## Cost of Retained Earnings

Retained earnings belong to existing shareholders — they represent profits not distributed as dividends. Their cost is an opportunity cost: the return shareholders forgo by not receiving those earnings as dividends to reinvest elsewhere.

### Approach 1: Opportunity Cost (Simplest)

Kr = Ke — treat retained earnings as equivalent to equity, since both carry the same risk.

### Approach 2: D/P + g with Investor Friction

If earnings were paid as dividends, shareholders would:

1. Pay personal income tax (t_p) on the dividend

2. Incur brokerage cost (b) to reinvest

3. Then earn the going market return

Kr = [D₁ / P₀] × (1 – t_p) × (1 – b) + g

This is always less than the full cost of new equity because new equity also carries flotation costs.

### Approach 3: CAPM

Kr = Rf + β(Rm – Rf) — same as Ke under CAPM.

### Key Relationship

Kr < Ke_new (cost of new equity)

Because new equity involves flotation costs that reduce NP, while retained earnings have no issuance cost.

Worked example

### Example 1

Q33 — Y Ltd (PYQ)

Retained earnings = ₹7,50,000 | Opportunity return = 10% | Brokerage = 3% | Personal tax = 30%

Kr = 10% × (1 – 0.30) × (1 – 0.03)

= 10% × 0.70 × 0.97

= 6.79%

Interpretation: After paying 30% income tax on the dividend received and 3% brokerage to reinvest, shareholders net only 6.79%. That is the true opportunity cost of retention.

### Example 2

Q32 — Full friction model

P₀ = ₹140 | Brokerage = 3% on market price | g = 5% | D₁ = ₹14 | Personal tax = 22%

Kr = [14/140] × (1 – 0.22) × (1 – 0.03) + 0.05

= 0.10 × 0.78 × 0.97 + 0.05

= 0.07566 + 0.05 = 12.57%

⚠️ Common exam mistakes

Treating retained earnings as free (zero cost) — they always carry an opportunity cost.
Using the firm's corporate tax rate instead of the shareholder's personal income tax rate.
Confusing cost of retained earnings with cost of new equity — new equity has flotation costs on top, making it more expensive.
Failing to apply the (1–b) brokerage adjustment when explicitly given in the problem.

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 →