Understand WACC and discount rate calculation

2.6.3 · Stock-Market › Valuation Methods

Intuition Kyun Chahiye WACC

Socho tum ek business khareed rahe ho jo 10 saal tak cash generate karega. Aaj tumhe kitna dena chahiye? Tum future cash ko seedha add nahi kar sakte kyunki aaj ka paisa future ke paison se zyada valuable hai. Tumhe ek discount rate chahiye jo future cash ko present value mein convert kare.

Lekin yahan key insight hai: companies DO sources se paisa uthati hain—debt (loans, bonds) aur equity (shareholders). Har source alag return maangta hai. Debt sasta hota hai (interest tax-deductible hota hai + less risky), equity mehanga hota hai (shareholders zyada risk lene ke liye zyada return chahte hain). WACC woh blended cost hai jo is capital structure ko reflect karta hai.

YEH KYUN MATTER KARTA HAI: WACC woh minimum return hai jo ek company ko apne projects par earn karna chahiye taaki saare investors satisfy ho sakein. Ise DCF valuation, NPV calculations, aur investment decisions mein discount rate ke roop mein use karo.

Core Concept: WACC kya hai?

YEH specific components kyun hain?

Weights ( $E / V$ aur $D / V$ ): Actual capital mix ko reflect karte hain. Ek company jo 70% equity-financed hai, woh equity cost ko zyada heavily weight karti hai.
Cost of equity ( $r_{e}$ ): Shareholders SABSE zyada risk lete hain (bankruptcy mein sabse last mein pay hote hain), isliye woh SABSE ZYADA return demand karte hain. Koi tax benefit nahi.
Cost of debt $(1 - T_{c}) \cdot r_{d}$ : Interest tax-deductible hoti hai, isliye government effectively debt ko subsidize karti hai. Agar tum 8% interest pay karte ho lekin 25% taxes mein bachat hoti hai, to after-tax cost hai $8% \times (1 - 0.25) = 6%$ .

Figure — Understand WACC and discount rate calculation

WACC ko First Principles se Derive Karna

FUNDAMENTAL QUESTION: Agar main is company ko $1 deta hoon, to use kitna return generate karna chahiye taaki debt-holders AUR equity-holders dono satisfy ho sakein?

Step 1: Capital Structure Weights ko Samajhna

Ek company ki total value do sources se aati hai:

$V = E + D$

Agar tum company mein invest karte ho, tum implicitly uske debt aur equity ka ek portfolio khareed rahe ho. Har ek ka fraction tumhara expected return determine karta hai:

$Expected return = (weight of equity) \times (equity return) + (weight of debt) \times (debt return)$

$r_{portfolio} = \frac{E}{E + D} \cdot r_{e} + \frac{D}{E + D} \cdot r_{d}$

Step 2: Debt par Tax Shield

Hum debt cost ko $(1 - T_{c})$ se kyun adjust karte hain?

Jab ek company interest pay karti hai, woh taxable income reduce kar deti hai. Ise tax shield kehte hain.

Interest payment: $I = r_{d} \cdot D$
Tax saved: $T_{c} \cdot I = T_{c} \cdot r_{d} \cdot D$
Net cost: $I - tax saved = r_{d} \cdot D - T_{c} \cdot r_{d} \cdot D = \cdot (1 - T_{c})$

Debt ke har dollar ka effective cost hai:

$After-tax cost of debt = r_{d} \cdot (1 - T_{c})$

Equity ka koi tax benefit NAHI hota—dividends tax-deductible nahi hote.

Step 3: Final WACC Formula

Dono ko combine karke:

Har Component Calculate Karna

1. Cost of Equity ( $r_{e}$ )

PROBLEM: Equity ka koi explicit "interest rate" nahi hota jaise debt ka hota hai. Hume infer karna padta hai ki shareholders kya return expect karte hain.

Method: Capital Asset Pricing Model (CAPM)

YEH formula kyun hai?

Investors required return ko do parts mein baantte hain:

Time value of money ( $r_{f}$ ): Wait karne ka compensation (risk-free bonds bhi yahi pay karte hain).
Risk premium ( $β \cdot (r_{m} - r_{f})$ ): Market risk bear karne ke liye extra return.

