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Eva · 2020年11月23日

问一道题：NO.PZ2016031001000054 [ CFA I ]

  1. CFA I
  2. Fixed Income

问题如下：

A bond offers an annual coupon rate of 4%, with interest paid semiannually. The bond matures in two years. At a market discount rate of 6%, the price of this bond per 100 of par value is closest to:

选项：

A.

93.07.

B.

96.28.

C.

96.33.

解释：

B is correct.

The bond price is closest to 96.28. The formula for calculating this bond price is:

PV=PMY(1+r)1+PMY(1+r)2+PMY(1+r)3+PMY+FV(1+r)4PV=\frac{PMY}{{(1+r)}^1}+\frac{PMY}{{(1+r)}^2}+\frac{PMY}{{(1+r)}^3}\text{+}\frac{PMY+FV}{{(1+r)}^4}

where:

PV = present value, or the price of the bond

PMT = coupon payment per period

FV = future value paid at maturity, or the par value of the bond

r = market discount rate, or required rate of return per period

PV=2(1+0.03)1+2(1+0.03)2+2(1+0.03)3+2+100(1+0.03)4PV=\frac2{{(1+0.03)}^1}+\frac2{{(1+0.03)}^2}+\frac2{{(1+0.03)}^3}\text{+}\frac{2+100}{{(1+0.03)}^4}

PV = 1.94 + 1.89 + 1.83 + 90.62 = 96.28

请问用计算器怎么做？
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1 个答案

吴昊_品职助教 · 2020年11月23日

同学你好：

PMT=2，N=4，FV=100，I/Y=3，可以求得PV= -96.28

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NO.PZ2016031001000054 问题如下 A bonoffers annucoupon rate of 4%, with interest paisemiannually. The bonmatures in two years. a market scount rate of 6%, the priof this bonper 100 of pvalue is closest to: A.93.07. B.96.28. C.96.33. B is correct.The bonpriis closest to 96.28. The formula for calculating this bonpriis: PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+PMT+FV(1+r)4PV=\frac{PMT}{{(1+r)}^1}+\frac{PMT}{{(1+r)}^2}+\frac{PMT}{{(1+r)}^3}\text{+}\frac{PMT+FV}{{(1+r)}^4}PV=(1+r)1PMT​+(1+r)2PMT​+(1+r)3PMT​+(1+r)4PMT+FV​PV=2(1+0.03)1+2(1+0.03)2+2(1+0.03)3+2+100(1+0.03)4PV=\frac2{{(1+0.03)}^1}+\frac2{{(1+0.03)}^2}+\frac2{{(1+0.03)}^3}\text{+}\frac{2+100}{{(1+0.03)}^4}PV=(1+0.03)12​+(1+0.03)22​+(1+0.03)32​+(1+0.03)42+100​PV = 1.94 + 1.89 + 1.83 + 90.62 = 96.28考点bonvaluation解析债券半年付息一次，每一期的coupon为100×4%/2=2，通过未来现金流折现求和，可得债券价格为96.28。也可利用计算器N=2×2=4，I/Y=6/2=3，PMT=4/2=2，FV=100，求得PV= -96.28故B正确。 如题。

2023-06-26 21:06 1 · 回答

NO.PZ2016031001000054问题如下A bonoffers annucoupon rate of 4%, with interest paisemiannually. The bonmatures in two years. a market scount rate of 6%, the priof this bonper 100 of pvalue is closest to:A.93.07.B.96.28.C.96.33. B is correct.The bonpriis closest to 96.28. The formula for calculating this bonpriis: PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+PMT+FV(1+r)4PV=\frac{PMT}{{(1+r)}^1}+\frac{PMT}{{(1+r)}^2}+\frac{PMT}{{(1+r)}^3}\text{+}\frac{PMT+FV}{{(1+r)}^4}PV=(1+r)1PMT​+(1+r)2PMT​+(1+r)3PMT​+(1+r)4PMT+FV​PV=2(1+0.03)1+2(1+0.03)2+2(1+0.03)3+2+100(1+0.03)4PV=\frac2{{(1+0.03)}^1}+\frac2{{(1+0.03)}^2}+\frac2{{(1+0.03)}^3}\text{+}\frac{2+100}{{(1+0.03)}^4}PV=(1+0.03)12​+(1+0.03)22​+(1+0.03)32​+(1+0.03)42+100​PV = 1.94 + 1.89 + 1.83 + 90.62 = 96.28考点bonvaluation解析债券半年付息一次，每一期的coupon为100×4%/2=2，通过未来现金流折现求和，可得债券价格为96.28。也可利用计算器N=2×2=4，I/Y=6/2=3，PMT=4/2=2，FV=100，求得PV= -96.28故B正确。 请问老师为什么PMT是2呢？

2022-06-24 01:02 1 · 回答