Learn sensitivity and scenario analysis — Hinglish notes

2.6.8 · Stock-Market › Valuation Methods

Core Concepts

Why One-at-a-Time vs. Multiple Inputs?

Sensitivity analysis pure elasticity isolate karta hai: "Agar sirf WACC ±2% move kare, toh value ±$X move karti hai." Yeh diagnostic hai—tum discover karte ho ki revenue growth tumhara model dominate karti hai, toh research time wahi refine karne mein lagao, na ki tax rate par obsess karo.

Scenario analysis correlation capture karta hai: Recession mein, revenue growth aur margins aur default risk sab saath move karte hain. Inhe independently vary karna (sensitivity) compound effect miss kar jaata hai. Ek scenario unhe ek realistic joint outcome mein bundle karta hai.

Deriving the Sensitivity Framework

Ek valuation function se shuru karo: $V = f (θ_{1}, θ_{2}, \dots, θ_{n})$ jahan $θ_{i}$ inputs hain (growth $g$ , discount rate $r$ , terminal margin $m$ , etc.).

First-order sensitivity (elasticity): $Elasticity_{i} = \frac{\partial V / V}{\partial θ _{i} / θ _{i}} = \frac{θ _{i}}{V} \cdot \frac{\partial V}{\partial θ _{i}}$

YEH FORMULA KYU? Hum chahte hain output mein percentage change divided by input mein percentage change—yahi elasticity ki definition hai. Ek DCF ke liye: $V = \sum_{t = 1}^{n} \frac{F C F _{t}}{( 1 + r ) ^{t}} + \frac{T V}{( 1 + r ) ^{n}}$

Agar hum sirf $r$ vary karein: $\frac{\partial V}{\partial r} = - \sum_{t = 1}^{n} \frac{t \cdot F C F _{t}}{( 1 + r ) ^{t + 1}} - \frac{n \cdot T V}{( 1 + r ) ^{n + 1}}$

YEH KYA BATATA HAI: Har cash flow apni time-distance se weighted hota hai; door ke cash flows (jaise terminal value) $r$ ke liye hyper-sensitive hote hain kyunki denominator exponential hai. 1% zyada discount rate 10, 20 saalon tak compound hota hai.

IMPLEMENT KAISE KAREIN:

Ek base-case $V_{0}$ fix karo jisme saare inputs best estimates par hon.
$θ_{i}$ ko ±10%, ±20% (ya relevant ranges) se perturb karo.
Har baar $V$ recalculate karo. Elasticity dikhane ke liye, normalized change $Δ V / V$ (value mein fractional change) ko $Δ θ_{i} / θ_{i}$ (input mein fractional change) ke against plot karo. Alternatively, tornado chart ke liye, absolute $Δ V$ (dollars mein) ko $θ_{i}$ mein percentage change ke against plot karo—bas consistent raho ki kaun sa axis normalized hai.
Inputs ko absolute impact ke hisaab se rank karo → tornado chart (bars sorted by magnitude).

Figure — Learn sensitivity and scenario analysis

Scenario Analysis: The Three Worlds

Formula Constructing Scenarios

Correlated drivers identify karo: revenue growth, operating margin, capex intensity, terminal growth, cost of capital.
Narrative logic banao:
- Bull: Strong economy → high growth (↑), expanding margins (↑), low default premium (WACC ↓).
- Base: Moderate growth, stable margins, normal WACC.
- Bear: Recession → low/negative growth (↓), margin compression (↓), rising risk premium (WACC ↑).
Probabilities assign karo (subjective): e.g., 20% bull, 60% base, 20% bear (yahi weights neeche worked example mein use hue hain; tum inhe apni conviction reflect karne ke liye choose karte ho aur inhe 100% sum karna chahiye).
Expected value compute karo: $E [V] = \sum_{i} P_{i} \cdot V_{i}$ jahan $P_{i}$ scenario probability hai, $V_{i}$ us scenario mein intrinsic value hai.

