Learn dividend discount model (DDM)

2.6.6 · Stock-Market › Valuation Methods

Derivation: Pehle Principles Se

Ek fundamental sawaal se shuru karo: Jab main ek stock khareedta hoon toh main kya khareed raha hoon?

Year 1: Mujhe ek saal mein dividend $D_{1}$ milta hai. Woh aaj kitna worth hai?
- Worth $\frac{D _{1}}{1 + r}$ kyunki main aaj $\frac{D _{1}}{1 + r}$ rate $r$ par invest kar sakta hoon aur agli saal $D_{1}$ pa sakta hoon.
Year 2: Mujhe $D_{2}$ do saal mein milta hai. Present value?
- $\frac{D _{2}}{( 1 + r ) ^{2}}$ — do baar discounted kyunki yeh do saal door hai.
Pattern: Har future dividend $D_{t}$ ka present value $\frac{D _{t}}{( 1 + r ) ^{t}}$ hai.
Sum them all: $P_{0} = \frac{D _{1}}{( 1 + r )} + \frac{D _{2}}{( 1 + r ) ^{2}} + \frac{D _{3}}{( 1 + r ) ^{3}} + \dots = \sum_{t = 1}^{\infty} \frac{D _{t}}{( 1 + r ) ^{t}}$

Discount rate $r$ kyu? Yeh aapka required rate of return hai—woh minimum jo aap demand karte ho compensate karne ke liye:

Time value of money: Aap kahin aur invest kar sakte the
Risk: Dividends guaranteed nahi hote
Opportunity cost: Is stock ko khareed ke aap kya chhodte ho

Figure — Learn dividend discount model (DDM)

The Gordon Growth Model (Constant Growth DDM)

Infinite sum se Derivation:

$P_{0} = \sum_{t = 1}^{\infty} \frac{D _{t}}{( 1 + r ) ^{t}}$ se shuru karo.

Agar $D_{1}$ agli saal ka dividend hai aur dividends $g$ se badhte hain:

$D_{1} = D_{1}$
$D_{2} = D_{1} (1 + g)$
$D_{3} = D_{1} (1 + g)^{2}$
$D_{t} = D_{1} (1 + g)^{t - 1}$

Substitute karo: $P_{0} = \sum_{t = 1}^{\infty} \frac{D _{1} ( 1 + g ) ^{t - 1}}{( 1 + r ) ^{t}} = D_{1} \sum_{t = 1}^{\infty} \frac{( 1 + g ) ^{t - 1}}{( 1 + r ) ^{t}}$

Sum ko simplify karo: $= D_{1} \sum_{t = 1}^{\infty} (\frac{1 + g}{1 + r})^{t - 1} \cdot \frac{1}{1 + r}$

$x = \frac{1 + g}{1 + r}$ maano, toh humein $\sum_{t = 1}^{\infty} x^{t - 1} = \sum_{k = 0}^{\infty} x^{k}$ chahiye.

Geometric series: $\sum_{k = 0}^{\infty} x^{k} = \frac{1}{1 - x}$ jab $∣ x ∣ < 1$ (yaani $g < r$ ).

Toh: $P_{0} = \frac{D _{1}}{1 + r} \cdot \frac{1}{1 - \frac{1 + g}{1 + r}} = \frac{D _{1}}{1 + r} \cdot \frac{1 + r}{( 1 + r ) - ( + g )} = \frac{D _{1}}{r - g}$

Yeh kyu matter karta hai: Gordon model mature, dividend-paying companies ko value karne ka workhorse hai. Simple, elegant, jab assumptions hold hoti hain toh deadly accurate.

Worked Examples

Worked example Example 2: Multi-Stage Growth

Given: Ek tech company abhi $D_{0} = \emptyset$ 1.00$ deti hai. Expected growth:

Years 1-3: $g_{1} = 20%$ (high growth phase)
Year 4 se aage: $g_{2} = 5%$ (mature growth)
Required return: $r = 12%$

Find: $P_{0}$ .

Multi-stage kyu? Young companies pehle fast badhti hain, phir slow ho jaati hain. Single-stage Gordon yeh capture nahi karta.

Step 1: High-growth years ke liye dividends calculate karo. $D_{1} = 1.00 \times 1.20 = $1.20$ $D_{2} = 1.20 \times 1.20 = $1.44$ $D_{3} = 1.44 \times 1.20 = $1.728$ Step 2: $D_{4}$ calculate karo (stable growth ka pehla saal). $D_{4} = 1.728 \times 1.05 = $1.8144$

Step 3: Year 3 ke end par terminal value nikalo (year 4 se aage ke sabhi dividends ki value, year 3 ke hisaab se). $P_{3} = \frac{D _{4}}{r - g _{2}} = \frac{1.8144}{0.12 - 0.05} = \frac{1.8144}{0.07} = $25.92$ Yeh step kyu? Year 3 par company perpetual growth mein enter karti hai. Hum Gordon use karte hain us infinite stream ko year 3 ke hisaab se value karne ke liye.

