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柏小颖 · 2020年10月06日

问一道题：NO.PZ2016031001000055 [ CFA I ]

  1. CFA I
  2. Fixed Income

问题如下：

A bond offers an annual coupon rate of 5%, with interest paid semiannually. The bond matures in seven years. At a market discount rate of 3%, the price of this bond per 100 of par value is closest to:

选项：

A.

106.60.

B.

112.54.

C.

143.90.

解释：

B is correct.

The bond price is closest to 112.54.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)14PV=\frac{PMY}{{(1+r)}^1}+\frac{PMY}{{(1+r)}^2}+\frac{PMY}{{(1+r)}^3}\text{+}\cdots\text{+}\frac{PMY+FV}{{(1+r)}^{14}}

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=2.5(1+0.015)1+2.5(1+0.015)2+2.5(1+0.015)3+⋯+2.5+100(1+0.015)14PV=\frac{2.5}{{(1+0.015)}^1}+\frac{2.5}{{(1+0.015)}^2}+\frac{2.5}{{(1+0.015)}^3}\text{+}\cdots\text{+}\frac{2.5+100}{{(1+0.015)}^{14}}

PV = 2.46 + 2.43 + 2.39 + … + 2.06 + 83.21 = 112.54

这题用公式的计算，我能理解。可是用计算机计算，那几个数是怎么来的？能解释一下吗
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1 个答案

WallE_品职答疑助手 · 2020年10月06日

同学您好，

用计算机CF的那个键，cf1重复了13次，所以f1输入13.依次如下。

cf1=2.5，f1=13 ，cf2=102.5，f2=1

如果对计算器的使用问题有疑问的话，请参考计算器使用说明。

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NO.PZ2016031001000055 问题如下 A bonoffers annucoupon rate of 5%, with interest paisemiannually. The bonmatures in seven years. a market scount rate of 3%, the priof this bonper 100 of pvalue is closest to: A.106.60. B.112.54. C.143.90. B is correct.The bonpriis closest to 112.54.The formula for calculating this bonpriis: PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+⋯+PMT+FV(1+r)14PV=\frac{PMT}{{(1+r)}^1}+\frac{PMT}{{(1+r)}^2}+\frac{PMT}{{(1+r)}^3}\text{+}\cts\text{+}\frac{PMT+FV}{{(1+r)}^{14}}PV=(1+r)1PMT​+(1+r)2PMT​+(1+r)3PMT​+⋯+(1+r)14PMT+FV​PV=2.5(1+0.015)1+2.5(1+0.015)2+2.5(1+0.015)3+⋯+2.5+100(1+0.015)14PV=\frac{2.5}{{(1+0.015)}^1}+\frac{2.5}{{(1+0.015)}^2}+\frac{2.5}{{(1+0.015)}^3}\text{+}\cts\text{+}\frac{2.5+100}{{(1+0.015)}^{14}}PV=(1+0.015)12.5​+(1+0.015)22.5​+(1+0.015)32.5​+⋯+(1+0.015)142.5+100​PV = 2.46 + 2.43 + 2.39 + … + 2.06 + 83.21 = 112.54考点bonvaluation解析债券半年付息一次，每一期的coupon为100×5%/2=2.5，通过未来现金流折现求和，可得债券价格为112.54。也可利用计算器N=7×2=14，I/Y=3/2=1.5，PMT=5/2=2.5，FV=100，求得PV= -112.54故B正确。

2022-06-28 04:55 1 · 回答

112.54. 143.90. B is correct. The bonpriis closest to 112.54.The formula for calculating this bonpriis: PV=PMY(1+r)1+PMY(1+r)2+PMY(1+r)3+⋯+PMY+FV(1+r)14PV=\frac{PMY}{{(1+r)}^1}+\frac{PMY}{{(1+r)}^2}+\frac{PMY}{{(1+r)}^3}\text{+}\cts\text{+}\frac{PMY+FV}{{(1+r)}^{14}}PV=(1+r)1PMY​+(1+r)2PMY​+(1+r)3PMY​+⋯+(1+r)14PMY+FV​ where: PV = present value, or the priof the bonPMT = coupon payment per perioFV = future value paimaturity, or the pvalue of the bonr = market scount rate, or requirerate of return per perioPV=2.5(1+0.015)1+2.5(1+0.015)2+2.5(1+0.015)3+⋯+2.5+100(1+0.015)14PV=\frac{2.5}{{(1+0.015)}^1}+\frac{2.5}{{(1+0.015)}^2}+\frac{2.5}{{(1+0.015)}^3}\text{+}\cts\text{+}\frac{2.5+100}{{(1+0.015)}^{14}}PV=(1+0.015)12.5​+(1+0.015)22.5​+(1+0.015)32.5​+⋯+(1+0.015)142.5+100​ PV = 2.46 + 2.43 + 2.39 + … + 2.06 + 83.21 = 112.54老师，这个用计算器怎么计算

2020-09-02 22:54 1 · 回答

这道题我用计算器算的是111.34，cf0=0，cf1=2.5，f1=14，cf2=100，f2=1，I=1.5，计算npv，麻烦老师看下这个过程问题在哪里

2020-08-31 23:59 2 · 回答