06.2 · Cost of capital¶

Why this matters: the discount rate is the exchange rate between the future and the present. Move it by one percentage point and a long-duration valuation moves by 10–15%. It is also the number analysts most often fudge — nudging WACC until the DCF agrees with the price they already believed. This lesson gives you a defensible way to build it for an Indian company, a sense of the plausible range, and the honesty to treat it as a hurdle you set rather than a truth you discover.

Learning objectives — after this lesson you can:

Build a cost of equity with CAPM for an Indian company: risk-free rate, equity risk premium, beta — and know the weaknesses of each input.
Choose a risk-free rate and ERP that are consistent (currency, inflation, horizon) and defend them with current data.
Estimate beta three ways (regression, adjusted, bottom-up) and explain why the regression is unreliable for Indian small caps.
Compute the after-tax cost of debt from a rating and the WACC with target weights, and reproduce the Kaveri reference WACC of 12.19%.
State practical WACC ranges for Indian large, mid and small caps, and explain the trader's view of WACC as a hurdle.

Prerequisites: 06.1 What value is, 04.5 Leverage, solvency & liquidity · Time: ~90 min

1. What the discount rate represents¶

The cost of capital is the return investors could earn on alternative investments of equivalent risk — the opportunity cost of putting money into this company. Three consequences:

It is set by the market's alternatives, not by the company's wishes or its historical cost of borrowing.
It should reflect only risk that cannot be diversified away (systematic risk). Company-specific risks — a state agency not paying Kaveri — belong in the cash-flow scenarios, not the discount rate (06.4).
Each cash-flow stream is matched with its own rate: FCFF (to all capital providers) with the WACC; FCFE or dividends (to shareholders) with the cost of equity.

\[\text{WACC} = \frac{E}{D+E}\,k_e + \frac{D}{D+E}\,k_d(1 − t)\]

where $k_e$ is the cost of equity, $k_d$ the pre-tax cost of debt, $t$ the tax rate (interest is tax-deductible), and the weights are target market-value weights.

2. Cost of equity: CAPM¶

The Capital Asset Pricing Model says the expected return on a stock is the risk-free rate plus a premium proportional to its systematic risk:

\[k_e = r_f + \beta \times \text{ERP}\]

$r_f$: risk-free rate — the yield on a default-free bond in the currency of the cash flows, matched to their horizon.
ERP: equity risk premium — the extra return investors demand for holding the equity market rather than the risk-free asset.
$\beta$: the stock's sensitivity to the market — how much its returns move for a 1% move in the index.

CAPM is theoretically elegant, empirically weak (betas explain little of the cross-section of returns; small, cheap and high-quality stocks earn more than it predicts), and universally used anyway because the alternatives (multi-factor models, implied costs of capital) add estimation problems of their own. Use it with judgement and show your inputs.

2.1 The risk-free rate¶

For Indian-rupee cash flows use the 10-year Government of India bond yield. As of 18-Sep-2026 it was about 7.07% (Trading Economics); it had been near 6.5% in early 2026 before rising on supply and global yields. The reference valuation, dated 31-Mar-2026, uses 6.5% — so an analyst valuing Kaveri today would start ~55 bps higher. That single input change lowers the base value by roughly ₹25–30/share (see the sensitivity in 06.4): discount rates are not stable, and neither are DCF values.

Two consistency rules:

Currency and inflation. ₹ cash flows → ₹ risk-free rate, which embeds ~4% expected Indian inflation. If you model in USD (some IT companies), use the US Treasury yield and USD-denominated cash flows. Never mix. The difference between the Indian and US 10-year yields (~3 pp) is mostly the expected inflation differential and should be mirrored in the growth rates.
Default risk. Purists strip a sovereign default spread from emerging-market government yields (India's rating is BBB-/Baa3, investment grade; the spread is small). Most Indian practitioners use the G-sec yield unadjusted and put country risk into the ERP. Do one or the other, not both.

