Question

The Shamrock Corporation has just issued two bonds, 1) a 15-year, $1000 par zero-coupon bond with 12% yield to maturity and 2) a 3-year, 6.5% coupon, $100 par bond with a yield to maturity of 7%. (Assume semi-annual compounding)

a) What is the market price of the zero-coupon bond in three year?b) What is the current market price of a coupon bond?

Answer 1

a) Market price of zero coupon bond in three years

Market price of zero coupon bond = Maturity value or face value/(1+r)^n

r= reqd. rate of return or YTM and n= number of years to maturity.

Maturity value = 1000$, r=12%, n=15-3=12 i.e., 12 years to maturity.

Market price at the end of third year= 1000/(1+0.12)^12

=1000/3.90

=$ 256.4

b) Current market price of coupon bond

Bond price= C/(1+i) + C/(1+i)^2 + .......M/(1+i)^n

In this C= Coupon interest, i=discount rate, M=Maturity value and n=no of years to maturity.

Now since semi annual compounding is to be done, C=100*6.5%*6/12=$ 3.25, i= 7*6/12=3.5%, n=3*2=6 and M=$ 100

Note: it is assumed that coupon rate and yield to maturity given in the question is annual rate and not semi annual and that is why coupon and interest rate have been divided by 2.

Bond price= 3.25/(1+0.035) + 3.25/(1+0.0035)^2 + 3.25/(1+0.0035)^3 + 3.25/(1+0.0035)^4 + 3.25/(1+0.0035)^5 + 3.25/(1+0.0035)^6 + 100/(1+0.0035)^6

Bond price= 3.14 + 3.03 + 2.93 + 2.83 + 2.74 + 2.64 + 81.35

= $98.66

Current market price =$98.66