Question

1 Calculate the Yield to Maturity (YTM) of a 10-year annual coupon-ed bond with a coupon rate of 7%, a price of $1050, and a face value of $1000.

2 a Calculate the Yield to Maturity (YTM) of a 10-year semiannual coupon-ed bond with a coupon rate of 7%, a price of $1050, and a face value of $1000.

   b Calculate this bond's Current Yield (CY).

3 In previous Questions 4 and 5, with all the same maturity, coupon rate, market rate and face value, explain why the YTM of the bond is different.

Answer 1

1)

K = N

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

k=1

K =10

1050 =∑ [(10*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^10

k=1

YTM% = 9.21

2)

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =10x2

1050 =∑ [(10*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^10x2

k=1

YTM% = 9.22

current yield = coupon rate*par value/current price

Current yield%=(10/100)*1000/1050

Current yield% = 9.52

3)YTM on a semiannual coupon bond is higher than annual coupon bond because in semi annual coupon bond as half of the coupon is paid 6 months before the year end more interest can be earned on this coupon because of higher reinvestment period for these coupons