Deepen understanding of equity as an asset class

2.1.1 · Stock-Market › Equity & Fixed Income

Equity KYA hai?

"Residual" KYU? Kisi company ke cash flows ek strict order mein pay kiye jaate hain jise capital structure waterfall kehte hain:

$Revenue \to Suppliers \to Employees \to Interest (debt) \to Tax \to whatever remains Equity holders$

Kyunki equity sabse last mein hoti hai, iska payoff uncertain hai aur upar ki taraf unbounded hai.

Hum aaj ka fair price $P_{0}$ chahte hain. Pehla principle: ek share utna worth hai jitna present value of all cash jo woh kabhi bhi aapko dega — yaani uske future dividends.

Step 1 — ek saal: Agar aapko dividend $D_{1}$ milta hai aur aap agale saal $P_{1}$ mein bech sakte hain, aur aap return $r$ maangte hain: $P_{0} = \frac{D _{1} + P _{1}}{1 + r}$ Kyun? Kyunki $P_{0} (1 + r)$ wahi hona chahiye jo aapko agale saal milega, warna aap kahin aur invest karte.

Step 2 — recursively substitute karein: Lekin $P_{1} = \frac{D _{2} + P _{2}}{1 + r}$ . Substitute karne par: $P_{0} = \frac{D _{1}}{1 + r} + \frac{D _{2} + P _{2}}{( 1 + r ) ^{2}}$ Yeh hamesha ke liye chalate rahein. Final price term $\frac{P _{n}}{( 1 + r ) ^{n}} \to 0$ jab $n \to \infty$ (ek finite price bahut bade growth se divide hoti hai). Toh:

Step 3 — maanein ki dividends constant rate $g$ se badhte hain: toh $D_{t} = D_{1} (1 + g)^{t - 1}$ . $P_{0} = \sum_{t = 1}^{\infty} \frac{D _{1} ( 1 + g ) ^{t - 1}}{( 1 + r ) ^{t}}$ Yeh ek geometric series hai jiska ratio $x = \frac{1 + g}{1 + r}$ hai. Sum karne par (valid hai jab $r > g$ ): $P_{0} = \frac{D _{1}}{1 + r} \cdot \frac{1}{1 - \frac{1 + g}{1 + r}} = \frac{D _{1}}{r - g}$

$r > g$ KYU zaroori hai: agar dividends aapke discount rate se hamesha tez badhte rahein, toh sum diverge ho jaata hai (infinite value) — economically ek perpetual company ke liye impossible hai.

Equity "equity risk premium" KYU kamaati hai

Figure — Deepen understanding of equity as an asset class

Worked Examples

Common Mistakes (Steel-manned)

Forecast-then-Verify

Active-Recall Flashcards

Ek equity holder ka company par kaunse prakar ka claim hota hai?

Ek residual claim — sirf debt, tax, suppliers ke baad pay kiya jaata hai.

Equity ki koi maturity date kyun nahi hoti?

Yeh perpetual ownership hai, koi loan nahi jo repay karna ho.

General Dividend Discount Model batayein.

P_{0} = \sum_{t = 1}^{\infty} D_{t} / (1 + r)^{t}

— saare future dividends ki PV.

Gordon Growth Model aur uski condition batayein.

P_{0} = D_{1} / (r - g)

, valid sirf jab

r > g

ho.

Required equity return ko do parts mein decompose karein.

Dividend yield

D_{1} / P_{0}

+ growth

g

Equity risk premium kyun kamaati hai?

Yeh residual, sabse uncertain payoff hai, isliye investors

r = r_{f} + ERP

risk-free rate se upar maangte hain.

Liquidation mein agar assets < debt ho toh equity holder ka payoff kya hoga?

Zero (limited liability losses ko invested amount par floor karti hai).

Agar

D_{0}

abhi-abhi pay hua hai, toh

D_{1}

kya hoga?

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

Required return

r

badhne par

P_{0}

ka kya hota hai?

P_{0}

girta hai (

D_{1} / (r - g)

mein bada denominator).

Book equity aur market equity mein farq kya hai?

Book = Assets − Liabilities (accounting); Market = expected future cash flows ki PV.

Recall Feynman: 12-saal ke bachche ko samjhayein

Socho tumhara parivaar ek lemonade stand ka malik hai. Pehle tumhe lemons, cups, aur woh paisa chukana hoga jo tumne ek dost se udhar liya tha. Jo bhi coins bacha rahega woh tumhara hai — yahi "bacha hua" hissa equity ki malik hona matlab hai. Kuch din bahut zyada bachta hai (zabardast!), kuch din kuch nahi (sad). Kyunki tum kabhi nahi jaante kitna milega, lekin yeh bahut zyada ho sakta hai, isliye stand ka malik hona exciting hai lekin risky bhi. Bilkul aise hi ek company ka piece (ek share) kharidhna kaam karta hai.

Connections

Fixed Income & Bonds — senior claim; fixed coupons vs residual dividends se contrast karein.
Capital Structure Waterfall — kyun equity line mein last mein hoti hai.
Discount Rate & Time Value of Money — valuation ke peeche $1/ (1 + r)^{t}$ ka engine.
Equity Risk Premium — residual risk hold karne ka reward.
Dividend Discount Model — Gordon Growth ka parent model.
Limited Liability — kyun downside zero par floored hai.