Question

Question 1

a. A bond that pays interest semiannually is selling for 100% of its $1,000 par value. The bond has a 4% coupon rate and paid a coupon 1 month ago. What is this bond's invoice price?

b.A bond has a $1,000 par value,10 years to maturity, a 4.5% coupon, and currently sells for $1,037. The bond pays coupons semiannually. The bond is callable 3 years from today with a call price of $1,020. What is this bond's yield to maturity?

Answer 1

Part (a) Invoice value = Clean Price + accrued interest = 100% x Par value + Annual coupon rate x 1 / 12 x Par Value = 100% x 1000 + 4% x 1 / 12 x 1,000 = $  1,003.33

Part (b)

Yield to maturity (YTM) can be calculated using the RATE function of excel.

Coupon payments are semi annual. Frequency is half yearly, period = half year

Inputs are:

Period = Numbers of half years in 10 years to maturity = 2 x 10 = 20

PMT = payment per period = Half yearly coupon = 4.5% / 2 x 1000 = 22.50

PV = - Price of the bond = -1,037

FV = Par value of the bond = 1,000

Hence, YTM per period = Semi annual YTM = RATE (Period, PMT, PV, FV) = RATE(20, 22.5, -1037,1000) = 2.02%

Hence, YTM annualized = 2 x Semi annual YTM = 2 x 2.02% = 4.05%