Learn about reverse DCF — Hinglish notes

2.6.10 · Stock-Market › Valuation Methods

What Is Reverse DCF?

Reverse Discounted Cash Flow ek valuation technique hai jahan tum current stock price se backwards kaam karte ho taaki yeh determine kar sako ki market kaunsa implied growth rate ya terminal assumptions price kar rahi hai.

Standard DCF formula: $P_{0} = \sum_{t = 1}^{n} \frac{F C F _{t}}{( 1 + W A C C ) ^{t}} + \frac{T V}{( 1 + W A C C ) ^{n}}$

jahan $T V = \frac{F C F _{n + 1}}{W A C C - g}$ (perpetuity growth).

Forward DCF mein, tum $g$ (growth rate) choose karte ho, $P_{0}$ calculate karte ho, aur market price se compare karte ho.

Reverse DCF mein, tum:

$P_{0}$ = current market price set karte ho
Unknown solve karte ho (usually implied $g$ ya terminal multiple)

Derivation from First Principles

Step 1: Standard DCF foundation Kisi company ki value saare future cash flows ka sum hai, aaj tak discount karke: $P_{0} = \sum_{t = 1}^{\infty} \frac{F C F _{t}}{( 1 + r ) ^{t}}$

Kyun? Aaj ka ek dollar kal ke ek dollar se zyada worth hai (time value of money). Discount rate $r$ (WACC) risk aur opportunity cost account karta hai.

Step 2: High-growth aur stable phases mein split karo Companies hamesha 30% grow nahi karti. Model karo:

Phase 1 (years 1 to $n$ ): High growth rate $g$
Phase 2 (year $n + 1$ onward): Stable terminal growth $g_{t}$

$P_{0} = High-growth PV t = 1 \sum n \frac{F C F _{0} ( 1 + g ) ^{t}}{( 1 + r ) ^{t}} + Terminal value PV \frac{F C F _{n} ( 1 + g _{t} )}{( r - g _{t} ) ( 1 + r ) ^{n}}$

Terminal formula kyun? Yeh ek perpetuity hai: $\sum_{k = 1}^{\infty} \frac{C}{( 1 + r ) ^{k}} = \frac{C}{r}$ (geometric series). Growth ke saath, terminal value year $n$ par $\frac{F C F _{n} ( 1 + g _{t} )}{r - g _{t}}$ hoti hai, aur hum us lump sum ko $(1 + r)^{n}$ se divide karke $n$ saal peeche discount karte hain.

Step 3: Reverse trick Ab $P_{0}$ ko market price $P_{market}$ par fix karo aur $g$ ko unknown treat karo: $P_{market} = \sum_{t = 1}^{n} \frac{F C F _{0} ( 1 + g ) ^{t}}{( 1 + r ) ^{t}} + \frac{F C F _{0} ( 1 + g ) ^{n} ( 1 + g _{t} )}{( r - g _{t} ) ( 1 + r ) ^{n}}$

Yeh $g$ mein ek nonlinear equation hai. Tum ise numerically solve karte ho (Excel Goal Seek, Python scipy.optimize, ya iteration).

Algebraically kyun nahi solve kar sakte? $g$ summation mein bhi appear karta hai aur exponentials ke andar bhi—koi closed form nahi hai. Numerical methods (Newton-Raphson, bisection) jaldi converge karte hain.

Worked example Example 1: SaaS Startup Valuation Check

Given:

Current stock price: $P_{\text{market}} = \$ 50$
Current FCF: $F C F_{0} = \frac{E B I T ( 1 - T ) + D & A - Δ N W C - C a pE x}{( 1 + W A C C ) ^{0}} t e x t$ 2$ per share
WACC: $r = 10%$
High-growth period: $n = 10$ years
Terminal growth: $g_{t} = 3%$
Find: Implied high-growth rate $g$

Setup: $50 = \sum_{t = 1}^{10} \frac{2 ( 1 + g ) ^{t}}{1. 1 ^{t}} + \frac{2 ( 1 + g ) ^{10} ( 1.03 )}{( 0.10 - 0.03 ) \cdot 1. 1 ^{10}}$

Numerically solve karo. Note karo $1. 1^{10} \approx 2.594$ .

