Consider a bond with a 62 percent coupon rate paid semiannua

Consider a bond with a 6.2 percent coupon rate, paid semiannually, that has 20 years until it matures. If the current market interest rate is 7.4 percent, and the bond is priced at $925, what\'s the bond\'s present value? Should you buy this bond? Explain why or why not.

Solution

Present value of bond=Present value of semi-annual interest payments+Present value of bond repayment at the end Interest payment per semi-annually=925*6.2%*1/2=$28.68 Market interest rate per semi-annually=7.4%*1/2=3.7% Present value of semi-annual interest payments @3.7% for 40 periods=28.68*20.70803=593.91 Present value of bond repayment at the end of 40th period @3.7%=925*0.233803=216.27 Present value of bond=593.91+216.27=$ 810.18 Conclusion: You should buy this bond Reason: Normally,investor will get more interest rate in the market. But,Bond will be issued at discount at $810.18 Redemption of bond will happen at $925 Lower interest is compensated by discount on issue. Moreover,Investor will receive fixed interest payments for 20 years ($28.68) Year PVF @ 3.7% 1 0.96432015 2 0.92991336 3 0.89673419 4 0.86473886 5 0.83388511 6 0.80413222 7 0.7754409 8 0.74777329 9 0.72109286 10 0.69536437 11 0.67055388 12 0.64662862 13 0.62355701 14 0.60130859 15 0.579854 16 0.55916489 17 0.53921398 18 0.51997491 19 0.50142228 20 0.48353161 21 0.46627928 22 0.44964251 23 0.43359933 24 0.41812857 25 0.40320981 26 0.38882335 27 0.37495019 28 0.36157202 29 0.34867119 30 0.33623066 31 0.324234 32 0.31266538 33 0.30150953 34 0.29075171 35 0.28037774 36 0.2703739 37 0.260727 38 0.2514243 39 0.24245352 40 0.23380282 Total 20.7080319