PROBABILITY-WEIGHT KYU? Sirf ek range (" $50 t o$ 120") tumhe nahi batati ki kahan anchor karo. Agar bear case unlikely hai aur bull case likely, toh tumhe bull value ki taraf skew karna chahiye. Expected value $E [V]$ tumhara risk-adjusted anchor hai.

Worked Example: Valuing a Retailer

Base Case:

Revenue growth: 5%/year for 5 years
EBIT margin: 8%
WACC: 9%
Terminal growth: 2%
Result: $V_{0} =$ 75.00$

Sensitivity Table (One-Variable)

| Input | -20% | -10% | Base | +10% | +20% | |----|------|------|------|---| | Revenue growth (5%) | $62.30∣$ 68.50 | $75.00∣$ 82.10 | $89.80∣∣ E B I T ma r g in (8$ 69.00 | $72.00∣$ 75.00 | $78∣$ 81.00 | | WACC (9%) | $88.40∣$ 81.20 | $75.00∣$ 69.50 | $64.70∣∣ T er mina l g r o w t h (2$ 70.20 | $72.50∣$ 75.00 | $77.80∣$ 80.90 |

YEH RANGES KYU? Revenue growth $27.50 s w in g k a r t ahai ($ 89.80 - $62.30), W A C C$ 23.70 swing karta hai—yahi dominate karte hain. EBIT margin sirf $12 swing karta hai, toh yeh kam critical hai. Action: Revenue forecasts refine karne mein aur business/financial risk assess karne mein (WACC components) time lagao.

Scenario Analysis

Scenario	Rev Growth	EBIT Margin	WACC	Term Growth	Value	Probability
Bear	1%	6%	11%	1%	$48.20	20%
Base	5%	8%	9%	2%	$75.00	60%
Bull	8%	10%	8%	3%	$108.50	20%

Expected Value: $E[V] = 0.20 \times 48.20 + 0.60 \times 75.00 + 0.20 \times 108.50 = 9.64 + 45.00 + 21.70 = \$ 76.34$$

YEH KYA BATATA HAI: Wide range ( $48-$ 108) ke bawajood, probability-weighted fair value $76.34 hai, j o ba sec a se k e k aa f i c l ose hai . A g a r s t oc k$ 82 par trade ho raha hai, tum expected value se zyada pay kar rahe ho lekin bull case ke andar ho—yeh tabhi acceptable hai jab tumhe conviction ho ki bull scenario underpriced hai.

Common Mistakes

Practical Workflow

Apna base DCF banao best-estimate inputs ke saath.
4–6 key inputs identify karo (usually: revenue growth, margin, WACC, terminal growth, capex).
Har input ke liye sensitivity tables banao (±20%, ±10%, base, +10%, +20%).
Ek tornado chart plot karo: Inputs ko $Δ V$ range se rank karo.
3 scenarios construct karo:
- Bear: Coherent pessimistic story (recession, competition, margin pressure).
- Base: Tumhara original model.
- Bull: Coherent optimistic story (market expansion, pricing power).
Probabilities assign karo (market-implied vol, analyst consensus, ya judgment use karo; inhe 100% sum karna chahiye).
$E [V]$ calculate karo aur current price se compare karo.
Stress-test karo: "Kaun se input changes is stock ko current price par attractive banate?" (Goal-seek analysis.)

Recall Ek 12-Saal-Ke Bachche Ko Explain Karo

Imagine karo tum guess kar rahe ho ki tumhara lemonade stand is summer kitna paisa kamaega. Tumhare hisaab se tum 100 cups $2 e a c h =$ 200 mein bechoge. Lekin kya hoga agar bahut garmi ho (150 cups) ya baarish ho (50 cups)? Kya hoga agar tumhare costs badh jaayein?

Sensitivity analysis ek cheez ek time par test karna hai: "Agar main 150 cups bechun lekin baaki sab same rahe, toh main $300 k amaa t ah oo n ."" A g a r m er ecos t s d o u b l e h o j aa y e in l e k in s a l es 100 hi r ahi, t o hmain$ 100 kamaata hoon." Tum figure out karte ho ki kaun se guesses sabse zyada matter karte hain.

