Suppose that a 6.250% semi-annual coupon paying bond is priced at 105.760 per 100 of par value. The tenor of the bond is 13 years. What is the yield to maturity?
No of periods \(=12\) years \(^{*} 2=24\) semi annual periods
Coupon per period = (Coupon rate / No of coupon payments per year) * Face value
Coupon per period \(=(6.250 \% / 2) * \$ 100\)
Coupon per period \(=\$ 3.125\)
Bond Price \(=\sum\) Coupon \(/(1+\mathrm{YTM})\) period \(+\) Face value \(/(1+\mathrm{YTM})^{\text {period }}\)
\(\$ 105.5=\$ 3.125 /(1+\mathrm{YTM} / 2)^{1}+\$ 3.125 /\left(1+\mathrm{YTM} / 2 \mathrm{e}^{2}+\ldots+\$ 3.125 /(1+\mathrm{YTM} / 2 \mathrm{e})^{24}+\$ 100 /(1+\mathrm{YTM} /\right. 2)^{24}\)
Using Texas Instruments BA 2 Plus Calculator
\(\mathrm{SET} \mathrm{N}=24, \mathrm{FV}=100, \mathrm{PMT}=3.125, \mathrm{PV}=-105.5\)
\(\mathrm{CPT} I / Y =2.8070\)
\(Y T M=2^{*} I / Y\)
\(\mathrm{YTM}=2 * 2.8070\)
\(\mathrm{YTM}=5.6139 \%\) or \(5.613 \%\)
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