ls="--", lw=0.8, label="amount lent")
    axes[1].set_xlabel("rate per year (%)")
    axes[1].set_ylabel("present value")
    axes[1].set_title("Present value of each schedule")
    axes[1].legend()
    plot_cash_flows(schedules["front-loaded"][0], schedules["front-loaded"][1], ax=axes[0], title="front-loaded schedule")
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/time_value/present_value/images/sphx_glr_plot_01_fibonacci_present_value_001.png
   :alt: front-loaded schedule, Present value of each schedule
   :srcset: /api/gallery/time_value/present_value/images/sphx_glr_plot_01_fibonacci_present_value_001.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.064 seconds)


.. _sphx_glr_download_api_gallery_time_value_present_value_plot_01_fibonacci_present_value.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../../lite/lab/index.html?path=api/gallery/time_value/present_value/plot_01_fibonacci_present_value.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_01_fibonacci_present_value.ipynb <plot_01_fibonacci_present_value.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_01_fibonacci_present_value.py <plot_01_fibonacci_present_value.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_01_fibonacci_present_value.zip <plot_01_fibonacci_present_value.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_