Scenario analysis poore weather patterns imagine karna hai: "Hot summer = zyada sales + main zyada charge kar sakta hoon + kam costs (no spoilage)" vs. "Rainy summer = kam sales + kam prices (discounts) + zyada costs (wasted lemons)." Tum alag worlds ke liye plan karte ho, na ki sirf alag numbers ke liye.

Connections

Discounted Cash Flow (DCF) Models – Woh valuation model jise tum stress-test kar rahe ho
Weighted Average Cost of Capital (WACC) – Aksar sabse high-sensitivity input
Terminal Value Calculation – DCF sensitivity mein dominate karta hai exponential discounting ki wajah se
Monte Carlo Simulation – Advanced extension: saare inputs ko simultaneously probability distributions ke saath vary karo
Option Pricing and Real Options – Asymmetry (upside optionality) capture karta hai jo scenarios approximate karte hain
Risk-Adjusted Return Metrics – Scenario probabilities Sharpe ratio, downside deviation mein feed hoti hain
Market-Implied Expectations – Reverse-engineer karo ki current stock price kaunse scenarios assume karti hai

#flashcards/stock-market

What is sensitivity analysis in valuation? :: Ek one-variable-at-a-time technique jo measure karti hai ki intrinsic value kitni change hoti hai jab tum ek single input (growth, WACC, margin) ko ek range mein vary karte ho jabki baki saare inputs constant rakhte ho. Yeh identify karta hai ki kaun se assumptions tumhare conclusion par sabse zyada leverage rakhte hain.

What is scenario analysis?

Complete alternative states of the world banana jisme multiple inputs ko simultaneously ek coherent narrative (Bull/Base/Bear cases) mein change kiya jaata hai. Har scenario ek alag valuation produce karta hai, jo tumhe ek false-precision point estimate ki jagah ek range aur expected value deta hai.

Why use tornado charts in sensitivity analysis?

Inputs ko valuation par unke absolute impact (

Δ V

range) se rank karne ke liye. Chart visually dikhata hai ki kaun se variables sabse zyada matter karte hain—apna research time un high-impact inputs ko refine karne mein lagao, low-impact ones polish karne mein nahi.

How do you calculate expected value from scenarios?

E [V] = \sum_{i} P_{i} \cdot V_{i}

, jahan

P_{i}

scenario

i

ki subjective probability hai aur

V_{i}

us scenario mein intrinsic value hai. Yeh ek probability-weighted anchor deta hai sirf range ki jagah.

Why can't you just vary WACC and call it complete sensitivity analysis?

Kyunki WACC tumhara highest-sensitivity input nahi bhi ho sakta. Ek tornado chart aksar reveal karta hai ki revenue growth ya terminal growth variance dominate karte hain. 80/20 rule kehta hai us 20% inputs par focus karo jo 80% value swing drive karte hain—ek low-impact input polish karna wasted effort hai.

What's the difference between base case and expected value?

Base case tumhara modal (sabse likely single outcome) estimate hai. Expected value saare scenarios ke across probability-weighted average hai, jo differ karta hai agar distribution skewed ho. Decisions ke liye expected value use karo, storytelling ke liye base case.

Why do distant cash flows (terminal value) dominate discount rate sensitivity?

Exponential compounding ki wajah se:

\frac{T V}{( 1 + r ) ^{10}}

vs.

\frac{T V}{( 1 + r ) ^{11}}

. 1% zyada

r

ek bade power tak raise hota hai, present value drastically shrink kar deta hai. Derivative

\frac{\partial V}{\partial r} \propto - \frac{n \cdot T V}{( 1 + r ) ^{n + 1}}

time

n

ke saath linear scaling dikhata hai.

What makes a good scenario (vs. random input combinations)?

Coherent narrative logic. Ek recession scenario mein low growth + margin compression + rising WACC saath bundle hone chahiye (correlated effects). Tumhare paas "high growth + high unemployment" nahi ho sakta bina mechanism explain kiye. 3–4 plausible stories par tikke raho, 27 combinations par nahi.