## Cost of Equity: Capital Asset Pricing Model (CAPM)

CAPM links required return to systematic (market) risk measured by beta.

Ke = Rf + β × (Rm – Rf)

Rf = Risk-free rate (government bond yield)
Rm = Expected market return
(Rm – Rf) = Market Risk Premium (MRP)
β = Beta — sensitivity of the stock to market movements

### Beta Interpretation

Beta	Meaning
β > 1	More volatile than market (aggressive)
β = 1	Moves with market
β < 1	Less volatile (defensive)
β = 0	Risk-free

### Portfolio Beta

β_portfolio = Σ (Wᵢ × βᵢ)

Weights based on market value of each investment.

### Divisional Beta (Conglomerate)

β_company = Σ (MV of divisionᵢ / Total equity MV × βᵢ)

To value a specific division, use that division's own beta — not the company-wide beta.

### CAPM + Gordon Model: Equilibrium Price

When beta changes → Ke changes → equilibrium price changes:

P₀ = D₁ / (Ke – g)

Higher beta → higher Ke → lower share price.

Worked example

### Example 1

Q24 — Basic CAPM

Rf = 10%; β = 1.75; Rm = 15%

Ke = 10 + 1.75 × (15 – 10) = 10 + 8.75 = 18.75%

### Example 2

Q26 — Portfolio return and beta

Rf = 9%; Rm = 15%; MRP = 6%

Investment A: 80% weight, β = 0.8 → Ke_A = 9 + 0.8×6 = 13.8%

Investment B: 20% weight, β = 1.4 → Ke_B = 9 + 1.4×6 = 17.4%

Overall return = 0.80×13.8 + 0.20×17.4 = 11.04 + 3.48 = 14.52%

Portfolio β = 0.80×0.8 + 0.20×1.4 = 0.64 + 0.28 = 0.92

Verification: 9 + 0.92×6 = 14.52% ✓

### Example 3

Q27 — Expected value of required return using probability-weighted beta

Expected β = 0.2×1.00 + 0.3×1.10 + 0.2×1.20 + 0.2×1.30 + 0.1×1.40

= 0.20 + 0.33 + 0.24 + 0.26 + 0.14 = 1.17

(a) Using mode β = 1.10: Ke = 10 + 1.10×5 = 15.5%

(b) Range: β=1.00 → Ke=15%; β=1.40 → Ke=17%. Range = 15% to 17%

### Example 4

Q28 — XYZ Computers: divisional beta and CAPM (PYQ)

Total equity MV = 100+100+50+150 = ₹400 Billion

Company β = (100×1.10 + 100×1.50 + 50×2.00 + 150×1.00)/400

= (110+150+100+150)/400 = 510/400 = 1.275

Ke (company) = 7.5 + 1.275×8.5 = 7.5 + 10.84 = 18.34%

Printer division β = 1.00:

Ke (printers) = 7.5 + 1.00×8.5 = 16.0%

Use the printer division's beta (1.00) to value that division — using company beta (1.275) would overstate risk and undervalue the division.

### Example 5

Q56 — Equilibrium price change when beta rises

D₁ = ₹3; g = 8%; Rf = 10%; Rm = 14%; MRP = 4%

Present (β = 1.50): Ke = 10 + 1.50×4 = 16%; P₀ = 3/(0.16–0.08) = ₹37.50

After decision (β = 1.75): Ke = 10 + 1.75×4 = 17%; P₀ = 3/(0.17–0.08) = ₹33.33

Financial risk-increasing decision destroys ₹4.17 per share of value.

⚠️ Common exam mistakes

Using Rm as the risk premium instead of (Rm – Rf) — the premium is the excess over the risk-free rate.
For divisional WACC, applying the company-wide beta to every division — each division carries its own systematic risk.
Confusing Rf and Rm in the formula placement.
Computing portfolio return by weighted-averaging Ke values directly (valid result, but understanding portfolio beta is required for exam theory marks).

Reference:

Now that you've read this — what's next?

Move from understanding → mastery in 3 clicks. Each option below picks up from this lesson's topic.

🔥 Drill 5 Qs on this → ✍️ Adaptive practice →

Cost of Equity — Capital Asset Pricing Model (CAPM)

Worked example

⚠️ Common exam mistakes