Beta systematic risk measure karta hai:

$β = 1$ : Stock market ke saath chalta hai (average risk).
$β > 1$ : Stock market se zyada volatile hai (tech stocks, $β \approx 1.3$ ).
$β < 1$ : Stock kam volatile hai (utilities, $β \approx 0.7$ ).

Beta kaise find karein? Stock returns ko market returns ke against 2-5 saal ke liye regression karke. Sources: Bloomberg, Yahoo Finance, company investor relations.

2. Cost of Debt ( $r_{d}$ )

SAWAL: Company AAJ kis interest rate par pay karti hai?

Method 1: Existing Bonds par Yield to Maturity (YTM)

Agar company ke traded bonds hain, to YTM credit risk ke market ke current assessment ko reflect karta hai.

$Bond Price = \sum_{t = 1}^{n} \frac{C}{( 1 + r _{d} ) ^{t}} + \frac{F}{( 1 + r _{d} ) ^{n}}$

$r_{d}$ (the YTM) ke liye solve karo. Financial calculators ya Excel ka RATE() function yeh handle karta hai.

Method 2: Recent Loans par Interest Rate

Latest debt issuance ya credit facility check karo. Agar multiple debt instruments hain to average karo.

Worked example Cost of Debt Calculation

Ek company ne 5-year bond issue kiya 7% coupon ke saath, jo currently $950 p a r t r a d e h or ahahai (p a r v a l u e$ 1,000).

Step 1: Bond $70/ y e a r p a y k a r t ahai, 5 s aa l m e in$ 1,000 par mature hoga. Step 2: YTM formula use karo (ya Excel):

=RATE(5, 70, -950, 1000) = 8.24%

8.24% > 7% kyun? Bond par se neeche trade ho raha hai kyunki market rates badh gayi hain YA credit risk badh gayi hai. Effective cost (YTM) ab 8.24% hai.

Cost of debt: $r_{d} = 8.24%$

3. Market Values ( $E$ aur $D$ )

ZAROORI: Balance sheet ki book values NAHI, market values use karo.

Equity: $E = Shares outstanding \times Current stock price$
Debt: Traded bonds ke liye market price use karo. Bank loans ke liye, book value ≈ market value (agar recent hai).

Market values kyun? Investors current market rates ki parwah karte hain, historical accounting costs ki nahi.

Complete WACC Example

Worked example Full WACC Calculation

Company X ka Data:

Market cap (equity): $500M
Debt outstanding: $300M
Corporate tax rate: 25%
Risk-free rate: 4%
Market return: 11%
Company beta: 1.2
Cost of debt (YTM): 6%

Step 1: Cost of equity calculate karo $r_{e} = r_{f} + β \cdot (r_{m} - r_{f})$ $r_{e} = 4% + 1.2 \times (11% - 4%)$ $r_{e} = 4% + 1.2 \times 7% = 4% + 8.4% = 12.4%$ YEH step kyun? Shareholders 12.4% demand karte hain kyunki stock market se 20% zyada volatile hai ( $β = 1.2$ ), isliye unhe 7% equity risk premium se aage extra compensation chahiye.

Step 2: After-tax cost of debt

$r_{d} \cdot (1 - T_{c}) = 6% \times (1 - 0.25) = 6% \times 0.75 = 4.5%$

YEH step kyun? Tax shield 6% interest cost ko 4.5% effective cost tak reduce kar deta hai.

Step 3: Capital structure weights

Total value: $V = E + D = 500 + 300 = 800 M$

$w_{e} = \frac{E}{V} = \frac{500}{800} = 0.625 (62.5%)$ $w_{d} = \frac{D}{V} = \frac{300}{800} = 0.375 (37.5%)$

YEH step kyun? Company 62.5% equity-financed hai, isliye blend mein equity cost ko zyada weight milta hai.

Step 4: WACC calculate karo $WACC = w_{e} \cdot r_{e} + w_{d} \cdot r_{d} \cdot (1 - T_{c})$ $WACC = 0.625 \times 12.4% + 0.375 \times 4.5%$ $WACC = 7.75% + 1.69% = 9.44%$

INTERPRETATION: Company X ko apne investments par kam se kam 9.44% return earn karna chahiye taaki debt-holders (jo 6% interest paate hain) aur equity-holders (jo 12.4% expect karte hain) dono satisfy ho sakein. DCF valuation mein 9.44% ko discount rate ke roop mein use karo.

