Question

Calculate the price of a 3.5 percent coupon bond, with 3.5 years to maturity, and semi-annual payments. Zero-coupon spot (strip) rates are as follows. YTM on a zero coupon security is a nominal annual rate with semi-annual compounding.

Maturity YTM

6 months 1.20% per year

12 months 1.30%

18 months 1.40%

24 months 1.50%

30 months 1.50%

36 months 1.70%

42 months 1.90%

a. Calculate the price of this bond.

b. What is the yield to maturity of this coupon bond? Show details of your work and present answer to a minimum of two decimal places, example X.xx%.

Answer 1

Price of the bond = Coupon Payment 1 / (1+Spot rate) + Coupon Payment 2 / (1+Spot rate)^2 .... Coupon Payment n / (1+Spot rate)^n

= 3.5 / (1 + 0.012) + 3.5 / (1 + 0.013)^2 + 3.5 / (1 + 0.014)^3 + 3.5 / (1 + 0.015)^4 + 3.5 / (1 + 0.015)^5 + 3.5 / (1 + 0.017)^6 + 100 + 3.5 / (1 + 0.019)^7 Assuming the Face value of the bond is Rs. 100

= 3.46 + 3.41 + 3.36 + 3.30 + 3.25 + 3.16 + 90.72

Price of the bond = Rs. 110.66

Price of the bond = 3.5 / (1 + YTM) + 3.5 / (1 + YTM)^2 + 3.5 / (1 + YTM)^3 + 3.5 / (1 + YTM)^4 + 3.5 / (1 + YTM)^5 + 3.5 / (1 + YTM)^6 + 100 + 3.5 / (1 + YTM)^7

110.66 = 3.5 / (1 + YTM) + 3.5 / (1 + YTM)^2 + 3.5 / (1 + YTM)^3 + 3.5 / (1 + YTM)^4 + 3.5 / (1 + YTM)^5 + 3.5 / (1 + YTM)^6 + 100 + 3.5 / (1 + YTM)^7

Using a financial calculator (BAII Plus)

PV = -110.66

N = 7

FV = 100

PMT = 3.5

CPT I/Y

YTM = 1.86