I’m working through this chapter that covers LIFO vs FIFO and converting between the two. I’m a little stuck on problem #4. It says in the problem that 70% of Zenab’s inventory is calculated under LIFO; 30% is under FIFO. So the question is, how do we get Zenab to 100% LIFO? In other words, how do we get COGS to reflected 100% LIFO, as the ratios in the appendix (pp A-17 and pp A-18) indicate. And why can’t we compute inventory at 100% LIFO? Also, with converting Faybech to LIFO, I know that COGS(LIFO) = COGS(FIFO) + BI x r r is calculated as LIFO Effect/BI. So how did we get the figures in p A-18 for Faybech? I’m typing this right now at a college library. I’ll probably have more questions about this when I get home. Volume 3–and particularly the current study sessions and readings–is definitely a time consuming reading. While the concepts are familiar, disassembling the ideas and putting the pieces back together takes a lot of time.

May anyone help?

Hi, gdiddy. The solution presented in the Appendix masks many arduous and lengthy intermediate steps. I was able to recalculate all of the the numbers presented in the solution, but will need have more specifics in terms of which numbers in the solution you are trying to recalculate. It would be efficient if you could specificy, for example, 4A(ii) and let me know the number in the solution you are trying to calculate. Thank you.

Two things I’m trying to figure out: How did the appendix arrive at the ratios at the bottom of page A-17? Specifically, how did we convert Zenab’s COGS from 70%LIFO/30%FIFO to 100% FIFO to arrive at gross margin of 0.332 and pretax income/sales of 0.047? I’ve tried numerous calculations but cannot come up with the ratios given on 4©(ii). Furthermore, how did the book arrive at Faybech’s COGS of 53,675 after converting from FIFO to LIFO (top of A-18, 4©(ii)? I thought when convertin from FIFO to LIFO COGS, we need to add the product of beginning inventory and rate of increase in prices to FIFO COGS. What were the inputs to calculate 53,675? Thanks.

Hi, giddy. You asked about the following questions in question 4(ii): (1) The gross profit margin of 0.332 and the pretax income/sales of 0.047 for Zenab under a LIFO COGS regime (2) The $53,675 for Faybech under the LIFO COGS regime. To answer either of these two questions, you need to compute the (industry) inflation index r. As we do not have industry information available, we will, as the reading suggests, use data from a competing firm, which in this case is Zenab. To be sure that the Zenab¡¯s data will yield a reasonable estimate, we visually inspect to the see that Zenab¡¯s FIFO inventory balances in 2001 and 2002 are fairly close. This turns out to be the case, since the ending balances for Zenab¡¯s inventory are $24,900 and $25,200 in 2001 and 2002, respectively. As such, we should apply the following formula to Zenab: (*) r=(Change in “LIFO reserve” )/BI_F Now, the numerator is straightforward: $5,100 less $3,600, or $1,500. The denominator is a bit tricky to apply, as this problem is not as straightforward as the example given in the reading. The reason there is a twist is that the BIF is not $24,900. Why? The reason is that, unlike the examples in the reading that assume BI_F is (pure) FIFO, the beginning balance in 2002 (i.e., the ending balance in 2001) is not. As stated in the problem, Zenab has 70% of its ending inventory in FIFO and 30% of its inventory in FIFO. So, in 2001, the entire FIFO balance of Zenab¡¯s inventory is $24,900 + $3,600 = $28,500. So it appears that we can say BI_F = $28,500. In this case, we would be naively WRONG!! Why is BI_F = $28,500 wrong? Recall that the spirit behind equation (*) is to find the (specific) inflation index for the inventory in question. So, really we want to the LIFO reserve to be matched to the part of the LIFO inventory it is adjusting. If part of the inventory is already in FIFO, then there is no need to adjust this part of the ending inventory balance. So the formula should really read: (**) r=(Change in LIFO reserve )/“BI_F restricted to the LIFO portion of inventory” So what part of Zenab’s ending 2001 inventory is LIFO? Seventy percent, of course! So this is a very neat conceptual breakthrough. However, there appears to be some judgment involved in determining what the phrase “BIF restricted to the LIFO portion of inventory” actually means in terms of our calculation. This is where I differ from the text¡¯s conversion. I believe that the inflation index should be based on strictly that portion of the ending inventory to which the LIFO reserves applies. Presumably, we apply the LIFO reserve to only the LIFO portion of the inventory. As such, we would be inclined to write: r=$1,500/(70% “of” $24,900)=0.0860 However, the text’s calculation of r (which is not shown in the answer key) is as follows: r=$1,500/(70% “of” ($24,900+$3,600))=0.0751 Applying the text’s value of r to Faybech, we have that Faybech’s 2002 LIFO COGS is: $52,000 + ($22,300 times 0.0751) = $53,675. This much gets us the Faybech side of the problem. The Zenab side of the problem is not done, since we need to convert the mixed reported COGS of $61,300 to LIFO COGS. To do this, we need to figure out what 2002 inventory purchases are. We use the time honored method of a balance roll-forward, i.e., $24,900 (beginning reported) + Purchases - $61,300 (COGS reported) = $25,200 (reported ending). So 2002 purchases are $61,600. Now convert the 2002 reported beginning and reported ending inventory balances to FIFO: -------------------------------------Reported-------LIFO reserve------FIFO Beginning Inventory-------------24,900----------3,600-------------28,500 Ending Inventory-----------------25,200----------5,100-------------30,300 Apply the balance roll-forward method again: $28,500 (FIFO beginning) + $61,600 (Purchases) - COGS FIFO = $30,300 (FIFO ending). So COGS FIFO is $59,800. We now can apply the conversion formula from COGS FIFO to COGS LIFO as follows: COGS LIFO = $59,800 + ($28,500 times 0.0751) = $61,940. Now gross margin for Zaneb is $92,700 - $61,940 = $30,760. The gross profit margin is thus $30,760/$92,700 = 0.332. Subtracting selling and general expense of $26,400 from the gross margin of $30,760 gives a pretax income of $4,360. As fraction of sales, this pretax income of $4,360 is 0.047. Hope this helps.