2.2 The equity risk premium¶

Three ways to estimate it:

Method	How	India figure (Sep-2026)	Weakness
Historical	Average excess return of equities over bonds over decades	Indian data since ~1990 gives 5–8% depending on window and index; Nifty's ~12–13% nominal return vs ~7–8% G-sec	Short, noisy history; survivorship
Damodaran's country-risk build-up	Mature-market ERP (4.17% in the 2026 workbook) + a country risk premium from India's sovereign rating/CDS scaled by equity vs bond volatility	7.31% total ERP for India in the July 2026 update (Damodaran, ERPs by country, Jul-2026; country risk data)	Mechanical; USD-based (apply to a USD rf, or accept the approximation with ₹ rf)
Implied	Solve the market's DCF backwards: what ERP makes the index's expected cash flows equal its price?	Varies with index level; at Nifty ~20–22x forward earnings, implied ERPs of 5–6% over G-secs are typical	Depends on the growth assumption used for the index

The reference valuation uses 6.0% — between the implied figure and Damodaran's build-up, and typical of Indian sell-side practice (5.5–7%). Reasonable people differ by 1–2 pp here; what matters is that you state the number, source it, and keep it consistent across the companies you compare.

India notes

A persistent puzzle: Indian equities trade at high multiples (Nifty 20–25x, mid/small caps higher) that imply a low cost of equity, while textbook builds (7% rf + 6–7% ERP + beta ≈ 13–14%) say it should be high. Explanations offered: structural domestic flows (SIPs), scarcity of quality growth, expectations of faster earnings growth, and simple overvaluation. The valuation consequence is that a 13% cost of equity will make most Indian quality stocks look expensive — which may be correct, and is the reason reverse DCF (06.6) is more useful here than a point estimate.

2.3 Beta¶

Beta measures how a stock's returns co-move with the market's. Three estimates:

1. Regression beta. Regress the stock's weekly or monthly returns on the index's (Nifty 500 is a better market proxy than Nifty 50 for mid/small caps) over 2–5 years:

import numpy as np, pandas as pd, yfinance as yf     # disable VPN first
px = yf.download(["KAVERIPMP.NS", "^CRSLDX"], period="5y", interval="1wk")["Close"]   # fictional ticker
r = np.log(px).diff().dropna()
beta = r.cov().iloc[0, 1] / r.iloc[:, 1].var()

Problems in India: thin trading (stale prices bias beta toward zero), short histories, high estimation error (standard errors of 0.2–0.4 are common), and betas that change with leverage and business mix. A 0.6 regression beta for an illiquid small cap does not mean it is low-risk.

2. Adjusted beta. Bloomberg's shrinkage toward 1: $\beta_{adj} = 0.67\,\beta_{raw} + 0.33$. Recognises that betas mean-revert and estimation error is large.

3. Bottom-up beta. Average the unlevered betas of listed peers in the same business, then re-lever for the company's own capital structure (Hamada):

\[\beta_{unlevered} = \frac{\beta_{levered}}{1 + (1 − t)\,D/E}, \qquad \beta_{levered} = \beta_{unlevered}\,[1 + (1 − t)\,D/E]\]

Suppose four listed pump/motor peers have regression betas of 1.10, 0.95, 1.25, 1.05 with D/E of 0.10, 0.05, 0.30, 0.15:

t = 0.2517
peers = [(1.10, 0.10), (0.95, 0.05), (1.25, 0.30), (1.05, 0.15)]
unlev = [b / (1 + (1 - t) * de) for b, de in peers]        # 1.02, 0.92, 1.02, 0.94
avg_u = sum(unlev) / len(unlev)                             # 0.975
kaveri_beta = avg_u * (1 + (1 - t) * 0.27)                  # D/E 0.27 → 1.17
print([round(x, 2) for x in unlev], round(avg_u, 3), round(kaveri_beta, 2))

Bottom-up betas have lower error (averaging) and reflect the business rather than one stock's trading history. The reference valuation uses 1.05 — between a plausible regression and the bottom-up 1.17; a slightly higher beta would lower the value further.

2.4 Kaveri's cost of equity¶

\[k_e = 6.5\% + 1.05 \times 6.0\% = 12.80\%\]

from fi.valuation import capm, wacc
ke = capm(rf=0.065, beta=1.05, erp=0.06)                 # 0.1280

Sensitivity — the honest way to present any cost of equity:

ERP \ β	0.90	1.05	1.20
5.0%	11.0%	11.8%	12.5%
6.0%	11.9%	12.8%	13.7%
7.0%	12.8%	13.9%	14.9%

(All at rf 6.5%; add ~0.6 pp across the board at today's 7.07% G-sec.) The plausible range is 11–15% — a spread that moves Kaveri's value by roughly ±30%. Precision beyond one decimal is theatre.

