Question

1. The face value for Karen’s Limited bonds is $100,000 and has a 2 percent annual coupon. The percent annual coupon bonds matures in 2022, and it is now 2012. Interest on these bonds is paid annually on December 31 of each year, and new annual coupon bonds with similar risk andmaturity are currently yielding 12 percent. How much should Karen sell her bonds today?  

2. What is the semi-annual coupon bond’s nominal yield to maturity (YTM), if the years to maturity is 15 years, and sells for 119% with coupons rate of 10%? Assume the par value of the bond is $1,000.

3. MJI Corporation bonds mature in 6 years and have a yield to maturity of 8.5 percent. The par value of the bonds is $1,000. The bonds have a 10 percent coupon rate and pay interest on a semi-annual basis. Assuming there are no changes to interest rates during the course of the year, what are the current yield and capital gains yield on the bonds for this year?

Answer 1

1). To find the bond's price, we need to put the following values in the financial calculator:

N = 2022 - 2012 = 10;

I/Y = 12;

PMT = 2%*1000 = 20;

FV = 1000;

Press CPT, then PV, which gives us -434.98

Hence, Bond's Price is $434.98

2). To find the YTM, we need to put the following values in the financial calculator:

N = 15*2 = 30;

PV = -119%*1000 = -1190;

PMT = (10%/2)*1000 = 50;

FV = 1000;

Press CPT, then I/Y, which gives us 3.91

So, Periodic Rate = 3.91%

Hence, Nominal YTM = Periodic Rate * No. of periods in a year

= 3.91% * 2 = 7.83%

3). To find the bond's price, we need to put the following values in the financial calculator:

N = 6*2 = 12;

I/Y = 8.5/2 = 4.25;

PMT = (10%/2)*1000 = 50;

FV = 1000;

Press CPT, then PV, which gives us -1069.38

Hence, Bond's Price is $1069.38

Current Yield = Annual Coupon Payment / Current Bond Price

= [10% * $1000] / $1069.38 = $100 / $1069.38 = 0.0935, or 9.35%

Capital Gains Yield = YTM - Current Yield = 8.5% - 9.35% = -0.85%