1001y11001y21150 y225 2 a 債券殖利率 123810

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100/(1+Y)+1,100/(1+Y)^2=1,150 Y=2.25% (2) A 債券殖利率 =12.38%>10%= 票面利率 B 債券殖利率 =2.25%<10%= 票面利率 (3) A 債券當期收益率 =100/960=10.42% B 債券當期收益率 =100/1,150=8.70% 13. 花田 公司發行 3 年期債券,面額 10,000 元,票面利率 12% ,每年付息一次。 已知 面值 10,000 元之 1 年期零息債券價格為 9,500 元, 2 年期零息債券價格 8,800 元, 三年零息債券價格為 8,000 元,試問 花田 公司發行之 3 年期 債券價格為多少? Ans: 假設一年期殖利率 r1 10,000/(1+r1)=9,500 r1=5.2632% 假設 年期殖利率 r2 10,000/(1+r2)^2=8,800 r2=6.6004% 假設三年期殖利率為 r3 10,000/(1+r3)^3=8,000 r3=7.7217% P=1,200/(1+5.2632%)+1,200/(1+6.6004%)^2+11,200/(1+7.7217%)^3=11,156.007 14. 白虎 公司發行了一張公司債, 10 年到期,面額為 10,000 元。這張公司債前 3 年沒有 何的利息,從 4 開始連續 7 年每半年支付 400 元的利息, 3 年每半年支付 550 元的利息,若此債券的殖利率為 6% ,試問: (1) 債券目前的價格為多少? (2) 3 年後債券的價格為多少? (3) 7 年後債券的價格為多少?
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Ans: (1)400*(1/0.03-1/(0.03*1.03^8))/1.03^6+550*(1/0.03-1/ (0.03*1.03^6))/1.03^14+10,000/1.03^20 =9,858.08 (2)400*(1/0.03-1/(0.03*1.03^8)) +550*(1/0.03-1/ (0.03*1.03^6))/1.03^8+10,000/1.03^14=1,1771.068 (3)550*(1/0.03-1/(0.03*1.03^6)) +10,000/1.03^6=1,1354.30 15. 假如 王品汽車 公司發售 10 年期債券,面值 1,000 元,票面利率 10% ,半年 付息 1 次。試問: (1) 債券發行 2 年後市場利率降為 6% ,則售價為多少? (2) 假如債券發行 2 年後市場利率升為 12% ,則市價變為多少? (3) 條件如 (1) (2) 小題,且從 時以後 到期日的市場利率一 維持在 6% 12% 不變,則這 8 年內 王品 公司債的價格 走勢 為何? Ans: (1) 251 , 1 ) 03 . 1 ( 000 , 1 ) 03 . 1 ( 03 . 0 1 03 . 0 1 50 16 16 PV (2) 16 16 1 1 1,000 50 898.94 0.06 0.06(1.06) (1.06) PV (3) (1) 小題的債券價值會 年下降, 後等於面值 1,000 元, (2) 小題的債券 價值會 年上升, 後等於面值 1,000 元。 16. 今天購買一張 麒麟 公司的債券,該債券 5 年到期,面額 10,000 元,票 面利息為 9% ,市場利率為 11% 。試問: (1) 該公司債之價值為多少? (2) 這一年間,青 的當期收益率為多少? (3) 若一年後市場利率下降 10% ,試問該公司債價格變為多少? (4) 這一年間,青 的資本利得率為多少? Ans: (1) 10,000*9%*(1/11%-1/(11%*1.11^5))+10,000/1.11^5=9,260.82
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