Question

Bond P is a premium bond with a 9 percent coupon. Bond D is a 5 percent coupon bond currently selling at a discount. Both bonds make annual payments, have a YTM of 7 percent, and have five years to maturity. What is

the current yield for bond P? For bond D? If interest rates remain unchanged, what is the expected capital gains yield over the next year for bond P? For bond D? Explain your answers and the interrelationships among the various types of yields.

Answer 1

Bond B (Premium Bond)
Par Value of Bond =1000
Coupon of Bond P =9%*1000 =90
Number of Years =5
YTM =7%
Price of Bond P =PV of Coupons+PV of Par Value =90*((1-(1+7%)^-5)/7%)+1000/(1+7%)^5=1082
Current Yield of Bond P =Coupon/Price of Bond P =90/1082 =8.32%

Coupon of Bond D =5%*1000 =50
Number of Years =5
YTM =7%
Price of Bond D =PV of Coupons+PV of Par Value =50*((1-(1+7%)^-5)/7%)+1000/(1+7%)^5=918
Current Yield of Bond D =Coupon/Price of Bond P =50/918 =5.45%

Capital Gain of Bond P =YTM-Current Yield =7%-8.32% =-1.32%
Capital Gain of Bond D =YTM-Current Yield =7%-5.45% =1.55%

If coupon rate is higher than YTM then capital gain is negative and if coupon rate is less than YTM capital gain is positive.Capital gain is positive for discount bond and negative for premium bond