Trial $g = 20%$ :

High-growth PV: $\sum_{t = 1}^{10} \frac{2 \cdot 1. 2 ^{t}}{1. 1 ^{t}}$ . Ratio hai $\frac{1.2}{1.1} = 1.0909$ , toh $2 \sum_{t = 1}^{10} 1.090 9^{t}$ . Yeh step kyun? Har term growth-over-discount ratio ko compound karti hai. Geometric sum $\sum_{t = 1}^{10} 1.090 9^{t} \approx 16.67$ , jo $2 \cdot 16.67 = 33.34$ deta hai.
Terminal (year 10 par value): $\frac{2 \cdot 1. 2 ^{10} \cdot 1.03}{0.07} = \frac{2 \cdot 6.19 \cdot 1.03}{0.07} = \frac{12.75}{0.07} \approx 182.2$ . Ek baar discount karo 10 saal peeche: $P V = \frac{182.2}{2.594} \approx 70.2$ .
Total: $33.34 + 70.2 = 103.5$ (bahut zyada)

Trial $g = 10%$ :

High-growth PV: ratio $\frac{1.1}{1.1} = 1$ , toh $2 \sum_{t = 1}^{10} 1 = 2 \cdot 10 = 20$ .
Terminal at year 10: $\frac{2 \cdot 1. 1 ^{10} \cdot 1.03}{0.07} = \frac{2 \cdot 2.594 \cdot 1.03}{0.07} = \frac{5.343}{0.07} \approx 76.3$ ; $P V = \frac{76.3}{2.594} \approx 29.4$ .
Total: $20 + 29.4 = 49.4$ (thoda sa 50 se kam)

Iterate kyun? Function $g$ mein monotonic hai. Kyunki $g = 10%$ se $\approx 49.4$ aata hai aur $g = 20%$ se $\approx 103.5$ , answer $10%$ se thoda upar hai. Goal Seek ke saath: implied $g \approx 10.2%$ .

Interpretation: Market expect karti hai ki yeh SaaS company apna FCF sirf ~10% se 10 saalon tak grow karegi, phir hamesha ke liye 3%. Ab khud se poocho: Company ke TAM aur competition ko dekhte hue, kya 10% bahut pessimistic hai (buy) ya fair hai?

Worked example Example 2: Mature Company (Low Growth Already Priced)

Given:

$P_{\text{market}} = \$ 80$
$FCF_0 = \$ 5$
$r = 8%$ , $n = 5$ , $g_{t} = 2%$
Find: Implied $g$

Setup ( $1.0 8^{5} \approx 1.469$ ): $80 = \sum_{t = 1}^{5} \frac{5 ( 1 + g ) ^{t}}{1.0 8 ^{t}} + \frac{5 ( 1 + g ) ^{5} \cdot 1.02}{( 0.08 - 0.02 ) \cdot 1.0 8 ^{5}}$

Trial $g = 0%$ :

High-growth PV: $5 \sum_{t = 1}^{5} \frac{1}{1.0 8 ^{t}} = 5 \cdot 3.993 = 19.96$ . Kyun? Koi growth nahi toh yeh ek plain 5-year annuity hai.
Terminal at year 5: $\frac{5 \cdot 1.02}{0.06} = \frac{5.1}{0.06} = 85.0$ ; ek baar discount karo: $P V = \frac{85.0}{1.469} = 57.86$ .
Total: $19.96 + 57.86 = 77.8$ (thoda 80 se kam)

Trial $g = 2%$ :

High-growth PV: ratio $\frac{1.02}{1.08} = 0.9444$ , $5 \sum_{t = 1}^{5} 0.944 4^{t} \approx 5 \cdot 4.183 = 20.9$ .
Terminal at year 5: $\frac{5 \cdot 1.0 2 ^{5} \cdot 1.02}{0.06} = \frac{5 \cdot 1.104 \cdot 1.02}{0.06} = \frac{5.63}{0.06} = 93.8$ ; $P V = \frac{93.8}{1.469} = 63.9$ .
Total: $20.9 + 63.9 = 84.8$ (80 se zyada)

Iterate kyun? $g = 0%$ se $77.8$ aata hai, $g = 2%$ se $84.8$ ; root $g \approx 0.8%$ ke paas hai. Goal Seek ke saath: implied $g \approx 0.8%$ .

Interpretation: Market expect karti hai ki 5 saalon mein almost koi growth nahi hogi. Yeh ek mature, stable company hai—price low expectations reflect karti hai. Dividend investors ke liye accha hai, lekin agar disruption aaye toh risky hai.

