Question

ABC company issued bonds on January 1, 2006. The bonds had a coupon rate of 5.5%, with interest paid semiannually. The face value of the bonds is $1,000 and the bonds mature on January 1, 2021. What is the yield to maturity for these bonds on January 1, 2012 if the market price of the bond on that date is $950?

(i) Describe and interpret the assumptions related to the problem. (ii) Apply the appropriate mathematical model to solve the problem. (iii) Calculate the correct solution to the problem

Answer 1

i.Yield to maturity can be defined as what would be the rate of return if one buys the bond and holds till maturity.It can also be defined as value of discount rate for which the intrinsic value of the bond equals its market price.

In the given problem it is assumed that coupon rate is per annum

ii.yield to maturity can be calculated using following model..

market price at any time = remaining interest payments discounted using YTM + Par value dicounted using YTM

where V = market price of bond

i= coupon interest

YTM = yield to maturity

n= number of periods interest will be paid

F = principal amount

since semi annual interest payments involved it can be modified as

the formula needed to be changed because we discount semi annual interest coupons with semi annual discount rate..

iii. the detailed calculation can be found in below excel worksheet

we can calculate YTM using Rate function in excel which takes following parameters into account.

nper = number of periods( in the problem bonds have still 9 years to mature and interest is paid semiannually which makes clear that interest paid for 18 periods)

PMT = periodical payment( interest coupon of 5.5% is paid annually ..and 27.5$ is paid per period)

pv = present market value of bond ( which is 950$)

FV= face value ( which is 1000$)

we can insert following function to obtain YTM in excel

rate(nper,pmt,pv,fv)

rate(18,27.5,-950,1000)

note: Pv in above formula taken as negative because pv is outflow.

the above function results 3%

the above result is semi annual...6% will be YTM for annual.