Largest component of zero-coupon bond

CFA Level I Fixed Income
#1

The largest component of returns for a 7-year zero-coupon bond yielding 8% and HTM is

a) Capital gains

b) Interest Income

c) Reinvestment income.

OA: B Source: Schweser

I thought zero-coupon bonds don’t have coupons so b) and c) are out. Hence, I was left with a). Can someone please explain why a) is incorrect and b) is correct?

#2

A zero coupon bond is purchased at a discount. When the bond matures, it matures at par. The difference between the par amount and the purchase price is interest income.

#3

Capital gains is the gains made from selling a security. The question states the bond is held to maturity…

Even if it wasn’t HTM you have no info on the size of the capital gains because you need the price at which the bond was bought and the price at which it was sold.

#4

With all due respect, the YTM (8%) tells you the price at which it was bought ($577.48, assuming semiannual compounding), and the fact that it was held to maturity tells you the price at which it was sold ($1,000.00).

Irrespective of that, for tax purposes the gain is treated as interest income, not as capital gains.

#5

S2000magician,

Thanks for your help. I don’t the question is asking about tax treatment. If I buy a zero-coupon bond at $577 and sell it at $1000, wouldn’t it be considered capital gains? I’m not quite sure why the question states that there is an interest income when no coupon (i.e. cash) is paid. Is the question assuming that we are using accrual accounting (instead of cash accounting) for accounting for capital gains in the price of bond from $577 to $1000? I’d sincerely appreciate if you could clarify what is interest income and what is capital gains in these questions.

I look forward to hearing from you.

#6

Yes: under accrual accounting you amortize the discount over the remaining life of the bond, and it appears on the income statement as interest income.

#7

Thanks S2000magician for confirming. Could you please provide a good example for capital gains for zero-coupon bond? I’d appreciate your help.

#8

When not held to HTM.

Say you buy it at 900, par value - 1000. Rates decline and are now 6%. The bond now trades at 950 in the secondary market, That’s your apital gains if you sell it.

#9

Not all of that $50 would be capital gains. You would have to compute the amortization during the holding period (even if it’s only a month or two) and treat that as interest income; the remainder would be capital gains.