l老师这个题完全不懂能不能 把计算过程 详细写一遍 谢谢！

问题如下：

Consolidated Enterprises issues €10 million face value, five-year bonds with a coupon rate of 6.5 percent. At the time of issuance, the market interest rate is 6.0 percent. Using the effective interest rate method of amortization, the carrying value after one year will be closest to:

选项：

€10.17 million.

€10.21 million.

€10.28 million.

解释：

A is correct.

The coupon rate on the bonds is higher than the market rate, which indicates that the bonds will be issued at a premium. Taking the present value of each payment indicates an issue date value of €10,210,618. The interest expense is determined by multiplying the carrying amount at the beginning of the period (€10,210,618) by the market interest rate at the time of issue (6.0 percent) for an interest expense of €612,637. The value after one year will equal the beginning value less the amount of the premium amortised to date, which is the difference between the amount paid (€650,000) and the expense accrued (€612,637) or €37,363. €10,210,618 – €37,363 = €10,173,255 or €10.17 million.

解析：公司发行了10 million面值，5年期的债券。票面利率为6.5%，发行时候的市场利率为6%。使用effective interest rate method进行会计计量。题目问发行一年后的债券账面价值是多少。

方法一：首先计算债券的发行价格，得到债券初始入账价值后使用BASE法则计算出第一年年末债券的账面价值。

票面利息coupon=10,000,000×6.5%=650,000

初始入账价值：N=5, PMT=650,000, I/Y=6, FV=10,000,000, CPT: PV=-10,210,618

第一年损益表中的interest expense=10,210,618×6%=612,637

年末账面价值=10,210,618+612,637-650,000=10,173,255，选项A正确。

方法二：债券价值等于未来现金流折现求和。因此可以直接站在第一年年末的时点，计算未来现金流在该时点的现值：

N=4，PMT=650,000, I/Y=6, FV=10,000,000, CPT: PV=-10,173,255，选项A正确。

上述两种方法都可以得到正确答案。