## Cost of Equity: Realized Yield Approach

The realized yield approach computes the actual return earned on a share over a specific holding period, based on dividends received and capital gain/loss on sale. It is particularly useful when the dividend stream is irregular.

### For a single period (one year)

```

Ke = (D1 + P1 − P0) / P0

= D1/P0 + (P1−P0)/P0

= Dividend yield + Capital gain yield

```

### For multiple periods (IRR method)

Find the rate `r` that equates the present value of all future dividends plus the terminal sale price to the initial purchase price:

```

P0 = Σ[Dt/(1+r)^t] + Pn/(1+r)^n

```

This is solved by trial-and-error (like an IRR calculation), then interpolated.

### Practical computation (multi-year)

For each year t:

```

Return in year t = (Dt + Pt − Pt−1) / Pt−1

```

The average or IRR of these annual returns is the realized yield.

### When to use this approach

Irregular dividend patterns (cannot use Gordon Model)
When you know the actual holding period and sale price
Retrospective performance measurement

Worked example

### Example 1

Q23 – Mr. Mehra, Alpha Limited (5-year holding)

Purchase price = ₹1,000; Annual dividend = 10% × face value

Assuming face value not given — dividend = 10% × 1,000 = ₹100 per year (assumed)

Sale price at end of year 5 = ₹1,128

Find r such that:

1,000 = 100×PVIFA(r,5) + 1,128×PVIF(r,5)

Try r = 12%:

PV = 100×3.605 + 1,128×0.567 = 360.5 + 639.6 = 1,000.1 ≈ 1,000

Ke ≈ 12%

Interpretation: The investor earned exactly 12% per year on this investment.

### Example 2

Q22 – Realized yield from year-by-year data

Year	DPS	Price (start)	Annual return
1	1.00	9.00	(1.00+9.75−9.00)/9.00 = 19.44%
2	1.00	9.75	(1.00+11.50−9.75)/9.75 = 28.72%
3	1.20	11.50	(1.20+11.00−11.50)/11.50 = 6.09%
4	1.25	11.00	(1.25+10.60−11.00)/11.00 = 7.73%

Note: Year 5 price is 10.60 — compute similarly for year 5.

Use IRR of these cash flows for the geometric mean return as the realized Ke.

### Example 3

Q29 – Single period realized yield

Purchase price = ₹500, D1 = ₹40, P1 = ₹520

Ke = (40 + 520 − 500) / 500 = 60/500 = 12%

⚠️ Common exam mistakes

Using the beginning-of-year price in the denominator but including end-of-year values inconsistently.
Forgetting to include the capital gain (P1 − P0) as part of the return — realized yield includes both dividends and price appreciation.
For the IRR method: not including the terminal sale price in the final year's cash flow.

Reference:

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Cost of Equity — Realized Yield Approach

Worked example

⚠️ Common exam mistakes