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惠媛🍭 · 2022年12月07日

我没有用上 DOL，就是纯数学的办法，可以用么？

  1. CFA I
  2. Corporate Issuers

NO.PZ2016021705000040

问题如下：

The Fulcrum Company produces decorative swivel platforms for home televisions. If Fulcrum produces 40 million units, it estimates that it can sell them for $100 each. Variable production costs are $65 per unit and fixed production costs are $1.05 billion. Which of the following statements is most accurate? Holding all else constant, the Fulcrum Company would:

选项：

A.

generate positive operating income if unit sales were 25 million.

B.

have less operating leverage if fixed production costs were 10 percent greater than $1.05 billion.

C.

generate 20 percent more operating income if unit sales were 5 percent greater than 40 million.

解释：

C is correct.

Because DOL is 4, if unit sales increase by 5 percent, Fulcrum’s operating earnings are expected to increase by 4 × 5% = 20%. The calculation for DOL is:

DOL=40 million×(100−65)[40 million×(100−65)]−1.05 billion=1.40.35=4DOL=\frac{40\ million\times(100-65)}{[40\ million\times(100-65)]-1.05\ billion}=\frac{1.4}{0.35}=4

DOL= ( 40million )( $100−$65 ) [ ( 40million )( $100−$65 ) ]−$1.05billion = $1.400billion $1.400billion−$1.05billion = $1.4 $0.35 =4

A：直接建立方程：100x=65x+1050000000 x=30 因此25不对

B：固定成本增加，意味着要更多的销售才能覆盖，自然杠杆就增加了。

C：原来是40的时候，收入=40*35-1050=350

40*20%=42，收入=42*35-1050=420

因此，提升为：（420-350）/350

我这个解题思路是不是 很笨？能不能用？


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1 个答案

王琛_品职助教 · 2022年12月12日

嗨，从没放弃的小努力你好：


1）A：直接建立方程：100x=65x+1050000000 x=30 因此25不对

思路没问题

其实选项 A 的考点是 Operating Breakeven Points，同学的思路正是公式推导的过程

即讲义中的公式 Q_OBE = FC / (P-VC) 的由来

老师在课程中，也是这样推导的，请参考基础班讲义墨迹版 P418

2）B：固定成本增加，意味着要更多的销售才能覆盖，自然杠杆就增加了。

思路没问题

其实选项 B 的考点是 DOL 的「计算」式，参考基础班讲义墨迹版 P403

其中，分母上会减去 Fixed Cost （FC）；如果减去的 Fixed Cost 越多（分母越小），那么算出来的DOL 越大

B 选项是说，如果在原来的 Fixed cost 1.05 billion 的基础上，Fixed cost 增加 10%，他说 Operating Leverage 会降低

显然他说反了，Fixed Cost 增加使得 DOL 增加

3）C：原来是40的时候，收入=40*35-1050=350，40*20%=42，收入=42*35-1050=420，因此，提升为：（420-350）/350，我这个解题思路是不是 很笨？能不能用？

思路没问题

中间有一行我理解是手误，应该是：40*(1+5%)=42

解题思路可以用，只是可能相比直接使用 DOL，计算量会更大一些

另外，选项 C 其实考查的是 DOL 的「定义」式，咱们在做题的过程中，除了做对解答，也建议总结一下，看一下站在「出题人」的角度，想考查什么考点，考查的角度是什么，这样备考效率会更高哈

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