Question

Suppose that a 5.525% semi-annual coupon paying bond is priced at 92.993 per 100 of par value. The tenor of the bond is 14 years.  What is the yield to maturity? 

Answer 1

No of periods \(=13\) years \(^{*} 2=26\) semi annual periods

Coupon per period = (Coupon rate / No of coupon payments per year) * Face value

Coupon per period \(=(5.525 \% / 2) * \$ 100\)

Coupon per period \(=\$ 2.7625\)

Bond Price \(=\sum\) Coupon \(/(1+\mathrm{YTM})^{\text {period }}+\) Face value \(/(1+\mathrm{YTM})^{\text {period }}\)

\(\$ 92.773=\$ 2.7625 /(1+\mathrm{YTM} / 2)^{1}+\$ 2.7625 /(1+\mathrm{YTM} / 2)^{2}+\ldots+\$ 2.7625 /(1+\mathrm{YTM} / 2)^{26}+\$ 100 /(1+ \mathrm{YTM} / 2 \mathrm{~L}^{26}\)

Using Texas Instruments BA 2 Plus Calculator

\(\mathrm{SET} \mathrm{N}=26, \mathrm{FV}=100, \mathrm{PMT}=2.7625, \mathrm{PV}=-92.773\)

\(\mathrm{CPT} I / Y=3.1749\)

\(Y T M=2^{*} I / Y\)

\(Y T M=2 * 3.1749\)

\(\mathrm{YTM}=6.3499 \%\) or \(6.350 \%\)