## 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)