Hey cadlag, Thanks for the detailed writeup, I really appreciate it. Your post is so long that I’m going to print it out and carry it in my book. Regarding the calculation of r, I’m not sure I understand why we are computing the rate of growth only the LIFO portion of inventory. I guess what I’m confused about is, why does the formula use a denominator of beginning inventory FIFO, when you’re talking of measuring the rate of increase on the beginning inventory FIFO restricted to LIFO portion? Didn’t we add the LIFO reserve amounts to current assets on 4©(i) to calculate current ratios and inventory turnover under a FIFO scenario? Thanks again.

Hi, gdiddy. Your follow-up question goes to the very heart of this problem. I think the explanation in my above solution relating to your follow-up question is skimpy so that I will elaborate here. In fact, there is a typo in my write-up above, but it does not change how I arrived that the Appendix’s numbers. It only changes my personal opinion on the Appendix’s solution method. Let us go back to the fundamentals of the inflation index, r. By definition, it is the change in the LIFO reserve divided by the beginning FIFO balance. Naturally, you would then want to find out what Zaneb’s beginning inventory balance in 2002 is in terms of FIFO numbers, right? Based on the information given, you would take the reported mixed LIFO/FIFO balance of $24,900 and add the LIFO reserve of $3,600 to get the beginning 2002 FIFO beginning balance of $28,500. Nothing wrong so far, right? Now think about what makes up the $24,900: $17,430 (i.e., 70% LIFO) and $7,470 (i.e., 30% FIFO). When you are trying to calculate the inflation index, you don’t need to take into the account the $7,740 portion of the 2002 beginning balance because FIFO accounting already leaves inventory balances that are reflective of market prices and inflation. What you do need to be concerned about is the $17,430 LIFO portion – remember LIFO inventory balances generally are not reflective of market prices and inflation. Upon converting the $17,430 to FIFO, you should be able to get a sense of what inflation is really like for Zaneb’s inventory holdings. To do the conversion, I personally think we ought to do this: 70% of $24,900 plus $$3,600 = $17,430 + $3,600 = $21,030. The inflation index would then be $1,500/$21,030 = 0.0713. The text’s method is slightly different. It takes 70% of ($24,900 + $3,600) = $19,950. So the text’s inflation index (which is not shown at all) is $1,500 / $19,950 = 0.0751. I hope there is a faster way to do this problem. If there is not, then I am very surprised by how silent the Appendix is with regard to how the inflation index is arrived at. Conceptually and technically, it is such a crucial aspect of this problem to have been omitted entirely in the Appendix. Actually, there is another view of the defintion of the inflation index that may illuminate this whole discussion, but I think I had better stop here. Many more readings to get to. Hope this helps.