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三三 · 2023年06月26日

Market Discount Rate 是YTM嘛?

NO.PZ2016031001000054

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=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=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

考点:bond valuation

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

故选项B正确。

如题。

1 个答案

吴昊_品职助教 · 2023年06月26日

嗨,爱思考的PZer你好:


确切来说,market discount rate不止只有YTM,YTM是市场折现率的一种,是single discount rate,也就是说存续期内,各期的折现率都统一。本题中,折现率统一,各期之间没有发生变化,所以对应就是YTM。

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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。 请问老师为什么PMT是2呢?

2022-06-24 01:02 1 · 回答

96.28. 96.33. B is correct. The bonpriis closest to 96.28. The formula for calculating this bonpriis: 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}PV=(1+r)1PMY​+(1+r)2PMY​+(1+r)3PMY​+(1+r)4PMY+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(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请问用计算器怎么做?

2020-11-23 07:03 1 · 回答