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吴晓丽 · 2021年02月15日

三个解答为什么只有第一个分母没有减去interest

NO.PZ2016021705000067

问题如下：

William Jones is evaluating three possible means of borrowing $1 million for one month:

Drawing down on a line of credit at 7.2 percent with a 1/2 percent commitment fee on the full amount with no compensating balances.

A banker’s acceptance at 7.1 percent, an all-inclusive rate.

Commercial paper at 6.9 percent with a dealer’s commission of 1/4 percent and a backup line cost of 1/3 percent, both of which would be assessed on the $1 million of commercial paper issued.

Which of these forms of borrowing results in the lowest cost of credit?

选项：

A.

Line of credit.

B.

Banker’s acceptance.

C.

Commercial paper.

解释：

B is correct.

1. Line of credit

$Line\ cost = \frac{Interest+Commitment\ Fee}{Net\ Proceed}\times12$

$\frac{(0.072\times1,000,000\times\frac{1}{12})+(0.05\times1,000,000\times\frac{1}{12})}{1,000,000}\times12$

$=\frac{6,000+416.67}{1,000,000}\times12$

$=0.077\ or\ 7.7\%$

2. Banker’s acceptance

$Banker's\ acceptance\ cost=\frac{Interest}{Net\ Proceed}\times12$

$=\frac{(0.071\times1,000,000\times\frac{1}{12})}{1,000,000-(0.071\times1,000,000\times\frac{1}{12})}\times12$

$=\frac{5916.67}{994,083.33}\times12$

$=0.0714\ or\ 7.14\%$

3. Commercial paper

$Commercial\ paper\ cost=\frac{Interest+Dealer's\ commission+Backup\ costs}{Net\ Proceed}\times12$

$=\frac{(0.069\times1,000,000\times\frac{1}{12})+(0.0025\times1,000,000\times\frac{1}{12})+(0.003333\times1,000,000\times\frac{1}{12})}{1,000,000-(0.069\times1,000,000\times\frac{1}{12})}\times12$

$=\frac{5,750+208.33+277.78}{1,000,000-5,750}\times12$

$=0.0753\ or\ 7.53\%$

为什么第一个解答里面分母没有减去interest 呢

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1 个答案

王琛_品职助教 · 2021年02月16日

- 这里的背景是短期融资成本的计算，原则就是成本除以到手的钱
- 第二种和第三种融资工具，利息的表述方式是全包 "all inclusive"，包含了本金和利息，所以在计算成本时，分母也就是实际到手的钱，需要减去利息
- 老师在课上都有详细讲解哈，可以再听一下课；这三个公式需要掌握哈，考试时如果碰到，需要代入对应的公式，加油！

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NO.PZ2016021705000067 想问一下c项哪里表述rate是inclusive的了？谢谢老师

2021-02-17 01:00 1 · 回答

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