.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/asset_pricing/valuation/plot_03_gordon_growth.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_asset_pricing_valuation_plot_03_gordon_growth.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_asset_pricing_valuation_plot_03_gordon_growth.py:


Gordon growth
=============

Myron Gordon (1959) summed Williams's series for dividends that grow at
a constant rate, :math:`P_0 = D_1 / (r - g)`, and connected the growth
rate to the firm's investment: a firm that retains a share :math:`b` of
its earnings and earns :math:`ROE` on them grows at :math:`g = b \cdot ROE`.
Read backwards, the model gives the market's cost of equity as the
dividend yield plus growth.

.. GENERATED FROM PYTHON SOURCE LINES 14-30

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from financialkit.asset_pricing import gordon_growth_price, implied_cost_of_equity, sustainable_growth

    r = 0.09
    g = np.linspace(0.0, 0.08, 200)
    fig, ax = plt.subplots(figsize=(7, 4))
    ax.plot(g, gordon_growth_price(1.0, r, g))
    ax.axvline(r, color="C3", ls="--", label="g -> r: the price explodes")
    ax.set_xlabel("dividend growth g")
    ax.set_ylabel("price per unit of next dividend")
    ax.set_yscale("log")
    ax.legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/asset_pricing/valuation/images/sphx_glr_plot_03_gordon_growth_001.png
   :alt: plot 03 gordon growth
   :srcset: /api/gallery/asset_pricing/valuation/images/sphx_glr_plot_03_gordon_growth_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 31-36

Growth from retained earnings
-----------------------------

Retaining earnings adds value only if they earn more than the cost of
equity. With earnings of 1 per share, :math:`D_1 = 1 - b`.

.. GENERATED FROM PYTHON SOURCE LINES 36-47

.. code-block:: Python


    b = np.linspace(0.0, 0.7, 100)
    fig, ax = plt.subplots(figsize=(7, 4))
    for roe in (0.06, 0.09, 0.12):
        gb = sustainable_growth(roe, 1 - b)
        ax.plot(b, gordon_growth_price(1 - b, r, gb), label=f"ROE = {roe:.0%}")
    ax.set_xlabel("retention ratio b")
    ax.set_ylabel("price")
    ax.legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/asset_pricing/valuation/images/sphx_glr_plot_03_gordon_growth_002.png
   :alt: plot 03 gordon growth
   :srcset: /api/gallery/asset_pricing/valuation/images/sphx_glr_plot_03_gordon_growth_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 48-50

The implied cost of equity
--------------------------

.. GENERATED FROM PYTHON SOURCE LINES 50-54

.. code-block:: Python


    print(f"price 40, next dividend 2, growth 4%: r = {implied_cost_of_equity(40.0, 2.0, 0.04):.2%}")

    plt.show()




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

 .. code-block:: none

    price 40, next dividend 2, growth 4%: r = 9.00%





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

   **Total running time of the script:** (0 minutes 0.061 seconds)


.. _sphx_glr_download_api_gallery_asset_pricing_valuation_plot_03_gordon_growth.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/asset_pricing/valuation/plot_03_gordon_growth.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_03_gordon_growth.ipynb <plot_03_gordon_growth.ipynb>`

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

      :download:`Download Python source code: plot_03_gordon_growth.py <plot_03_gordon_growth.py>`

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

      :download:`Download zipped: plot_03_gordon_growth.zip <plot_03_gordon_growth.zip>`


.. only:: html

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

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