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Microlesson · 5-min read

Deep Discount (Zero Coupon) Bonds

## Deep Discount / Zero Coupon Bonds

A deep discount bond pays no periodic interest. The investor buys it at a steep discount to face value, and the entire return comes from the difference between purchase price and redemption value.

### Return Calculation

The compound annual growth rate from issue price to face value over n years:

```

(1 + Kd)^n = Face Value / Issue Price

Kd = (Face Value / Issue Price)^(1/n) − 1

```

### Log Method (used in exams)

```

log(1 + Kd) = [log(FV) − log(Issue Price)] / n

Antlog of result = (1 + Kd)

Kd = Antlog − 1

```

### Tax treatment

If no corporate tax: Kd = (FV/IP)^(1/n) − 1, as above.

With tax: the discount amortised annually is tax-deductible, but this is rarely tested at the CA Inter level unless explicitly stated.

### Why companies issue these

  • No cash interest outflow during the bond's life → helpful for projects with deferred cash flows
  • Issued at deep discount → smaller upfront proceeds but no coupon payments
  • Investors get capital appreciation rather than income (tax timing advantage)

Worked example

### Example 1

Q8A – IDB Zero Discount Bond

Face value = ₹1,00,000; Issue price = ₹2,500; Maturity = 25 years; No corporate tax

(1 + Kd)^25 = 1,00,000 / 2,500 = 40

Using logs:

log(40) = 1.6021

1.6021 / 25 = 0.06408

Antilog(0.06408) = 1.159

Kd = 1.159 − 1 = 15.9%

### Example 2

Q8B (Part A) – DFC Zero Discount Bond

Face value = ₹1,50,000; Issue price = ₹3,750; n = 25 years; No corporate tax

(1 + Kd)^25 = 1,50,000 / 3,750 = 40

Same ratio as Q8A → Kd = 15.9%

Observation: The ratio FV/IP = 40 in both cases, so the cost is identical regardless of the absolute size of the bond.

⚠️ Common exam mistakes

  • Using simple interest to compute the return instead of compound growth.
  • Forgetting to subtract 1 after taking the antilog — the antilog gives (1+Kd), not Kd.
  • Confusing deep discount bonds with bonds issued at a small discount — 'deep discount' means the issue price is a tiny fraction of face value.
Reference:
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