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Chris ZHANG · 2023年08月20日

这道题没理解，麻烦老师给讲解一下

  1. CFA I
  2. Quantitative

NO.PZ2023052407000001

问题如下：

Grupo Ignacia issued 10-year corporate bonds two years ago. The bonds pay an annualized coupon of 10.7 percent on a semiannual basis, and the current annualized YTM is 11.6 percent. The current price of Grupo Ignacia’s bonds (per MXN100 of par value) is closest to:

选项：

A.

MXN95.47

B.

MXN97.18

C.

MXN95.39

解释：

C is correct. The coupon payments are 5.35 (=10.7/2), the discount rate is 5.8 percent (=11.6%/2) per period, and the number of periods is 16 (=8×2). Using Equation 6, the calculation is as follows:


Alternatively, using the Microsoft Excel or Google Sheets PV function (PV(0.058,16,5.35,100,0)) also yields a result of MXN95.39.

A is incorrect. MXN95.47 is the result when incorrectly using coupon payments of 10.7, a discount rate of 11.6 percent, and 8 as the number of periods.

B is incorrect. MXN97.18 is the result when using the correct semiannual coupons and discount rate, but incorrectly using 8 as the number of periods.

这道题从头到尾没理解…

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3 个答案

星星_品职助教 · 2023年08月20日

@Chris ZHANG

是的，相当于求普通年金+一个FV的现值。

Chris ZHANG · 2023年08月20日

谢谢老师详细讲解。对于current price来说，我们是用未来的十六次coupon和fv回推到如今的期初年金是吧？

星星_品职助教 · 2023年08月20日

同学你好，

根据“an annualized coupon of 10.7 percent on a semiannual basis”，可知coupon每半年一付，金额为10.7%×100/2=5.35,。这是PMT的数值。

根据“the current annualized YTM is 11.6 percent”，YTM和coupon需要保持一致。所以I/Y为11.6/2=5.8

期末要还本金100，即FV=100.

根据“..issued 10-year corporate bonds two years ago”，可知剩余期限还有8年。N的期限需要和I/Y以及PMT一致，所以N=16。也就是还有16个半年。

如果列公式，则就是答案解析中的这个形式。

但实际并不用公式来硬解，统一使用计算器第三排，PMT=5.35，I/Y=5.8，N=16，FV=100，CPT PV=-95.3892.

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本题在基础班讲过非常类似的例题，如果完全不理解，可以复习相应部分。视频位置如下：

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