3. Cost of debt¶

The pre-tax cost of debt is what the company would pay to borrow today for the long term — not the average rate on its existing loans (which may be old, subsidised or short-term):

Source	Method	Kaveri
Traded bonds	Yield to maturity on the company's NCDs	None traded
Credit rating	G-sec yield + typical spread for the rating (AAA ~40–80 bps; AA ~80–150; A ~150–300; BBB ~300–500 bps — indicative; verify against current corporate-bond spreads)	"A" rating → 6.5% + ~2.4% ≈ 8.9% (reference)
Synthetic rating	Map interest cover to a rating (Damodaran's tables), then to a spread	Interest cover 7.9x → roughly A/A+ → consistent
Actual borrowing rate	Finance cost ÷ average debt	8.7% — consistent with the rating-based figure

After tax: $k_d(1 − t) = 8.9\% \times (1 − 0.2517) = 6.66\%$. The tax shield exists only if the company pays tax; loss-makers get no shield until they turn profitable.

4. Weights and the WACC¶

Use target weights at market values. Book weights understate equity for most companies (market cap ≫ book equity) and overstate the debt share. Kaveri: market cap ≈ ₹2,370 Cr at ₹390 vs net debt ~₹160 Cr → current market weight of debt ≈ 6%; the reference valuation uses a 10% target (management may lever modestly). The difference is small here; for a highly levered company the choice matters and should be stated.

\[\text{WACC} = 0.90 \times 12.80\% + 0.10 \times 6.66\% = \mathbf{12.19\%}\]

w = wacc(ke=0.1280, kd_pre_tax=0.089, tax_rate=0.2517, debt_weight=0.10)   # 0.1219

4.1 Practical ranges for Indian companies (nominal ₹, Sep-2026)¶

Segment	Cost of equity	WACC	Notes
Large-cap, stable (FMCG, IT majors)	11–12.5%	10.5–12%	Beta ~0.7–0.9; little debt
Large-cap, cyclical/levered (metals, autos, infra)	13–15%	10–12%	Higher beta; cheap debt lowers WACC but not risk
Mid-cap industrial (Kaveri's peer group)	12.5–14.5%	11.5–13.5%	Beta ~1.0–1.2; liquidity
Small-cap / micro-cap	14–18%	13–17%	Add a liquidity/size premium of 1–3 pp — regression betas understate risk
Banks / NBFCs	12–15% (use $k_e$ directly; WACC is not meaningful)	—	07.1
Regulated utilities, REITs/InvITs	10–12%	8.5–10%	Contracted cash flows; high leverage at low cost

Sell-side reports on Indian companies commonly show WACCs of 10–12% and cost of equity of 11–13%. When you see a WACC below the G-sec yield plus 3%, or a small cap discounted at a large-cap rate, you are looking at an input chosen to fit an answer.

5. WACC as a hurdle, not a truth¶

The academic framing says WACC is the "correct" rate. The practitioner's framing — Buffett's, and the one a trader will recognise — is that the discount rate is the return you require for tying up capital in this risk, and that it should be a hurdle you set consistently rather than a number you estimate to two decimals. Two consequences:

Use the same hurdle for comparable risks, so that your valuations rank opportunities correctly. Ranking is what a portfolio needs; absolute precision is what nobody has.
Put company-specific risk in the scenarios and the margin of safety. A 20% discount rate to "reflect the receivables risk" is a hidden, unauditable haircut; a bear case with a ₹60 Cr write-off and a 35% probability is an explicit one you can argue about.

Trader's lens

WACC is the funding rate of the trade. A market-maker does not agonise over whether their cost of capital is 11.9% or 12.3%; they know the desk's hurdle and whether an edge clears it by a margin that survives estimation error. Treat the DCF the same way: the question is not "is the value ₹320?" but "does the expected return from ₹390, across scenarios, clear a 13% hurdle by enough to compensate for how wrong I could be?"