Step 4: Sab kuch aaj tak discount karo. $P_{0} = \frac{D _{1}}{( 1.12 ) ^{1}} + \frac{D _{2}}{( 1.12 ) ^{2}} + \frac{D _{3}}{( 1.12 ) ^{3}} + \frac{P _{3}}{( 1.12 ) ^{3}}$ $= \frac{1.20}{1.12} + \frac{1.44}{1.2544} + \frac{1.728}{1.4049} + \frac{25.92}{1.4049}$ $= 1.071 + 1.148 + 1.230 + 18.45 = $21.90$

$P_{3}$ discount kyu karo? Yeh year 3 ki value hai, aaj ki nahi. Humein present value chahiye.

Common Mistakes

Active Recall Flashcards

#flashcards/stock-market

What does the Dividend Discount Model (DDM) value a stock as? :: The present value of all future dividends: $P_{0} = \sum_{t = 1}^{\infty} \frac{D _{t}}{( 1 + r ) ^{t}}$

What is the Gordon Growth Model formula?

P_{0} = \frac{D _{1}}{r - g}

where

D_{1}

is next year's dividend,

r

is required return, and

g

is constant growth rate

Why must

g < r

in the Gordon Growth Model?

Because if

g \geq r

, the geometric series diverges—mathematically it means the stock has infinite value, which is impossible. Also economically: if dividends grow faster than required return forever, no investor would ever sell.

In DDM, what is the "discount rate"

r

and why do we use it?

r

is your required rate of return—it compensates for time value of money, risk, and opportunity cost. We discount because

\

t o d a y i s w or t hm or e t han

$1$ in the future.

What's the difference between

D_{0}

and

D_{1}

in Gordon Growth Model?

D_{0}

is the dividend just paid (historical).

D_{1} = D_{0} (1 + g)

is next year's expected dividend. Gordon formula requires

D_{1}

because it values future cash flows.

How do you value a stock with multiple growth stages?

1) Calculate dividends during high-growth years, 2) Find terminal value at end of high-growth using Gordon model, 3) Discount all cash flows (dividends + terminal value) back to present.

Why does a higher required return

r

decrease stock price in DDM?

Because higher

r

means you're discounting future dividends more heavily. Each future dollar is worth less today when your required return is higher. Mathematically:

P_{0} = \frac{D _{1}}{r - g}

, so

r ↑

means

P_{0} ↓

What type of stock is Gordon Growth Model best suited for?

Mature, stable companies with predictable dividend growth (utilities, consumer staples). Not suitable for high-growth companies, non-dividend payers, or cyclical businesses.

Feynman Technique

Recall Ek 12-saal ke bacche ko explain karo

Socho tumhare dost ka ek lemonade stand hai. Tum use unse khareedne ke baare mein soch rahe ho. Tumhe kitna pay karna chahiye?

Dekho, woh stand tumhe har summer paisa dega—maano is saal $\$ 10 $, a g l i s aa l$ $11 $n e x t y e a r (k y u nk i w o h p r i ces t h o d iba d ha t e hain), u s k e baa d$ $12$ the year after, aur aise hamesha ke liye.

Lekin yahan ek baat hai: $\$ 11 $a g l i s aa l$ $11 $aaj k e j ai s aa c hhanahihai, na ? K y u nk ia g a r aa p k e p aa s$ $11$ aaj hote, toh aap use savings account mein rakh sakte the aur agli saal aur zyada pa sakte the. Toh future paisa ko "discount" karna padta hai taaki compare karna fair ho.

DDM bas ek fancy math hai jo kehta hai: "Bhavishya mein milne wali saari raqam jodo, lekin har future dollar ko thoda kam worth samjho kyunki woh door hai." Woh total hi lemonade stand (ya stock) ki value hai.

Gordon Growth Model ek shortcut hai: agar stand ki earnings har saal usi percent se hamesha ke liye badhti hain, toh aap infinite numbers add karne ki jagah ek simple formula use kar sakte ho. Yeh calculation ke liye ek cheat code jaisa hai!

Mnemonic

Connections

2.6.01-Understand-intrinsic-value-vs-market-price: DDM intrinsic value calculate karta hai
2.6.02-Time-value-of-money-inuation: DDM present value discounting apply karta hai
2.6.03-Learn-price-to-earnings-(PE)-ratio: PE relative valuation hai; DDM absolute valuation hai
2.6.08-Discounted-cash-flow-(DCF)-analysis: DDM, DCF ka ek special case hai (dividends ek type of cash flow hain)
2.5.03-Understanding-dividends-and-payout-ratios: Dividend policy $D_{t}$ aur $g$ inputs determine karti hai
3.2.04-Required-rate-of-return-andCAPM: CAPM, DDM ke liye $r$ calculate karta hai
2.6.10-Compare-valuation-methods: DDM vs. PE vs. DCF vs. asset-based

Is note ko active recall ke saath study karo: Answers cover karo, formulas scratch se derive karne ki koshish karo, examples bina dekhhe work karo. Mistakes ko steel-man karo—samjho ki woh tempting kyu lagte hain.

Core Intuition