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Lee13 · 2023年04月04日

When market interest rate is 6%, a company issues a $1 million bond with maturity of 3-year, a 5% coupon rate, and annual interest payments. Which of the following statements is the most correct when the market rate changes to 7% and the carrying value of the bond base on amortized cost.

NO.PZ2016012102000152

问题如下:

When market interest rate is 6%, a company issues a $1 million bond with maturity of 3-year, a 5% coupon rate, and annual interest payments.

Which of the following statements is the most correct when the market rate changes to 7% and the carrying value of the bond base on amortized cost.

选项:

A.

The book value of the bonds at the beginning of the Second year will be $990,566.04

B.

The book value of the bonds at the beginning of the Second year will be $973,269.88

C.

The book value of the bonds at the beginning of the Second year will be $981,666.07

解释:

C is correct.

Since the amortized costs will not be affected by the change in market rates, we use 6% to calculate the beginning book value of the bond

N=3 I/Y=6 PMT=1,000,000×5%=50,000 FV=1,000,000 then CPT PV=973,269.88

The new book value= Beginning book value + interest expense -coupon rate=973,269.88+973,269.88×6%-50,000=981,666.07

The ending book value of First Year= the beginning book value of Second Year

考点:债券利息费用的计算

由于摊余成本(amortized costs ), 用的是发行时的市场利率(market interest rate ),不受后续市场利率变化的影响 ,所以我们采用6%计算该债券的期初账面价值.

N=3 I/Y=6 PMT=1,000,000×5%=50,000 FV=1,000,000

CPT PV = 973,269.88

第一年债券的现值,使用计算器计算得出973,269.88


后续每年的账面价值 = 初始债券账面价值 + 利息费用 - 支付的债券票面利息

利息费用 = 初始账面价值 * 债券发行时的市场利息率(market interest rate )

第二年债券账面价值 = 973,269.88 + 973,269.88×6% - 50,000 = 981,666.07

您好,我看课件里讲的时候,何老师是直接用计算公式算出来的PV,可是我算的PV和用计算器算的不一样,可以列一下计算公式吗,谢谢!

1 个答案

王园圆_品职助教 · 2023年04月04日

同学你好,首先要注意,因为债券是按历史成本入账并且始终按照历史成本入账时刻的interest rate进行摊销的,所以市场利率的变化和债券价值的计算无关,所以本题折现率应该用6%而不是7%

公式:I=6,N=2,PMT = 1,000,000*5% =50,000,FV= 1,000,000 ,最后 PV = -981666.07

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