WACC ko Discount Rate ke Roop mein Use Karna

Discounted Cash Flow (DCF) Valuation

$Enterprise Value = \sum_{t = 1}^{n} \frac{FCF _{t}}{( 1 + WACC ) ^{t}}$

jahan $FCF_{t}$ year $t$ mein Free Cash Flow hai (cash jo SAARE investors ke liye available hai).

WACC yahan kyun? FCF debt aur equity holders dono ka hota hai, isliye hum BLENDED cost par discount karte hain.

Net Present Value (NPV) of Projects

$NPV = \sum_{t = 0}^{n} \frac{Cash Flow _{t}}{( 1 + WACC ) ^{t}}$

NPV > 0: Project WACC se zyada earn karta hai → Accept karo (value create hoti hai).
NPV < 0: Project WACC se kam earn karta hai → Reject karo (value destroy hoti hai).

Common Mistakes aur Confusions

Practical Adjustments

1. Changing Capital Structure ke liye Adjust Karna

Agar tum leveraged buyout (LBO) ya recapitalization value kar rahe ho, to debt/equity mix badlega. Current weights nahi, target capital structure use karo.

2. Alag Divisions ke liye Alag Discount Rates

Ek conglomerate ka WACC SAARE businesses ko average karta hai. Project-level NPV ke liye, ek division-specific beta use karo (us unit ke risk ko reflect karte hue) taaki custom WACC compute ho sake.

3. Country Risk Premium (Emerging Markets ke liye)

Non-US companies ke liye, $r_{f}$ ya $(r_{m} - r_{f})$ mein ek country risk premium add karo:

$r_{e} = r_{f} + β \cdot [(r_{m} - r_{f}) + CRP]$

Kyun? Emerging markets mein political risk, currency risk, aur kam liquidity hoti hai. Investors extra return demand karte hain.

Connections

Cost of Equity and CAPM – Beta calculation aur alternatives (DDM, APT) mein deep dive
Capital Structure and MM Theorem – Debt/equity mix firm value ko kaise affect karta hai (spoiler: trade-off theory ke under WACC minimization)
Discounted Cash Flow (DCF) Valuation – WACC DCF mein denominator hai; free cash flow numerators samjho
Net Present Value (NPV) and IR – Capital budgeting ke liye WACC hurdle rate ke roop mein
Tax Shield and Interest Deductibility – Debt sasta kyun hai aur tax policy optimal leverage ko kaise affect karti hai
Beta Estimation and Unlevering/Relevering – Divisional WACCs compute karte waqt changing leverage ke liye beta adjust karo
Enterprise Value vs Equity Value – WACC EV tak discount karta hai; equity value paane ke liye net debt subtract karo

Recall WACC ko 12-Saal ke Bachche ko Explain Karo

Socho tum aur tumhara dost ek lemonade stand shuru karna chahte ho. Tum apne $50 d aa l o (e q u i t y), a u r t u mha r im o m t u mh e$ 50 udhar deti hai (debt) lekin saal ke ant mein $5 interest wapas chahiye.

Cost of debt: Tumhari mom 10% return chahti hai ( $50 p a r$ 5). Lekin ek trick hai—tumhare dad ("government") kehte hain "Agar tum interest pay karte ho, to main tumhe 25% tax break de dunga." To tum SACH MEIN sirf $5 \times 0.75 = \$ 3.75$ pay karte ho. Tumhara debt 7.5% cost karta hai.

Cost of equity: TUM apne $50 p a r k am se k am$ 20% $banana c hah t e h o k y u nk i t u m r i s k l er ah e h o (a g a r s t an df ai l h o, s abk u c h t u mha r aj aa y e g a, l e k in t u mha r im o mk o p hi r bhi$ 50 milenge). To equity 20% cost karti hai.

WACC: Tumhare paas kul $100 hai ($ 50 tumhara, $50 mom ka). Aadha equity hai (20% cost), aadha debt hai (7.5% cost). Tumhari "blended cost" hai: $WACC = 0.5 \times 20% + 0.5 \times 7.5% = 10% + 3.75% = 13.75%$

MATLAB: Lemonade stand ko kam se kam 13.75% profit banana chahiye taaki tum DONO—tum aur tumhari mom—khush raho. Isse kam karo, to koi ek apna chahgya return nahi paayega!

