Question

1. A issued an unsecured bond with a 10% coupon rate paid semiannually. The bond matures in 8 years, has a par value of $1,000, and a yield to maturity of 8.5%. Based on this information, what is the price of this bond?

2. B issued a bond that will mature in 10 years. The bond has a face value of $1,000 and a coupon rate of 8%, paid semiannually. The bond is currently trading at $1,100, and is callable in 5 years at a call price of $1,050. What is the bond’s yield to call (YTC)?

3. C issued a $1,000 par, 8%, 10 year bond, which pays semiannual coupons. The bond is callable in 5 years at a call price of $1,050. If the current price of the bond is $1,100, what is its yield to maturity (YTM)?

Detailed Calculation process please!

Answer 1

1

K = Nx2

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

k=1

K =8x2

Bond Price =∑ [(10*1000/200)/(1 + 8.5/200)^k]     +   1000/(1 + 8.5/200)^8x2

k=1

Bond Price = 1085.8

2

K = Time to callx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTC/2)^k]     +   Call Price/(1 + YTC/2)^Time to callx2

k=1

K =5x2

1100 =∑ [(8*1000/200)/(1 + YTC/200)^k]     +   1050/(1 + YTC/200)^5x2

k=1

YTC% = 6.49

3

K = Nx2

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

k=1

K =10x2

1100 =∑ [(8*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^10x2

k=1

YTM% = 6.62