Company X has non-callable bonds outstanding. When originally issued, the bonds

Question

Company X has non-callable bonds outstanding. When originally issued, the
bonds sold for $980 per bond; today (January 1) their current market price is
$1,040 per bond. The company pays a semiannual interest payment of $30 per bond on June 30 and December 31 each year.

If the bonds are perpetual bonds,

a)What is the implied semiannual yield on these bonds as of today?

b)What are the nominal annual yield and the effective annual yield on these bonds?

If the bonds have a $1,000 par value and mature in 10 years,

c)What is the implied semiannual yield to maturity (YTM) on these bonds?

d)What are the nominal annual YTM and the effective annual YTM on these bonds?

Explanation / Answer

(a) Semi annual yield as of today= Semi annual interest/price= $30/$1040*100= 2.9% (b) Nominal annual yield= Annual Interest/Nominal Price= $60/$980= 6.1% Effective annual yield= Annual Interest/Current price= $60/$1040= 5.8% (c)Par Value (F)= $1000 Price(P)=$1040 Interest(C)=$30 Semi annual YTM = (C+(F-P)/n)/((F+P)/2) = {(30+(1000-1040)/10*2)/((1000+1040)/2)}=2.74% (d)For nominal YTM, price(P)= $980 For effective YTM, price(P)= $1040 Annual Interest(C)= $60 Nominal annual YTM = (C+(F-P)/n)/((F+P)/2) = {(60+(1000-980)/10)/((1000+980)/2)}=6.26% Effective annual YTM = (C+(F-P)/n)/((F+P)/2)= {(60+(1000-1040)/10)/((1000+1040)/2)}=5.49%

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