Learn about terminal value and growth assumptions

2.6.4 · Stock-Market › Valuation Methods

What is Terminal Value?

Do approaches hain:

Perpetuity Growth Method (Gordon Growth Model)
Exit Multiple Method (comparable multiples ka use karke)

Hum perpetuity growth method pe focus karenge, kyunki yeh long-term economics ke baare mein fundamental assumptions pe grounded hai.

The Perpetuity Growth Formula: Derived from First Principles

Jahaan:

$T V_{n}$ = Year $n$ ke end mein terminal value
$F C F_{n + 1}$ = Forecast period ke baad pehle year mein free cash flow
$W A C C$ = Weighted average cost of capital (discount rate)
$g$ = Perpetual growth rate

Chaliye ise derive karte hain. Maano year $n$ par, company $F C F_{n + 1}$ generate karti hai year $n + 1$ mein, phir rate $g$ se forever grow karti hai:

$Year n + 1 : F C F_{n + 1}$ $Year n + 2 : F C F_{n + 1} (1 + g)$ $Year n + 3 : F C F_{n + 1} (1 + g)^{2}$ $⋮$

Is infinite series ki present value (time $n$ par) hai:

$T V_{n} = \frac{F C F _{n + 1}}{( 1 + W A C C )} + \frac{F C F _{n + 1} ( 1 + g )}{( 1 + W A C C ) ^{2}} + \frac{F C F _{n + 1} ( 1 + g ) ^{2}}{( 1 + W A C C ) ^{3}} + \dots$

$F C F_{n + 1}$ ko factor out karo:

$T V_{n} = F C F_{n + 1} [\frac{1}{1 + W A C C} + \frac{1 + g}{( 1 + W A C C ) ^{2}} + \frac{( 1 + g ) ^{2}}{( 1 + W A C C ) ^{3}} + \dots]$

Maano $r = \frac{1 + g}{1 + W A C C}$ . Yeh ek geometric series ban jaati hai:

$T V_{n} = F C F_{n + 1} \cdot \frac{1}{1 + W A C C} [1 + r + r^{2} + \dots]$

Yeh step kyun? Geometric series jiska first term $a$ aur ratio $r$ hai (jahaan $∣ r ∣ < 1$ ), uska sum hota hai $\frac{a}{1 - r}$ .

Yahaan, $a = 1$ aur $r = \frac{1 + g}{1 + W A C C}$ :

$T V_{n} = F C F_{n + 1} \cdot \frac{1}{1 + W A C C} \cdot \frac{1}{1 - \frac{1 + g}{1 + W A C C}}$

Denominator ko simplify karo:

$1 - \frac{1 + g}{1 + W A C C} = \frac{( 1 + W A C C ) - ( 1 + g )}{1 + W A C C} = \frac{W A C C - g}{1 + W A C C}$

Yeh step kyun? Hum fractions ko combine kar rahe hain ek cleaner form paane ke liye.

Isliye:

$T V_{n} = F C F_{n + 1} \cdot \frac{1}{1 + W A C C} \cdot \frac{1 + W A C C}{W A C C - g} = \frac{F C F _{n + 1}}{W A C C - g}$

Key insight: Yeh formula tabhi kaam karta hai jab $g < W A C C$ . Geometric series tabhi converge karti hai jab $r = \frac{1 + g}{1 + W A C C} < 1$ , yaani jab $g < W A C C$ . Agar $g = W A C C$ , toh $r = 1$ aur infinite sum $+ \infty$ tak diverge kar jaata hai. Agar $g > W A C C$ , toh $r > 1$ aur sum converge hi nahi karta (formula jo negative number deta hai woh mathematically meaningless hai). Dono cases mein result economically impossible hai.

Figure — Learn about terminal value and growth assumptions

Growth Rate Assumptions: The Critical Choice

What is a Reasonable Growth Rate?

Koi bhi company economy se faster forever grow nahi kar sakti. Yeh raha reason:

Agar ek company 5% grow karti hai aur GDP 2% grow karta hai, toh company eventually poori economy se badi ho jaayegi (impossible)
Typical ranges:
- Conservative: 2-2.5% (roughly long-term GDP growth)
- Mature companies: 2-3%
- Industry leaders in growing sectors: 2.5-3.5%
- Kabhi mat use karo: >4% (jab tak tum justify na kar sako ki yeh company duniya dominate karegi)

Step 1: $F C F_{6}$ calculate karo $F C F_{6} = F C F_{5} \times (1 + g_{5 \to 6}) = 100 \times 1.04 = $104 M$

Yeh step kyun? Terminal value pehle cash flow ko use karta hai terminal period mein.

Step 2: Year 5 par terminal value calculate karo $T V_{5} = \frac{104}{0.08 - 0.025} = \frac{104}{0.055} = $1, 891 M$

Yeh step kyun? Hum Year 6 se aage ke saare cash flows ko value kar rahe hain, Year 5 par discount karke.

