28 — Dividend Discount Models, Multiples, and CAPM¶

Free learning pack¶

1. reference/equity/dividend_discount_model.md
2. reference/equity/relative_valuation_multiples.md
3. reference/equity/capm_and_beta.md
4. resources/equity.md

Do not search for more material until these are insufficient.

PREDICT¶

A stock pays a $2 dividend next year, grows dividends 4% a year forever, and you require a 9% return. Without calculating, what happens to the Gordon-growth value if the growth assumption rises toward 9% — does it rise smoothly, or does something break?

Formula (Gordon growth)¶

V = D1 / (r - g)

In [ ]:

dividend_next = 2.0
required_return = 0.09
growth_rate = 0.04

# MANUAL FIRST:
# compute the Gordon-growth value by hand.
value = None
print(value)

dividend_next = 2.0 required_return = 0.09 growth_rate = 0.04 # MANUAL FIRST: # compute the Gordon-growth value by hand. value = None print(value)

PREDICT (multiples)¶

Two companies have the same 40% payout ratio and the same 9% required return, but Company A grows 2% a year and Company B grows 6% a year. Without calculating, which one has the higher justified P/E, and is the gap between them small or large?

Formula (justified P/E)¶

P/E = payout_ratio / (r - g)

In [ ]:

payout_ratio = 0.40
required_return = 0.09
growth_a = 0.02
growth_b = 0.06

# MANUAL FIRST:
# compute the justified P/E for each company by hand.
pe_a = None
pe_b = None
print(pe_a, pe_b)

payout_ratio = 0.40 required_return = 0.09 growth_a = 0.02 growth_b = 0.06 # MANUAL FIRST: # compute the justified P/E for each company by hand. pe_a = None pe_b = None print(pe_a, pe_b)

PREDICT (CAPM)¶

A stock's returns have moved almost exactly 1.5x the market's on every up and down day this year. Without calculating a regression, what beta would you expect, and would you expect this stock's CAPM-required return to be above or below the market's own expected return?

Formula (CAPM)¶

beta = Cov(r_stock, r_market) / Var(r_market)

E[r] = r_f + beta * (E[r_market] - r_f)

In [ ]:

import numpy as np

market_returns = np.array([0.01, 0.02, -0.01, 0.03, 0.00])
stock_returns = 1.5 * market_returns  # exact 1.5x mover, for a clean hand check

risk_free_rate = 0.03
expected_market_return = 0.08

# MANUAL FIRST:
# compute beta by hand (Cov/Var over the two series above), then the
# CAPM-required return.
beta_value = None
expected_return = None
print(beta_value, expected_return)

import numpy as np market_returns = np.array([0.01, 0.02, -0.01, 0.03, 0.00]) stock_returns = 1.5 * market_returns # exact 1.5x mover, for a clean hand check risk_free_rate = 0.03 expected_market_return = 0.08 # MANUAL FIRST: # compute beta by hand (Cov/Var over the two series above), then the # CAPM-required return. beta_value = None expected_return = None print(beta_value, expected_return)

Experiment¶

Push growth_rate in the first cell up toward 0.09 (the required return) and rerun. Confirm your PREDICT answer about what breaks, and read gordon_growth_value's ValueError message in src/pm/equity/valuation.py to see how the repo enforces that constraint deliberately rather than letting it silently divide by a tiny number.

Reference¶

reference/equity/dividend_discount_model.md reference/equity/relative_valuation_multiples.md reference/equity/capm_and_beta.md

Promote¶

Use src/pm/equity/valuation.py (gordon_growth_value, justified_pe) and src/pm/equity/capm.py (beta, capm_expected_return) only after your own implementation.

Test¶

pytest tests/test_equity.py

ORAL CHECK¶

Explain to a PM why a stock's justified P/E and its Gordon-growth DDM value are the same claim viewed two different ways, and why CAPM's required return is the r that both formulas need as an input.

Try /tutor equity valuation or /tutor CAPM for an adaptive walkthrough.