How to Use Reverse DCF in Practice

Step-by-step:

Current price aur shares outstanding lo → Market cap
Current FCF estimate karo (TTM ya normalized)
Model parameters choose karo:
- High-growth period $n$ (typically 5–10 years)
- Terminal growth $g_{t}$ (GDP-jaisi, 2–4%)
- WACC (CAPM ya industry average use karo)
Equation set up karo left side par $P_{market}$ ke saath
$g$ solve karo (Excel Goal Seek, Python fsolve)
Implied $g$ ko sanity-check karo:
- Historical growth, analyst estimates, industry benchmarks se compare karo
- Agar implied $g$ 40% hai lekin industry 8% grow karti hai, toh stock overpriced hai
- Agar implied $g$ 5% hai lekin company ek bade market ko disrupt kar rahi hai, toh yeh underpriced ho sakta hai

Common mistake Galti: Implied Number par Blindly Trust Karna

Galat idea: "Reverse DCF kehta hai implied growth 18% hai, toh yahi hoga." Kyun sahi lagta hai: Math precise hai, toh output "zaroor" sach hogi.

Steel-man: Reverse DCF sahi tarah batata hai ki market kya price kar rahi hai agar tumhara model sahi hai. Lekin tumhara WACC estimate galat ho sakta hai, tumhara FCF mismeasured ho sakta hai, ya market irrational ho sakti hai (bubbles, panics). Implied growth ek hypothesis hai jo test karni hai, prediction nahi.

Fix: Reverse DCF se yeh poocho, "Kya yeh expectation competitive dynamics, regulations, TAM, management quality ko dekhte hue reasonable hai?" Scenarios se cross-check karo: "Agar unhone 5 saalon mein 10% market share capture kiya, toh iska kya FCF imply hoga? Kya yeh implied $g$ se match karta hai?"

Common mistake Galti: Terminal Value ko Double-Discount Karna

Galat idea: "Maine terminal value ko pehle se $(r - g_{t})$ se divide kar diya hai, aur yeh bahut door hai future mein, toh main ise $(1 + r)^{n}$ se phir divide karunga... aur safety ke liye ek baar aur."

Kyun sahi lagta hai: Divide karna "conservative hona" lagta hai, aur terminal value dekh ke darne wali lagti hai.

Reality: Perpetuity formula $\frac{F C F _{n} ( 1 + g _{t} )}{r - g _{t}}$ value year $n$ par deta hai. Tum ise aaj tak exactly ek baar $(1 + r)^{n}$ se discount karte ho. Do baar discount karna (e.g., 2594 se divide karna 2.594 ki jagah) true present value ko orders of magnitude se understate kar deta hai aur implied $g$ ko corrupt kar deta hai.

Fix: Terminal value = year $n$ par perpetuity, phir ek discount factor $(1 + r)^{n}$ . Apne decimals track karo: $1. 1^{10} = 2.594$ , na ki $2594$ .

Key Insights

Reverse DCF ek reality check hai, na ki ek valuation. Yeh nahi batata ki stock kahan trade karni chahiye—yeh batata hai ki market kya believe karti hai.
Implied growth ko fundamentals se compare karo: Agar NVDA ka implied $g$ 35% hai lekin semiconductor TAM 12% grow karta hai, toh ya toh NVDA massive share le raha hai ya stock frothy hai.
Bulls aur bears dono ke liye useful: Bulls ise use karte hain yeh dikhane ke liye ki "market bahut pessimistic hai" (implied $g$ low hai). Bears ise use karte hain yeh dikhane ke liye ki "market delusion mein hai" (implied $g$ unrealistic dominance maangti hai).
Scenario analysis ke saath achha pairing: 3 scenarios build karo (bull/base/bear) realistic FCF paths ke saath, har ek ka reverse-DCF karo, aur dekho kaunsa implied $g$ current price se match karta hai.