Step 3: TV ko present value mein discount karo (maano hum Year 0 par value kar rahe hain) $P V (T V) = \frac{1 , 891}{( 1.08 ) ^{5}} = \frac{1 , 891}{1.469} = $1, 287 M$

Yeh step kyun? Terminal value Year 5 par stated hai; hume aaj ki iske value chahiye.

Growth Rate	TV at Year 5	PV of TV (Year 0)	% Change
2.0%	$1,733M	$1,180M	baseline
2.5%	$1,891M	$1,287M	+9.1%
3.0%	$2,080M	$1,416M	+20.0%
3.5%	$2,311M	$1,573M	+33.3%

Yeh kyun matter karta hai: 1.5% growth difference se 33% valuation difference aa jaata hai. Isi liye analysts terminal growth rates ke baare mein endlessly argue karte hain.

3.0% case ke liye calculation: $T V_{5} = \frac{104}{0.08 - 0.03} = \frac{104}{0.05} = $2, 080 M$ $P V (T V) = \frac{2 , 080}{1.469} = $1, 416 M$

Yeh sahi kyun lagta hai: Recent performance tangible aur observable hai. Ise extrapolate karna tempting lagta hai.

The fix: Terminal growth ko steady-state maturity reflect karni chahiye, na ki current high-growth phase. 15% perpetual growth rate imply karta hai ki company eventually saari global economies se badi ho jaayegi. Iske bajaay:

Explicit forecast period (Years 1-5) use karo high growth model karne ke liye
Maano ki company Year 6 tak mature ho jaati hai
Terminal growth ko GDP growth (2-3%) ke close aana chahiye

Better approach: "Company 5 saalon tak 15% grow karti hai (explicit period), phir 2.5% terminal growth tak mature ho jaati hai."

Yeh sahi kyun lagta hai: "Company high-quality hai aur almost utni hi fast grow karegi jitna hamara required return hai."

The fix: Isse ek near-infinite valuation ban jaati hai kyunki denominator zero ke paas aa jaata hai. Economically, iska matlab hai ki tum believe karte ho ki cash flows almost usi rate par compound honge jitna tum risk lene ke liye require karte ho — yaani nearly risk-free doubling forever. Reality check: WACC aur $g$ ke beech minimum 2-3% spread maintain karo. Agar tum sach mein believe karte ho ki $g$ itna zyaada hai, toh justify karna hoga (aur likely explicitly forecast period extend karna hoga).

WACC vs. Growth Rate: The Relationship

Ise real interest rates ki tarah socho: agar inflation 3% hai aur tumhara bond 5% pay karta hai, toh tumhara real return ~2% hai. Similarly, agar cash flows 2% par grow hoti hain aur tum 8% require karte ho, toh tumhara real value capture 6% hai.

Connecting to the Full DCF Model

Jahaan:

Pehla term = Explicit forecast cash flows ki PV
Doosra term = Terminal value ki PV

Typical proportions:

Explicit period value: Total EV ka 20-40%
Terminal value: Total EV ka 60-80%

Yeh kyun matter karta hai: Tumhare terminal assumptions zyaadatar value drive karte hain, inhe highest-leverage inputs banaate hue.

Step 1: Explicit cash flows ki PV $P V_{e x pl i c i t} = \frac{50}{1.09} + \frac{60}{1.0 9 ^{2}} + \frac{70}{1.0 9 ^{3}} + \frac{82}{1.0 9 ^{4}} + \frac{95}{1.0 9 ^{5}}$ $= 45.87 + 50.50 + 54.05 + 58.08 + 61.73 = $270.23 M$

Step 2: Year 5 par terminal value $T V_{5} = \frac{100}{0.09 - 0.025} = \frac{100}{0.065} = $1, 538.46 M$

Step 3: Terminal value ki PV $P V (T V) = \frac{1 , 538.46}{1.0 9 ^{5}} = \frac{1 , 538.46}{1.5386} = $1, 000 M$

Step 4: Enterprise value $E V = 270.23 + 1, 000 = $1, 270.23 M$

Proportion check:

Explicit period: $270.23/1, 270.23 = 21.3%$
Terminal value: $1, 000/1, 270.23 = 78.7%$

Yeh demonstrate karta hai ki terminal assumptions kyun critical hain — yeh value ka almost 80% represent karti hain.

Exit Multiple Method (Alternative Approach)

Perpetual growth assume karne ki jagah, tum assume karte ho ki company Year $n$ par apni earnings ke ek multiple par sell hogi.

