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# premium and discount bonds question

#### andra2gtk

##### New Member
Hi,
I heard somebody saying today that zero bond XXX was issued at 100 and will be redeemed at 70. Is that possible? That would mean somebody would have to buy it for 100 but get only 70 back at maturity?So my questions are:
1. Is it possible to issue at par and redeem at discount a zero coupon bond?What about a coupon bearing bond?
2.Isn't always the redemption value equal to the par value? and the issue value equal to the PV of the redemption?

BR
Andra

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @andra2gtk

I can't pretend I know all usages but that's not familiar to me. Speaking for the FRM (as a narrow qualifier), par refers to the the amount the bond issuer will repay at maturity. In this sense, I don't really get "redeem at 70," because by that definition we assume "redeem at 100 or 1000" because we redeem exactly the par at maturity!

Now the quote is different than par; quote price is typically a percentage of par. So if your bond has a par of $1,000, then you could issue me your bond at 70 or 100 or 130 or any X ($700, $1000,$1300 or $X/100*1,000). So, there is nothing wrong with issue at 100 (i.e., 100% of par value) and redeem at 70 (70% of par), which might be purchase at$1,000 and redeem at \$700. But I don't see how that could be a zero coupon bond as the interest rate (on the depreciation) is negative (?), so the condition for that, typically, would be the same as if we purchased at a premium of, say, 130 and redeemed at par of 100: the coupon would need to (significantly) exceed the yield, in order that the loss on capital depreciation is more than compensated by the coupon income. Typically, we purchase at a discount (less than par) when the coupon < yield, or premium (greater than par) when coupon > yield. The buyer expect a yield and the yield comes into two components (coupon and capital appreciation) such that capital depreciation is expected when a bond is issued at a premium (i.e., greater than par) but that's because it's going to net against high coupon income.

Re: 2.Isn't always the redemption value equal to the par value?
Yes, I think that par value is a synonym for redemption value, and face value; par = redemption = face value.

Re: and the issue value equal to the PV of the redemption?
Yes, in the case of the zero-coupon bond, which is a special case of the issue value equal to the PV of all future cash flows; there is the question of bond issuance cost, which simple calcs omit. I don' normally refer to the "issue value," rather in FRM we call this theoretical price [in order to distinguish between the traded price], full price, or cash price. I hope that helps!