## Cost of Equity: Realised Yield Approach
Instead of projecting future dividends, the realised yield approach uses actual historical returns as a proxy for the required (expected) return.
### Single-Period Return
Ke = (D₁ + P₁ – P₀) / P₀ = Dividend Yield + Capital Gain Yield
### Multi-Period IRR Approach
For multiple years with irregular dividends, find r such that:
P₀ = Σ [Dₜ / (1+r)ᵗ] + Pₙ / (1+r)ⁿ
Use trial-and-error with linear interpolation — same mechanics as YTM for bonds.
### When to Use
When future dividends are unpredictable or irregular, historical realised return serves as a reasonable estimate of what investors require, given the stock's risk profile.
### Example 1
Q29 — Single-period realised yield
Purchase price = ₹500; D₁ = ₹40; Expected P₁ = ₹520
Ke = (40 + 520 – 500) / 500 = 60/500 = 12%
### Example 2
Q23 — Mr. Mehra: 5-year realised yield (IRR)
Purchase price = ₹1,000; Annual dividend = 10% on ₹1,000 FV = ₹100/year for 5 years; Sale price = ₹1,128
Find r: 1,000 = 100 × PVIFA(r,5) + 1,128 × PVIF(r,5)
Try r = 12%:
PV = 100 × 3.605 + 1,128 × 0.567 = 360.5 + 639.58 = ₹1,000.08 ≈ ₹1,000
Ke ≈ 12%
### Example 3
Q22 — Multi-year annual returns averaged
| Year | D | Opening P₀ | Closing P₁ | Return = (D+P₁–P₀)/P₀ |
|---|
| 1 | 1.00 | 9.00 | 9.75 | (1.00+0.75)/9.00 = 19.44% |
| 2 | 1.00 | 9.75 | 11.50 | (1.00+1.75)/9.75 = 28.21% |
| 3 | 1.20 | 11.50 | 11.00 | (1.20–0.50)/11.50 = 6.09% |
| 4 | 1.25 | 11.00 | 10.60 | (1.25–0.40)/11.00 = 7.73% |
Average Ke = (19.44 + 28.21 + 6.09 + 7.73)/4 = 15.37%
### Example 4
Q30 — Jet Ltd: total return and cash inflows
100 shares bought at ₹225; FV = ₹10; Dividend = 25% on FV = ₹2.50/share; Year-end price = ₹267.50
Dividend income = 100 × 2.50 = ₹250
Capital gain = 100 × (267.50 – 225) = ₹4,250
Total return = 4,500 / 22,500 = 20%
If shares sold: Cash inflows = (100 × 267.50) + 250 = ₹27,000