Question

Ramstucky Corp bonds just paid their annual coupon of 4%. They mature in 6 years. The required rate of return on the bonds is 5%. The call price of the bonds is 102, but they are not callable until after the second coupon payment.

1. What is the price of the bonds as a percentage of par?
2. What is the current yield?
3. What is the yield to first call?
4. If, immediately after the second coupon payment, the yield to maturity is 4.5% and you sell the bond at that time, what rate of return will you have received over the two years?

Answer 1

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =6

Bond Price =∑ [(4*100/100)/(1 + 5/100)^k]     +   100/(1 + 5/100)^6

k=1

Bond Price = 94.92%

current yield = coupon rate*par value/current price

Current yield%=(4/100)*100/94.92

Current yield% = 4.21

K = Time to call

Bond Price =∑ [(Annual Coupon)/(1 + YTC)^k]     +   Call Price/(1 + YTC)^Time to call

k=1

K =2

94.92 =∑ [(4*100/100)/(1 + YTC/100)^k]     +   102/(1 + YTC/100)^2

k=1

YTC% = 7.8

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =3

Bond Price =∑ [(4*100/100)/(1 + 4.5/100)^k]     +   100/(1 + 4.5/100)^3

k=1

Bond Price = 98.63

rate of return/HPR = ((Selling price+Number of Coupon amount*Coupon amount)/Purchase price-1)

=((98.63+2*4)/94.92-1)

=12.34%