average的问题

问题如下：

Crux’s inventory turnover ratio computed as of 31 December 2009, after the adjustments suggested by Groff, is closest to:

选项：

A.

5.67.

B.

5.83.

C.

6.13.

解释：

B is correct.

Crux’s adjusted inventory turnover ratio must be computed using cost of goods sold (COGS) under FIFO and excluding charges for increases in valuation allowances.

COGS (adjusted) = COGS (LIFO method) – Charges included in cost of goods sold for inventory write-downs – Change in LIFO reserve = $3,120 million – 13 million – (55 million – 72 million) = $3,124 million

Note: Minus the change in LIFO reserve is equivalent to plus the decrease in LIFO reserve. The adjusted inventory turnover ratio is computed using average inventory under FIFO.

Ending inventory (FIFO) = Ending inventory (LIFO) + LIFO reserve

Ending inventory 2009 (FIFO) = $480 + 55 = $535

Ending inventory 2008 (FIFO) = $465 + 72 = $537

Average inventory = ($535 + 537)/2 = $536

Therefore, adjusted inventory turnover ratio equals:

Inventory turnover ratio = COGS/Average inventory = $3,124/$536 = 5.83

考点：LIFO、FIFO转换公式

解析：为了实现三个公司ratio的可比性，Groff建议把LIFO转成FIFO，三个公司Crux和Mikko都是用LIFO，本题是让计算Crux公司转换为FIFO之后的inventory turnover ratio。

inventory turnover ratio=COGS/average inventory

• inventory的转换直接用公式：Ending inventory (FIFO) = Ending inventory (LIFO) + LIFO reserve
• COGS转换公式：COGSF = COGSL – Δ LIFO reserve

本题还有一个条件：调整的时候假设没有valuation allowance。

这里的valuation allowance是存货的一个备抵账户，其原理类似于depreciation：

1、产生valuation allowance的时候要增加valuation allowance，存货的net value就相应减少。

2、同时allowance要体现在COGS中，在COGS里加上相应的金额，以减少Net income。

如果假设没有这个备抵账户，那么存货减少的部分就要加回，我们这里不需要手动加回，因为题目给了存货gross的金额和net 的金额，其中net是扣掉了valuation allowance的，gross是没有扣减的，我们用gross inventory对应的数字来套公式即可。

但COGS要手动调整一下，有valuation allowance的话COGS里就包括这部分，如果没有的话我们就要从COGS里减掉之前计提的allowance，所以COGS转换公式就变成：

COGSF = COGSL –Charges included in cost of goods sold for inventory write-downs- Δ LIFO reserve

注意，如果题目没有提到assume no valuation allowance，那么直接用COGSF = COGSL – Δ LIFO reserve公式转换即可。