Common mistakes

Using the company's historical average borrowing rate as $k_d$.
Book-value weights.
A regression beta from an illiquid stock, taken at face value.
Mixing a ₹ risk-free rate with a USD ERP without acknowledging it (or mixing real growth with nominal rates).
Loading company-specific risk into WACC and the scenarios and the margin of safety.
Reporting WACC to two decimals without a sensitivity table.
Forgetting that the reference rf (6.5%) is dated: rebuild rf from today's G-sec when you value anything now.

Key terms¶

Term	Meaning
Cost of capital	Return investors could earn on alternatives of equivalent risk; the discount rate
WACC	Weighted average of the after-tax cost of debt and cost of equity at target market weights
Cost of equity ($k_e$)	Return equity investors require; by CAPM, $r_f + \beta \times \text{ERP}$
Risk-free rate	Yield on a default-free bond in the cash flows' currency; India: 10-yr G-sec
Equity risk premium (ERP)	Expected excess return of the equity market over the risk-free rate
Country risk premium	Extra premium for a country's sovereign/market risk, added to a mature-market ERP
Beta	Sensitivity of a stock's returns to the market's; systematic risk
Adjusted beta	Regression beta shrunk toward 1 (0.67β + 0.33)
Bottom-up (unlevered/relevered) beta	Peer-average business beta, re-levered for the company's D/E
Cost of debt ($k_d$)	Current long-term borrowing rate; after tax, $k_d(1 − t)$
Tax shield	The reduction in tax from deductible interest
Target weights	The long-run intended debt/equity mix at market values
Hurdle rate	The minimum return an investor requires; the practitioner's discount rate
Size / liquidity premium	Extra return demanded for small, illiquid stocks beyond CAPM

Check your understanding¶

Rebuild Kaveri's WACC with today's G-sec yield (7.07%), everything else unchanged.

Answer

$k_e$ = 7.07 + 1.05 × 6.0 = 13.37%; $k_d$ = 7.07 + 2.4 = 9.47% pre-tax → 7.09% after tax; WACC = 0.9 × 13.37 + 0.1 × 7.09 = 12.74%. About 55 bps higher than the reference 12.19%.

A small-cap chemicals company has a regression beta of 0.55 against Nifty 50 over three years, trades ₹40 lakh a day, and is 25% net-debt-financed. What cost of equity would you use, and why not 6.5 + 0.55 × 6 = 9.8%?

Answer

The 0.55 is an artefact of thin trading (stale prices) and index mismatch. Use a bottom-up beta from liquid chemicals peers (likely 1.0–1.3 relevered), a Nifty 500 benchmark, and add a 1–3 pp size/liquidity premium: $k_e$ of 14–16%. A 9.8% cost of equity for an illiquid small cap would produce absurd values.

Peers' unlevered beta averages 0.90. What is the relevered beta for a company with D/E of 1.0 at a 25% tax rate, and what does it do to $k_e$ at rf 7%, ERP 6%?

Answer

β = 0.90 × (1 + 0.75 × 1.0) = 1.575; $k_e$ = 7 + 1.575 × 6 = 16.45%. Leverage raises the cost of equity — which is why cheap debt does not lower WACC as much as the weights suggest.

Why should Kaveri's state-receivables risk not be handled by raising WACC?

Answer

It is company-specific (diversifiable) and discrete — either the states pay or they don't. A higher WACC penalises every cash flow in every year by a fudge factor no one can audit; a bear scenario with an explicit write-off and probability is transparent, and it lets you ask what would change the probability.

An analyst values an Indian IT company in USD with a 4.5% US Treasury rf and a 5% ERP, then applies a 10% nominal ₹ growth rate. What is wrong?

Answer

Currency inconsistency: USD discount rate (embedding ~2–2.5% US inflation) against ₹ growth (embedding ~4% Indian inflation) overstates value. Either convert cash flows to USD and grow them at USD rates, or use the ₹ G-sec rf with ₹ cash flows.

Go deeper¶

Aswath Damodaran, Investment Valuation (3rd ed.), chapters 7–8; and his annual ERP/country-risk updates (Jul-2026 country ERPs, 2026 country-risk paper).
McKinsey, Valuation, chapter on cost of capital — the target-weights, bottom-up-beta approach used here.
Michael Mauboussin & Dan Callahan, Cost of Capital: A Practical Guide to Measuring Opportunity Cost (Morgan Stanley, 2023).
Current data: India 10-year G-sec yield; RBI's bulletin for corporate-bond spreads by rating.

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