Question

Bond A is a premium bond with a 9 percent coupon. Bond B is a 5 percent coupon bond currently selling at a discount. Both bonds make annual payments, have a YTM of 6 percent, and have five years to maturity. The face value is $1000 for both bonds.

a. What is the current yield for Bond A? For Bond B?

b. If interest rates remain unchanged, what is the expected capital gains yield over the next year for Bond A? For Bond B?

c. Why is the capital gain yield of the premium bond different from that of the discount bond? Which bond is better in terms of yields?

d. What is the holding period return for each bond, if both bonds are held over the next year and sold at the year ned?

Answer 1

a. Current yield for bonds= $ annual coupon /current market price

So,

first we need to find the current selling price of the bonds to find their current yield

Current price of Bond A=

(($ coupon)*(1-(1+YTM)^-n)/YTM)+(Face Value/(1+YTM)^n)

ie.(($1000*9%)*(1-(1+6%)^-5)/6%)+(1000/(1+6%)^5)=

1126.37

Current Yield for Bond A=($ 1000*9%)/1126.37=

7.99%

Current price of Bond B=

ie.(($1000*5%)*(1-(1+6%)^-5)/6%)+(1000/(1+6%)^5)=

957.88

Current Yield for Bond B=($ 1000*5%)/957.88=

5.22%

b.If interest rates remain unchanged ie. 6%, expected capital gains yield(CGY) over the next year For Bond B?

CGY=(Price at end yr.1-Purchase price)/Purchase price

So, we need to find the price at end Yr.1 , ie. The change will be for only n = 4 yrs.(remaining to maturity) , for both the bonds

for Bond A

P1=(($1000*9%)*(1-(1+6%)^-4)/6%)+(1000/(1+6%)^4)=

1103.95

SO,

CGY (Bond A)=(1103.95-1126.37)/1126.37=

-1.99%

for Bond B

P1=(($1000*5%)*(1-(1+6%)^-4)/6%)+(1000/(1+6%)^4)=

965.35

SO,

CGY (Bond B)=(965.35-957.88)/957.88=

0.78%

c. Why is the capital gain yield of the premium bond different from that of the discount bond?

For a premium bond, market interest rates remaining same, price decreases from the original purchase price , giving a negative CGY.

whereas

For a discount bond, market interest rates remaining same, price appreciates from the original purchase price , giving a positive CGY.

Which bond is better in terms of yields?

Bond B

as 0.78% > -1.99%

d.Holding period return for each bond, if both bonds are held over the next year and sold at the year ned?

Holding period return (HPR)=(Price at end yr.1+ $ coupon for thr period-Purchase price)/Purchase price

Bond A

HPR (Bond A)=(1103.95+90-1126.37)/1126.37=

6.00%

Bond B

HPR(Bond B)=(965.35+50-957.88)/957.88=

6.00%