Recall Feynman: Ek 12-Saal ke Bacche ko Explain Karo

Socho tum ek lemonade stand dekhte ho jo $100 mein khareedne ko milta hai. Tum jaante ho yeh har saal $10 profit banata hai. Tum sochte ho, "Yeh achha deal hai agar yeh 20% saal grow kare, lekin bura hai agar sirf 5% grow kare." **Reverse DCF sawaal ulta kar deta hai:** Kisi ne pehle se \$ 100 mein stand khareed liya. Tum backwards kaam karte ho aur poochte ho, "Is price par pay karne ke liye unhhe kaisi growth mein believe karna hoga?" Tum math karte ho aur paate ho ki wo 18% growth expect kar rahe hain. Ab tum khud se poochte ho: "Kya yeh realistic hai? Kya yeh lemonade stand itni competition mein sach mein 18% grow kar sakta hai?"

Agar tumhe lagta hai haan, toh stand khareed lo (stock sasta hai). Agar nahi lagta, toh chale jao (stock mehnga hai). Tum future guess nahi kar rahe—tum check kar rahe ho ki current price us sab ke hisaab se sense banati hai jo tum lemonade stands ke baare mein jaante ho.

Connections

Discounted Cash Flow (DCF) — Forward version; reverse DCF uska mirror hai
Weighted Average Cost of Capital (WACC) — Discount rate; yahaan ki galtiyan poore result mein ripple karti hain
Terminal Value — Price ko dominate karta hai; chhoti changes bade swings laati hain
Sensitivity Analysis — Reverse DCF assumptions test karne ke liye zaroori
Market Efficiency — Reverse DCF assume karta hai ki price collective expectations reflect karti hai
Growth Rate Estimation — Yeh judge karna ek art hai ki implied $g$ achievable hai ya nahi
Free Cash Flow (FCF) — Raw input; garbage in, garbage out
Scenario Analysis — Reverse DCF ke saath combine karo: scenarios build karo, har ek ka reverse-DCF karo, triangulate karo

#flashcards/stock-market

Reverse DCF ka core idea kya hai? :: Current market price se backwards kaam karna taaki implied growth rate ya terminal assumptions determine ho sake jo market price kar rahi hai, na ki fair value forecast karna.

Woh reverse DCF equation likho jahan tum growth rate

g

solve karte ho.

P_{market} = \sum_{t = 1}^{n} \frac{F C F _{0} ( 1 + g ) ^{t}}{( 1 + r ) ^{t}} + \frac{F C F _{0} ( 1 + g ) ^{n} ( 1 + g _{t} )}{( r - g _{t} ) ( 1 + r ) ^{n}}

, phir

g

numerically solve karo (koi closed form nahi).

Reverse DCF equation algebraically kyun solve nahi kar sakte?

Unknown

g

summation ke andar bhi appear karta hai aur exponential terms mein bhi, jo ek transcendental equation banata hai jiska koi closed-form solution nahi hai. Goal Seek ya Newton-Raphson jaise numerical methods use karne padte hain.

Terminal (perpetuity) value ko aaj tak kitni baar discount karte hain?

Exactly ek baar,

(1 + r)^{n}

se. Perpetuity formula pehle se year

n

par value deta hai; do baar discount karna ek classic error hai jo present value ko bilkul collapse kar deta hai.

Agar reverse DCF implied growth 35% dikhata hai lekin industry 10% grow karti hai, toh yeh kya suggest karta hai?

Stock likely overpriced hai—market expect karti hai ki company industry ko massively outperform karegi, jo unrealistic ho sakta hai jab tak company ek huge TAM ke saath dominant disruptor na ho.

Terminal value zyaadatar DCF valuations mein dominate kyun karta hai?

Yeh ek perpetuity hai jo year

n + 1

se infinity tak ke saare cash flows represent karti hai. Discount hone ke bawajood, saalon ki itni badi tadaad ka matlab hai ki yeh aksar total present value ka 50–80% contribute karta hai.

Practically reverse DCF result ko kaise interpret karte hain?

Implied growth rate ko company ki historical growth, analyst forecasts, competitive position, aur industry benchmarks se compare karo. Poocho: "Kya yeh expectation realistic hai?" Agar nahi, toh stock mispriced ho sakta hai.

Reverse DCF ke saath log kya sabse badi galti karte hain? :: Implied growth rate ko ek prediction ya sach treat karna, instead of market ka woh assumption maanna jo business fundamentals ke against reality-test karna zaroori hai.

Reverse DCF run karte waqt kya sensitivity-test karna chahiye?

Terminal growth rate

g_{t}

, WACC, aur high-growth period length

n

g_{t}

mein chhoti changes (jaise 3% vs. 5%) implied

g

mein bahut bade swings cause kar sakti hain.