# Cost of Debentures (Kd)
Based on whether the principal is repaid on maturity, debt is irredeemable or redeemable.
## A. Cost of Irredeemable Debentures
Debentures that are never redeemed by the issuer. Cost (after tax):
```
Kd = (I / NP) × (1 − t)
```
Where `I₹ = annual interest, `NP₹ = net proceeds (or current market price), `t₹ = tax rate.
## B. Cost of Redeemable Debentures
Two approaches:
### (i) YTM Method (PV / IRR Method) — accurate
Kd is the IRR of the debenture's cash flows from today to maturity. Relevant cash flows:
| Year | Cash flow |
|---|---|
| 0 | Net proceeds (new issue) or current price `P₀₹ — an outflow |
| 1 to n | Interest net of tax: `I(1 − t)₹ |
| n | Redemption value `RV₹ |
Steps: (1) identify cash flows → (2) compute NPV at two guessed rates → (3) interpolate to find IRR (= Kd).
### (ii) Approximation Method (Shortcut / Formula) — approximate
When only interest is tax-deductible:
```
I(1 − t) + (RV − NP)/n
Kd = ─────────────────────────────
(RV + NP)/2
```
If discount on issue and/or premium on redemption are also tax-deductible:
```
I + (RV − NP)/n
Kd = ───────────────────── × (1 − t)
(RV + NP)/2
```
Where `I₹ = interest, `NP₹ = net proceeds/current price, `RV₹ = redemption value, `t₹ = tax rate, `n₹ = remaining life.
### Doubt busters
1. If not specified, use either method (YTM or Approximation).
2. Approximation gives an approximate Kd; YTM gives the accurate Kd.
3. Under approximation, either formula may be used with a logical assumption stated.
4. Net proceeds = Issue price − flotation cost.
5. If issue price not given → assume = current market price; if that too is absent → assume = face value.
6. If flotation costs not given → assume zero.
## Other issues in Kd
1. Amortization of Debenture/Bond — principal is repaid annually rather than at maturity, so the outstanding balance (and hence interest) falls each year, producing uneven cash flows. Value:
```
VB = Σ [ CFₜ / (1 + Kd)ᵗ ] for t = 1 to n
```
2. Convertible Debentures — holders may take cash or a fixed number of shares. Computed like redeemable debentures, but the redemption value = HIGHER of (a) cash value of debenture or (b) value of equity shares, assuming holders choose the more valuable option.
3. Zero Coupon Bond (Deep Discount Bond) — issued at a deep discount, redeemed at par, no coupon during its life. Kd found via YTM:
```
B₀ = RV / (1 + Kd)ⁿ
```
4. Short-Term Debt — part of current liabilities, not capital employed; exclude from WACC (e.g., creditors).
5. Long-Term Bank Loan — treated like normal redeemable Kd, but with no premium/discount:
```
Kd = Interest Rate × (1 − t)
```