Flashcards

#flashcards/stock-market

WACC kya hai aur ise kyun use kiya jaata hai? :: WACC (Weighted Average Cost of Capital) ek company ke debt aur equity financing ka blended cost hai. Yeh woh minimum return represent karta hai jo company ko apne investments par earn karna chahiye taaki saare investors satisfy ho sakein. DCF valuation aur NPV calculations mein discount rate ke roop mein use hota hai.

Full WACC formula kya hai?

WACC = \frac{E}{V} \cdot r_{e} + \frac{D}{V} \cdot r_{d} \cdot (1 - T_{c})

jahan E = equity value, D = debt value, V = E + D,

r_{e}

= cost of equity,

r_{d}

= cost of debt,

T_{c}

= tax rate.

Hum cost of debt ko (1 - Tc) se kyun multiply karte hain?

Interest expense tax-deductible hoti hai, isse tax shield milti hai. Agar company 8% interest pay karti hai aur 25% tax rate hai, to government unhe 2% (8% ka 25%) bachati hai, isliye after-tax cost sirf 6% hai. Equity dividends ka koi tax benefit nahi hota.

CAPM use karke cost of equity kaise calculate karte hain?

r_{e} = r_{f} + β \cdot (r_{m} - r_{f})

jahan

r_{f}

= risk-free rate,

β

= stock ka beta (systematic risk),

r_{m}

= expected market return,

(r_{m} - r_{f})

= equity risk premium.

WACC calculation mein beta kya measure karta hai?

Beta ek stock ki market movements ke saath sensitivity (systematic risk) measure karta hai.

β = 1

average risk hai,

β > 1

market se zyada volatile hai,

β < 1

kam volatile hai. Zyada beta → zyada cost of equity.

WACC mein E aur D ke liye book values ya market values use karni chahiye?

Hamesha MARKET values use karo. Book values historical accounting costs reflect karti hain, current investor expectations nahi. Equity ke liye market cap (shares × price) aur debt ke liye bonds ki market price use karo.

Discount rate ke roop mein WACC aur cost of equity use karne mein kya fark hai?

Free Cash Flow to Firm (FCFF) discount karne ke liye WACC use karo kyunki yeh saare investors ka hota hai. Cost of equity (

r_{e}

) sirf Free Cash Flow to Equity (FCFE) discount karne ke liye use karo, jo debt payments ke baad ki cash hai.

WACC ke liye cost of debt kaise dhundhen?

Company ke traded bonds par Yield to Maturity (YTM) use karo, ya recent debt issuance par interest rate. YTM company ke credit risk ka market ka current assessment reflect karta hai, coupon rate nahi.

Agar ek company ka WACC 10% hai, to project selection ke liye iska kya matlab hai?

Projects ko value create karne ke liye 10% se zyada return generate karna chahiye. Agar NPV (WACC par discounted) > 0 hai, project accept karo. Agar NPV < 0 hai, reject karo kyunki cost of capital se kam earn ho raha hai.

CAPM formula mein equity risk premium kya hai?

Equity risk premium

(r_{m} - r_{f})

hai, woh extra return jo investors stock market risk bear karne ke liye demand karte hain risk-free bonds hold karne ki jagah. Historically developed markets mein ~6-8%.

Capital structure mein zyada debt hone se WACC hamesha kyun nahi ghatta?

Haalaanki debt equity se sasta hota hai (tax shield ki wajah se), zyada debt financial risk badhata hai, jisse cost of debt (credit spreads wide ho jaate hain) aur cost of equity dono badhte hain (beta badhta hai). Ek optimal debt level hota hai jo WACC minimize karta hai.

Ek company ke paas

400 M e q u i t y,

200M debt, tax rate 30%,

r_{e}

= 14%,

r_{d}

= 7% hai. WACC kya hai?

w_{e} = 400/600 = 0.667

w_{d} = 200/600 = 0.333

. WACC =

0.667 \times 14% + 0.333 \times 7% \times (1 - 0.3) = 9.34% + 1.63% = 10.97%