Question

A3-18 You are currently holding a corporate bond. It has a remaining life of exactly 25 years till maturity. It has a coupon rate of 4.5% (nominal rate compounded semi-annually) and a face value of $1,000. Currently the market is demanding a nominal rate of 6% compounded semi-annually on bonds with similar risk, and maturity date. A) If your are thinking of selling the bond today, what is the current value of the bond? B) If you paid $900 for the bond today, what would be your "Yield To Maturity" YTM on this investment? C) Based on the same $900 purchase price today, what is the bonds "Current Yield"?

Answer 1

A) life rightarrow 25 years CR rightarrow 4.5% Therefore 4.5/2 rightarrow 2.25% for semi annual CA rightarrow 1000 * 2.25% rightarrow $22.5 Y + M (6 Months) rightarrow 6%/2 rightarrow 3% Therefore current Bond price (B_0) rightarrow YTM rightarrow CA + fv - B_0/fv + B_0/2 3% rightarrow 22.5 + 1000 - B_0/25 times 2/1000 + B_0/2 rightarrow 1125 + 1000 - B_0/50/1000 + B_0/2 3% (1000 + B_0/2)rightarrow 2125 - B_0/50 750 + 0.75 B_0 rightarrow 2125 - B_0 1.75 B_0 rightarrow 1375 Because B_0 (current price) rightarrow $785.714 \r\n B) if B_0 rightarrow 900 Therefore YTM rightarrow YTM rightarrow CA + fv - B_0/n/fv + B_0/2 rightarrow 22.5 + 1000 - 900/25 times 2/1000 + 900/2 rightarrow 1125 + 100/50/1900/2 rightarrow 24.5/950 rightarrow 2.5789% (for 6 Months) Because YTM (annually) rightarrow 5.158% c) current yield rightarrow CA/B_0 rightarrow 1000 * 4.5%/900 rightarrow 45/900 rightarrow 5%