Deepen understanding of equity as an asset class — Stock-Market notes

WHAT is equity?

WHY "residual"? A company's cash flows are paid out in a strict order called the capital structure waterfall:

$\text{Revenue} \rightarrow \text{Suppliers} \rightarrow \text{Employees} \rightarrow \text{Interest (debt)} \rightarrow \text{Tax} \rightarrow \underbrace{\text{Equity holders}}_{\text{whatever remains}}$

Because equity is last in line, its payoff is uncertain and unbounded on the upside.

We want the fair price today, $P_0$ . First principle: a share is worth the present value of all cash it will ever pay you — i.e. its future dividends.

Step 1 — one year: If you get dividend $D_1$ and can sell for $P_1$ next year, and you demand return $r$ : $P_0 = \frac{D_1 + P_1}{1+r}$ Why? Because $P_0(1+r)$ must equal what you receive next year, or you'd invest elsewhere.

Step 2 — substitute recursively: But $P_1 = \dfrac{D_2 + P_2}{1+r}$ . Substituting: $P_0 = \frac{D_1}{1+r} + \frac{D_2 + P_2}{(1+r)^2}$ Keep going forever. The final price term $\dfrac{P_n}{(1+r)^n}\to 0$ as $n\to\infty$ (a finite price divided by huge growth). So:

Step 3 — assume dividends grow at constant rate $g$ : so $D_t = D_1(1+g)^{t-1}$ . $P_0 = \sum_{t=1}^{\infty}\frac{D_1(1+g)^{t-1}}{(1+r)^t}$ This is a geometric series with ratio $x=\frac{1+g}{1+r}$ . Summing (valid when $r>g$ ): $P_0 = \frac{D_1}{1+r}\cdot\frac{1}{1-\frac{1+g}{1+r}} = \frac{D_1}{r-g}$

WHY $r>g$ matters: if dividends grew faster than your discount rate forever, the sum diverges (infinite value) — economically impossible for a perpetual company.

WHY equity earns the "equity risk premium"

Figure — Deepen understanding of equity as an asset class

Worked Examples

Common Mistakes (Steel-manned)

Forecast-then-Verify

Active-Recall Flashcards

What kind of claim does an equity holder have on a company?

A residual claim — paid only after debt, tax, suppliers.

Why does equity have no maturity date?

It is perpetual ownership, not a loan to be repaid.

State the general Dividend Discount Model.

P_0 = \sum_{t=1}^\infty D_t/(1+r)^t

— PV of all future dividends.

State the Gordon Growth Model and its condition.

P_0 = D_1/(r-g)

, valid only when

r>g

Decompose the required equity return into two parts.

Dividend yield

D_1/P_0

+ growth

g

Why does equity earn a risk premium?

It's the residual, most uncertain payoff, so investors demand

r=r_f+\text{ERP}

above the risk-free rate.

What is the equity holder's payoff in liquidation if assets < debt?

Zero (limited liability floors losses at the amount invested).

D_0

was just paid, what is

D_1

D_1 = D_0(1+g)

What happens to

P_0

when required return

r

rises?

P_0

falls (bigger denominator in

D_1/(r-g)

Difference between book equity and market equity?

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

Recall Feynman: explain to a 12-year-old

Imagine your family owns a lemonade stand. First you must pay for lemons, cups, and the money you borrowed from a friend. Whatever coins are left over are yours to keep — that "left over" part is what owning equity means. Some days there's lots left (great!), some days nothing (sad). Because you never know how much you'll get, but it could be a lot, owning the stand is exciting but risky. That's exactly how owning a piece of a company (a share) works.

Connections

Fixed Income & Bonds — the senior claim; contrast fixed coupons vs residual dividends.
Capital Structure Waterfall — why equity sits last in line.
Discount Rate & Time Value of Money — the $1/(1+r)^t$ engine behind valuation.
Equity Risk Premium — the reward for holding residual risk.
Dividend Discount Model — the parent model of Gordon Growth.
Limited Liability — why downside is floored at zero.

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, equity ka matlab hai ki tum kisi company ke maalik ban jaate ho — thoda sa hissa (share) tumhara hai. Lekin ek twist hai: tum sabse aakhri line mein khade ho. Company pehle apne suppliers, employees, phir loan wale (debt), phir tax bharti hai — jo bacha-khucha (residual) hota hai, wahi tumhara. Isliye equity ka return sabse zyada ho sakta hai, par risk bhi sabse zyada — kyunki kabhi bahut bachega, kabhi kuch nahi.

Ab ek share ki keemat kaise nikalein? Simple first principle: ek share utni hi worth hai jitne saare future dividends ki aaj ki value (present value). Isi se banta hai Dividend Discount Model: $P_0 = \sum D_t/(1+r)^t$ . Agar maan lein dividend har saal steady rate $g$ se badhta hai, to yeh geometric series ban jaati hai aur simplify hoke banta hai Gordon Model: $P_0 = D_1/(r-g)$ . Yaad rakho — yeh sirf tab valid hai jab $r > g$ , warna value infinite ho jayegi (jo real duniya mein possible nahi).

Ek important insight: required return $r$ ko do parts mein tod sakte ho — dividend yield ( $D_1/P_0$ ) plus growth ( $g$ ). Jab interest rates (yaani $r$ ) badhte hain, denominator $(r-g)$ bada ho jaata hai, isliye share price girti hai. Yahi reason hai ki jab RBI rates badhati hai, market thoda gir jaata hai.

Sabse badi galti students karte hain: "equity ka return zyada hai isliye hamesha achha hai." Nahi bhai — woh extra return risk ka inaam hai (equity risk premium). Aur limited liability ke kaaran tumhara loss zero pe ruk jaata hai — jitna invest kiya utna hi ja sakta hai, usse zyada nahi. Long-term ke liye equity strong hai, short-term needs ke liye bonds safe.

Test yourself — Equity & Fixed Income

Connections