.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/time_value/irr/plot_03_baldwin_mirr.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_irr_plot_03_baldwin_mirr.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_irr_plot_03_baldwin_mirr.py:


Baldwin's modified IRR
======================

Robert Baldwin's "How to Assess Investment Proposals" (*Harvard
Business Review*, 1959) proposed a fix for the IRR's two defects --
multiple roots and the implicit assumption that interim cash flows are
reinvested at the IRR itself. Compound the inflows to the horizon at a
realistic reinvestment rate, discount the outflows at the finance rate,
and report the one rate that links them:
:math:`\mathrm{MIRR} = (FV^+ / |PV^-|)^{1/n} - 1`. It always exists and
is unique.

.. GENERATED FROM PYTHON SOURCE LINES 16-21

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from financialkit.time_value import irr, irr_all, mirr








.. GENERATED FROM PYTHON SOURCE LINES 22-26

A high-IRR project
------------------
Its IRR assumes the early inflows earn the IRR again; at a 10%
reinvestment rate the realistic return is much lower.

.. GENERATED FROM PYTHON SOURCE LINES 26-31

.. code-block:: Python


    cf = [-1000.0, 800.0, 500.0, 200.0]
    print(f"IRR  = {irr(cf):.2%}")
    print(f"MIRR = {mirr(cf, 0.10, 0.10):.2%} (finance and reinvest at 10%)")





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

 .. code-block:: none

    IRR  = 30.20%
    MIRR = 19.77% (finance and reinvest at 10%)




.. GENERATED FROM PYTHON SOURCE LINES 32-34

The pump problem gets one answer
--------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 34-38

.. code-block:: Python


    pump = [-1600.0, 10_000.0, -10_000.0]
    print(f"pump IRRs: {irr_all(pump)}; MIRR at 10%: {mirr(pump, 0.10, 0.10):.2%}")





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

 .. code-block:: none

    pump IRRs: [0.25 4.  ]; MIRR at 10%: 5.60%




.. GENERATED FROM PYTHON SOURCE LINES 39-41

MIRR moves between the reinvestment rate and the IRR
----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 41-53

.. code-block:: Python


    reinvest = np.linspace(0.0, 0.6, 121)
    fig, ax = plt.subplots(figsize=(7, 4.5))
    ax.plot(100 * reinvest, [100 * mirr(cf, 0.10, r) for r in reinvest], label="MIRR")
    ax.axhline(100 * irr(cf), color="tab:red", ls="--", label="IRR")
    ax.plot(100 * reinvest, 100 * reinvest, ":", color="gray", label="reinvestment rate")
    ax.set_xlabel("reinvestment rate (%)")
    ax.set_ylabel("rate of return (%)")
    ax.set_title("Baldwin's MIRR equals the IRR only when reinvesting at the IRR")
    ax.legend()

    plt.show()



.. image-sg:: /api/gallery/time_value/irr/images/sphx_glr_plot_03_baldwin_mirr_001.png
   :alt: Baldwin's MIRR equals the IRR only when reinvesting at the IRR
   :srcset: /api/gallery/time_value/irr/images/sphx_glr_plot_03_baldwin_mirr_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.031 seconds)


.. _sphx_glr_download_api_gallery_time_value_irr_plot_03_baldwin_mirr.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/irr/plot_03_baldwin_mirr.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_03_baldwin_mirr.ipynb <plot_03_baldwin_mirr.ipynb>`

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

      :download:`Download Python source code: plot_03_baldwin_mirr.py <plot_03_baldwin_mirr.py>`

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

      :download:`Download zipped: plot_03_baldwin_mirr.zip <plot_03_baldwin_mirr.zip>`


.. only:: html

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

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