BF422 — Investments

Equity Valuation

Chapter 13 — Bodie, Kane & Marcus

Monmouth University

Overview

Road Map

I. Valuation Framework

Intrinsic value vs. market price, required return via CAPM

II. Dividend Discount Models

Constant-growth DDM, growth estimation, PVGO

III. Multistage Growth & P/E

Life cycles, two-stage DDM, P/E ratio analysis

IV. Free Cash Flow Models

FCFF, FCFE, firm valuation

Core idea: The search for mispriced securities (intrinsic value ≠ market price) is what maintains a nearly efficient market.

I

Valuation Framework

Intrinsic value, market price, and the required return

Framework Bodie Ch. 13

Intrinsic Value vs. Market Price

Intrinsic Value (IV)

Your assessment of the stock's true worth — the PV of all expected future cash payments to the investor.

Market Value (MV)

The consensus value set by all market participants — where supply meets demand.

Expected Holding Period Return

E(r) = (D₁ + P₁ − P₀) / P₀

Required Return (via CAPM)

k = r_f + β × [E(r_M) − r_f]

If IV > MV → stock is underpriced → buy.
If IV < MV → stock is overpriced → sell or short.

Checkpoint A

Intrinsic Value Exercise

ABC stock: Expected dividend = $4/share, current price P₀ = $48, expected year-end price P₁ = $52. Beta = 1.2, r_f = 6%, E(r_M) = 11%.

a) Expected HPR:

E(r) = (D₁ + P₁ − P₀) / P₀ = ?

%

b) Required rate of return (CAPM):

k = r_f + β × [E(r_M) − r_f] = ?

%

c) Intrinsic value V₀ = (D₁ + P₁) / (1 + k) = ?

$

II

Dividend Discount Models

Valuing stocks from their cash flows to shareholders

DDM Bodie Ch. 13

Constant-Growth DDM

If dividends grow at a constant rate g forever:

V₀ = D₁ / (k − g)

Implications

Valid only when g < k (otherwise price → ∞)
Stock price grows at rate g over time
Higher D₁ → higher value
Lower k → higher value
Higher g → higher value

Example (Q8)

Dividend just paid: $3/share, g = 8%, k = 14%.

D₁ = 3 × 1.08 = $3.24
V₀ = 3.24 / (0.14 − 0.08) = $54

DDM

Estimating the Growth Rate

g = ROE × b

where b = plowback (retention) ratio = 1 − payout ratio

Example

ROE = 12%, payout ratio = 60%.

b = 1 − 0.60 = 0.40

g = 12% × 0.40 = 4.8%

Intuition

The more a firm retains and reinvests at a high ROE, the faster earnings and dividends grow.

But growth is only valuable if ROE > k! Otherwise the firm destroys value by reinvesting.

Key insight: Growth for its own sake isn't valuable. Growth enhances value only when projects earn returns above the cost of capital (ROE > k).

DDM

Present Value of Growth Opportunities

V₀ = E₁/k + PVGO

Stock price = No-growth value + Value of growth opportunities

No-Growth Value

No-growth price = E₁ / k

If the firm pays out all earnings as dividends with zero reinvestment, this is the stock's value.

PVGO

PVGO = V₀ − E₁/k

The extra value the market assigns for reinvesting earnings in profitable projects.

If PVGO < 0 → firm should stop reinvesting!

DDM

DDM Sensitivity to Growth

Growth rate g: 4.0%

Sensitivity: A small change in g produces a huge change in price. This is the DDM's biggest weakness — it's very sensitive to growth assumptions.

Checkpoint B

PVGO & DDM Exercise

Q1: PVGO (Firm IBX)

Retention ratio b = 60%, ROE = 10%, k = 15%, D₁ = $2/share, E₁ = $5/share.

Step 1: g = ROE × b = ?

%

Step 2: V₀ = D₁/(k−g) = ?

$

Step 3: PVGO = V₀ − E₁/k = ?

$

Q2: What does negative PVGO mean?

III

Multistage Growth & P/E

When constant growth doesn't cut it

Multistage

Multistage Growth Models

Firms go through life cycle stages with different growth rates:

Early Years

Rapid growth, low payout, ample reinvestment opportunities. Competitors haven't entered yet.

Later Years

Growth slows, payout rises, fewer profitable projects. Competitors in the market.

Two-Stage DDM Approach:

Stage 1: Manually compute PV of dividends during the high-growth period
Stage 2: At the end of Stage 1, use constant-growth DDM for the terminal value
Total: V₀ = PV(Stage 1 dividends) + PV(Terminal value)

V₀ = Σ D_t/(1+k)^t + P_T/(1+k)^T
where P_T = D_T+1/(k − g_steady)

Multistage

P/E Ratio and Growth

From the DDM: V₀ = D₁/(k−g) = E₁(1−b)/(k−g)

P/E = (1 − b) / (k − g)

P/E is higher when:

Higher plowback (b) → higher growth g
Higher ROE → more valuable growth
Lower k → lower required return

But only if ROE > k! Otherwise, higher plowback reduces P/E.

Wall Street Rule of Thumb

"If the P/E ratio is less than the growth rate, you may have found yourself a bargain." — Peter Lynch

The PEG ratio = P/E ÷ g. PEG < 1 may signal undervaluation.

P/E pitfalls: Accounting earnings ≠ economic earnings. Historical cost, earnings management, business cycle effects, and inflation all distort P/E comparisons.

IV

Free Cash Flow Valuation

Cash flow available after reinvestment

FCF Bodie Ch. 13

Free Cash Flow to the Firm (FCFF)

FCFF = EBIT(1 − T_c) + Depreciation − Capital Expenditures − Δ Working Capital

Example (Q4)

EBIT = $100M, Depreciation = $20M, Tax rate = 35%, CapEx + ΔWC = $10M.

