Question

SOLVE WITHOUT CALCULATOR

Bond P is a premium bond with a coupon of 8.5 percent. Bond D has a coupon of 5.5 percent and is selling at a discount. Both bonds make annual payments, have a YTM of 7 percent, and have 10 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 interrelationship among the various types of yields

Answer 1

Use the below formulae to find the price of bond

current yield=coupon payment/price of bond

Bond price=(coupon*(1-((1+r)^-n))/i)+(par value*(1+r)^-n)
bond p:
Coupon=par value*coupon rate
=1000*8.5%=85
r=7% n=10
price=1105.35
Current yield=85/1105.35=7.69%
Bond D:
Coupon=par value*coupon rate
=1000*5.5%=55
r=7% n=10
price=894.65
Current yield=55/894.65=6.15%

For expected current yield we need to find price of bond after one year

bond p:
Coupon=par value*coupon rate
=1000*8.5%=85
r=7% n=9
price=1097.73
capital gain yield=(1097.73-1105.35)/1105.35=-0.69%

Bond D:
Coupon=par value*coupon rate
=1000*5.5%=55
r=7% n=9
price=902.27
capital gain yield=(902.27-894.65)/894.65=0.85%

YTM=Current yield+capital gain yield