Example: Agar Year 5 EBITDA = $150M aur comparable companies 8x EBITDA par trade karti hain: $$TV_5 = 150 \times 8 = \$ 1,200M$$

Pros: Simple, market reality mein grounded Cons: Circular logic (tum market multiples use kar rahe ho yeh determine karne ke liye ki market price sahi hai ya nahi), comparable valid rehne ki assumption

Hum perpetuity growth pe focus karte hain kyunki yeh theoretically cleaner hai aur long-term economics ke baare mein explicit assumptions force karta hai.

Recall Ek 12-Saal Ke Bachche Ko Explain Karo

Imagine karo tum figure out karne ki koshish kar rahe ho ki tumhara lemonade stand kitna worth hai. Tum is summer mein jo paisa kamaoge (June, July, August) use count kar sakte ho — woh easy hai. Lekin uske baad ke saare summers ka kya? Tum forever count nahi kar sakte!

Toh yeh trick hai: tum kehte ho, "Theek hai, agli summer se, mera lemonade stand har saal thoda aur paisa kamaega — shayad 2% zyaada kyunki main isme better hota ja raha hoon. Aur yeh forever aise karta rahega." Terminal value ek math formula hai jo "forever ka paisa" leta hai aur figure out karta hai ki woh aaj kitna worth hai.

Tricky part? Agar tum assume karo ki yeh bahut fast forever grow karega (jaise har saal 10%), toh formula kehta hai tumhara stand ek bazillion dollars ka hai. Lekin woh impossible hai — eventually tumhare paas duniya ka saara lemonade hoga! Isliye hume realistic rehna hoga aur ek chhoti si number use karni hogi jaise 2-3%, jo roughly poori economy ke grow hone ki speed hai.

Yeh itna zyaada matter isliye karta hai kyunki tumhare lemonade stand ki zyaadatar value un saare future years se aati hai, sirf is summer se nahi. Toh agar tum woh growth number thodi bhi galat estimate karo, toh tumhe lag sakta hai stand $100 k ahaij ab w o ha c t u a l l y$ 150 ka hai — woh ek badi mistake hai!

Connections

Discounted Cash Flow (DCF) Model - Terminal value last component hai
Weighted Average Cost of Capital (WACC) - Denominator mein discount rate
Free Cash Flow (FCF) Calculation - Jise hum perpetuity mein project kar rahe hain
Gordon Growth Model - Perpetuity growth method ka alternative naam
Sensitivity Analysis in Valuation - Testing ki growth assumptions value ko kaise affect karti hain
GDP Growth and Economic Indicators - Terminal growth rates ki ceiling
Exit Multiple Valuation - Alternative terminal value method

#flashcards/stock-market

DCF model mein terminal value kya hota hai?

Explicit forecast period ke baad ke saare cash flows ki present value, jo company ki worth ko ek going concern ke roop mein represent karta hai jo indefinitely continue karta hai.

Terminal value ke liye perpetuity growth formula kya hai?

T V_{n} = \frac{F C F _{n + 1}}{W A C C - g}

, jahaan

F C F_{n + 1}

forecast period ke baad pehla cash flow hai, WACC discount rate hai, aur

g

perpetual growth rate hai.

Terminal growth rate (g) WACC se kam kyun honi chahiye?

Kyunki underlying geometric series tabhi converge hoti hai jab

\frac{1 + g}{1 + W A C C} < 1

, yaani

g < W A C C

. Agar

g = W A C C

toh infinite sum

+ \infty

tak diverge karta hai; agar

g > W A C C

toh yeh converge hi nahi karta aur formula ka negative output meaningless hai. Economically, tumhare required return par ya usse zyaada sustained growth risk-free unlimited growth imply karta hai, jo impossible hai.

Terminal growth rates ke liye typical range kya hai?

2-3%, roughly long-term GDP growth se match karte hue. Koi bhi company economy se zyaada fast sustainably grow nahi kar sakti forever, warna woh eventually poori economy se badi ho jaayegi.

Enterprise value ka kitna proportion typically terminal value se aata hai?

Total enterprise value ka 60-80%, jo terminal assumptions ko DCF model mein sabse impactful inputs banaata hai.

Agar Year 5 FCF

80 M haij o Y e a r 6 m e in

84M ho jaata hai, WACC 10% hai, aur terminal growth 3% hai, toh Year 5 par TV kya hoga?

T V_{5} = \frac{84}{0.10 - 0.03} = \frac{84}{0.07} = 1200

1,200M$

Tum company ki current high growth rate (jaise 20%) ko terminal growth rate ke roop mein kyun use nahi kar sakte?

Kyunki terminal growth ko steady-state maturity reflect karni chahiye, na ki current high-growth phase. 20% perpetual growth rate eventually company ko saari economies se bada bana dega — economically impossible.

Spread (WACC - g) kya represent karta hai?

Real return ya value creation rate — woh actual return jo tum cash flows ki growth rate ke upar earn kar rahe ho, jo inflation ke upar real interest rates ke analogous hai.