## Cost of Redeemable Debentures

Redeemable debentures are repaid at a specified future date. The cost must account for both the periodic after-tax interest payments and the capital gain or loss when the debenture is redeemed.

### Approximation (Short-cut) Formula

```

Kd = [I(1−t) + (RV − NP)/n] / [(RV + NP)/2]

```

Where:

`I(1−t)` = Annual after-tax interest
`RV` = Redemption value (what the company pays back)
`NP` = Net proceeds at issue (or market price for existing debt)
`n` = Remaining years to maturity
`(RV − NP)/n` = Annual capital adjustment (amortised gain or loss)
`(RV + NP)/2` = Average capital employed over the life

### YTM (IRR) Method

Find the rate `r` at which the PV of all cash outflows (after-tax interest + redemption) equals the current inflow (NP or MP):

```

NP = Σ [I(1−t) / (1+r)^t] + [RV / (1+r)^n]

```

Solve by trial and error, then interpolate:

```

Kd = RL + [(NPV at RL) / (NPV at RL − NPV at RH)] × (RH − RL)

```

### Reading the capital adjustment sign

Issued at discount (NP < RV): gain on redemption → positive term → increases Kd
Issued at premium (NP > RV): loss on redemption → negative term → decreases Kd

### Tax on capital gain/loss

In the standard Indian CA exam approach, the capital gain/(loss) on redemption is not separately tax-adjusted unless the question explicitly asks for it. Only the interest component gets the tax shield.

Worked example

### Example 1

Q2 – Issued at 10% premium, redeemed at par after 5 years

Face = ₹100, Coupon = 10%, NP = ₹110 (10% premium), RV = ₹100, n = 5, tax = 35%

After-tax interest = 10 × (1 − 0.35) = ₹6.50

Kd = [6.50 + (100 − 110)/5] / [(100 + 110)/2]

= [6.50 − 2.00] / 105

= 4.50 / 105

= 4.29%

Interpretation: The redemption at par (less than issue price) reduces the effective cost.

### Example 2

Q7 – 12% debentures, 7-year maturity, 35% tax

I = 12; After-tax I = 12 × 0.65 = ₹7.80

Scenario	NP	Kd numerator	Kd denominator	Kd
At par	100	7.80 + 0/7 = 7.80	(100+100)/2 = 100	7.80%
10% discount	90	7.80 + 10/7 = 9.23	(100+90)/2 = 95	9.72%
10% premium	110	7.80 − 10/7 = 6.37	(100+110)/2 = 105	6.07%

With 2% brokerage at par: NP = 98

Kd = [7.80 + (100−98)/7] / [(100+98)/2]

= [7.80 + 0.286] / 99

= 8.086 / 99 = 8.17%

⚠️ Common exam mistakes

Using n = original life instead of remaining life when pricing existing debt.
Placing (RV − NP)/n in the denominator instead of the numerator.
Using average of face value and issue price instead of average of RV and NP for the denominator.
Forgetting that if issued at premium (NP > RV), the annual capital adjustment is negative, reducing Kd.
For YTM method: computing PV of outflows rather than matching NP to PV of future cash flows.

Reference:

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