FCFF = 100(1−0.35) + 20 − 10
FCFF = 65 + 20 − 10 = $75M

Firm Value

Discount FCFF at the WACC:

Firm Value = FCFF₁ / (WACC − g)

Equity value = Firm value − Debt

FCF

Free Cash Flow to Equity (FCFE)

FCFE = FCFF − Interest × (1 − T_c) + Increase in Net Debt

Example (Q5)

FCFF = $205M, Interest = $22M, T = 35%, Net debt increase = $25M.

FCFE = 205 − 22(1−0.35) + 25
FCFE = 205 − 14.3 + 25 = $215.7M

Equity Value

Discount FCFE at the cost of equity:

Equity Value = FCFE₁ / (k_e − g)

If FCFE grows at g = 2%, k_e = 11%:

= 215.7 / (0.11 − 0.02) = $2,396.7M

Checkpoint C

DDM & Growth Exercises

Q1: DDM with Reinvestment

Expected earnings E₁ = $3/share. Reinvestment rate b = 25%, ROE = 20%, k = 11%.

Step 1: g = ROE × b = ?

%

Step 2: D₁ = E₁ × (1−b) = ?

$

Step 3: V₀ = D₁/(k−g) = ?

$

Q2: ROE vs. Cost of Capital

Eagle Brand: E₁ = $1.25, k = 12%, g = 5%, b = 40%. By how much does ROE exceed k?

Hint: g = ROE × b → ROE = g/b

ROE − k = %

V

Relative Valuation

Pricing by comparison

Comparables

Valuation by Comparables

Compare a firm's valuation ratios to industry peers:

Ratio	Formula	Best For
P/E Ratio	Price / Earnings per share	Profitable, mature firms
P/B Ratio	Price / Book value per share	Asset-heavy firms (banks, REITs)
P/S Ratio	Price / Sales per share	Startups with no earnings yet
P/CF Ratio	Price / Cash flow per share	When earnings are distorted by accounting

Logic: If similar firms trade at 15× earnings and your firm earns $3/share, it should be worth ~$45/share.

Limitation: "Similar" firms may not be truly comparable. Industry averages mask wide variation in growth, risk, and margins.

Comparables

Book Value & Its Limitations

Book Value Problems

Based on historical cost, not market value
Excludes intangibles: brand, expertise, IP
Rarely equals market value (usually much lower)

Liquidation Value

The "floor" — break up the firm, sell assets, repay debt, distribute remainder.

If Market Value < Liquidation Value → potential arbitrage opportunity (buy, break up, profit).

Tobin's q

q = Market Value / Replacement Cost

q > 1 → market values the firm's assets above their replacement cost (growth premium).

q < 1 → market values the firm below replacement cost (potential undervaluation or poor management).

Summary

Comparing Valuation Models

Model	Inputs	Strengths	Weaknesses
DDM	Dividends, g, k	Theoretically sound	Very sensitive to g; useless for non-dividend firms
FCFF/FCFE	Cash flows, WACC/k	Works for non-dividend firms	Forecasting cash flows is hard
P/E Comparables	Peer ratios	Simple, market-based	"Similar" firms may differ significantly
P/B, P/S	Book value, sales	Useful for special cases	Historical cost; ignores growth

Best practice: Use multiple valuation methods and triangulate. If they converge, you have more confidence. If they diverge, investigate why.

DCF sensitivity warning: Small changes in growth rate, discount rate, or terminal value assumptions can produce wildly different valuations. Always perform sensitivity analysis.

Reference

Key Formulas

Expected HPR

E(r) = (D₁ + P₁ − P₀) / P₀

Intrinsic Value

V₀ = (D₁ + P₁) / (1 + k)

Constant-Growth DDM

V₀ = D₁ / (k − g)

Growth Rate

g = ROE × b

PVGO

PVGO = V₀ − E₁/k

P/E Ratio

P/E = (1−b) / (k−g)

FCFF

EBIT(1−T) + Dep − CapEx − ΔWC

FCFE

FCFF − Int(1−T) + ΔDebt

Quiz 1

Quiz: DDM & P/E

A stock has ROE = 12%, E₁ = $2, payout ratio = 75%, k = 10%.

a) What is the dividend D₁?

$

b) What is the growth rate g?

%

c) What is the stock price V₀?

$

d) What is the P/E ratio?

×

Quiz 2

Quiz: Free Cash Flow

A firm reports the following:

EBIT	$80 million
Depreciation	$15 million
Tax rate	30%
CapEx + ΔWC	$12 million

What is FCFF?

FCFF = EBIT(1−T) + Dep − CapEx − ΔWC

FCFF = $ million

If FCFF grows at 3% and WACC = 10%, what is the firm value?

Firm value = $ million

Takeaways

Key Takeaways

Intrinsic value = PV of all expected future cash flows. Compare to market price to find mispricing.
The constant-growth DDM (V₀ = D₁/(k−g)) is elegant but extremely sensitive to growth assumptions.
Growth is not inherently valuable — only when ROE > k. Negative PVGO means the firm should stop reinvesting.
Multistage models handle firms transitioning from high to steady-state growth.
FCFF and FCFE models work for non-dividend-paying firms — the more flexible valuation approach.
Comparable valuation (P/E, P/B, P/S) provides market-based sanity checks but requires truly comparable peers.
Use multiple models and triangulate. No single approach is perfect.

Equity valuation is as much art as science — the models provide structure, but the real skill is in the assumptions.