# Problems for CFA Level I

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1 Problems for CFA Level I Analysis of Inventories 1. Assume that purchases and unit costs throughout the year were as in Table 1. Inventory at beginning of Quarter I: 400 units at \$20 per unit = \$8,000. Inventory at end of Quarter IV: 600 units. (a) Calculate reported inventory at the end of the year under each of the following inventory methods: (i) FIFO Answer: 800 units have been sold throughout the year, 400 at \$20 per unit, 200 at \$22 per unit and 200 at \$24 per unit, for a total of COGS F = = \$17, 200. Since EI = BI + P COGS, this gives us EI F = 8, , , 200 = \$15, 800. There is a much simpler way to get this answer. We know that the ending inventory is 600 units, which is composed of 200 units at \$28 per unit, 300 units at \$26 per unit and 100 units at \$24 per units, for a total value of EI F = = \$15,

2 (ii) LIFO Answer: In this case, 200 units have been sold at \$28 per unit, 300 units have been sold at \$26 per unit and 300 units have been sold at \$24 per unit, for a total of Since this gives us COGS L = = \$20, 600. EI = BI + P COGS, EI L = 8, , , 600 = \$12, 400. Using the simpler method, we know that under LIFO, the 600 units in ending inventory is composed of 400 units at \$20 per unit and 200 units at \$22 per unit for a total of (iii) Average cost EI L = = \$12, 400. Answer: The total cost of all units purchased and all units in inventory at the beginning of the year is for an average cost of 25, , 000 = \$33, 000, 33, 000 1, 400 = \$ The value of ending inventory under the average cost method is then EI W = = \$14, 143. (b) Calculate the cost of goods sold for the year under each method listed in (a). Answer: COGS under the FIFO and LIFO methods are \$17,200 and 20,600, respectively. COGS under the average cost method is = \$18,

3 (c) Discuss the effect of the differences among the three methods on (i) Reported income for the year. Answer: Reported income will be highest under the FIFO method and lowest under the LIFO method. Reported income under the average cost method will lie in between. (ii) Stockholders equity at the end of the year. Stockholders equity will be highest under the FIFO method since earnings retained will be highest in this case. The LIFO method will produce the lowest stockholders equity and the average cost method will yield a stockholders equity in between. 2. Compare the effect of the use of the LIFO inventory method with the use of the FIFO method on each of the following, assuming rising prices and stable inventory quantities: (i) Gross profit margin Answer: Since COGS F < COGS L, Sales COGS F Sales > Sales COGS L. Sales (ii) Net income Answer: Same answer as in (i). (iii) Cash from operations Answer: Cash from operations is greater under the LIFO method because taxes are lower. (iv) Inventories Answer: The value of inventories is higher under the FIFO method. (v) Inventory turnover ratio Answer: Inventory turnover ratio is higher under the the LIFO method since COGS is higher under this method. 3

4 (vi) Working capital Answer: Same relationship as with inventories, i.e. method. higher under the FIFO (vii) Total assets. Answer: Same as in (vi). (viii) Debt-to-equity ratio Answer: Greater equity under the FIFO method. 3. The M&J Company begins operations on January 1, 20X0 with the balance sheet on Table 2. During the year, the company maintains its inventory accounting using the FIFO method. Before a provision for income tax, the balance sheet at December 31, 20X0, is as in Table 3. M&J has 20X0 sales of \$25,000. The company sells half of the units purchased during the year. Operating expenses (excluding COGS) are \$12,000. Prior to issuing financial statements, the company considers its choice of inventory method. Assume a tax rate of 40% and a dividend payout ratio of 50%. (a) Using the information provided, complete Table 4. Answer: Having the pretax income under the FIFO method, we can find COGS F as follows: COGS F = Sales Other expenses Pretax income F = 25, , 000 5, 000 = 8, 000. The tax rate being 40%, taxes paid under the FIFO method are Taxes F =.4 5, 000 = 2, 000 and thus FIFO net income is NI F = 5, 000 2, 000 = 3,

5 Units Per Unit Dollar Unit Quarter Purchased Cost (\$) Purchases (\$) Sales I , II , III , IV , Year 1,000 25, Table 1: Information for Question 1. Cash 10,000 Common Stock 10,000 Table 2: M&J s starting balance sheet. Cash 5,000 Common Stock 10,000 Inventory 10,000 Pretax Income 5,000 15,000 15,000 Table 3: M&J s closing balance sheet, before taxes. 5

6 With a payout ratio of 50%, this means dividends and retained earnings of \$1,500 each. Since beginning inventory is zero, (inventory) purchases are given by Purchases = COGS F + EI F = 8, , 000 = 18, 000. Hence cash from operations under the FIFO method is CFO F = Sales Purchases Other expenses Taxes F = 25, , , 000 2, 000 = 7, 000. Note that purchases are not affected by the inventory method. Once taxes are taken into account, the FIFO cash balance is After-tax cash balance F = Pre-tax cash balance F Taxes F Dividends F = 5, 000 2, 000 1, 500 = 1, 500. Another way to find the FIFO cash balance is to add the cash from operations from the starting cash balance, which gives After-tax cash balance F = Starting cash balance F + CFO F Dividends F = 10, ( 7, 000) 1, 500 = 1, 500. Under the LIFO method, since half of the purchases are sold during the year, COGS and ending inventory are the reverse of what we obtained with the FIFO method. That is, since purchases are equal to COGS plus ending inventory (recall that beginning inventory is zero), half the units purchased during the year is worth \$8,000 and the other half is worth \$10,000. Given the FIFO pretax income, we 6

7 found earlier that the first half of the units purchased are worth \$8,000 and the second half is worth \$10,000. Hence COGS L = 10, 000 and EI L = 8, 000. This gives us a pretax income of \$3,000 and thus a net income of \$1,800. LIFO Cash for operations is CFO L = Sales Purchases Other expenses Taxes L = 25, , , 000 1, 200 = 6, 200 and thus closing cash balance is 10, 000 6, = 2, 900. To find the figures for the weighted average method, the procedure is the same. The results of these calculations can be seen on Table 5. (b) Prepare a balance sheet for M&J at December 31, 20X0, assuming use of the: (i) LIFO inventory method Answer: See Table 6. (ii) Weighted-average method Answer: See Table 7. (iii) FIFO inventory method Answer: See Table The Zeta Corp. uses LIFO inventory accounting. The footnotes to the 20X4 financial statements contain the data in Table 9. You are also provided with the following data: The company has a marginal tax rate of 35%. COGS for 20X4 is \$3,800,000. Net income for 20X4 is \$340,000. Return on equity for 20X4 is 4.6%. (a) Calculate 20X4 net income for Zeta, assuming that it uses the FIFO inventory method. 7

8 Weighted FIFO Average LIFO Sales 25,000 25,000 25,000 COGS Other expenses 12,000 12,000 12,000 Pretax income Income tax expense Net income Dividends paid Retained earnings Cash from operations Closing cash balance Closing inventory Inventory purchases Table 4: Table to be completed for Question 3. Weighted FIFO Average LIFO Sales 25,000 25,000 25,000 COGS 8,000 9,000 10,000 Other expenses 12,000 12,000 12,000 Pretax income 5,000 4,000 3,000 Income tax expense 2,000 1,600 1,200 Net income 3,000 2,400 1,800 Dividends paid 1,500 1, Retained earnings 1,500 1, Cash from operations -7,000-6,600-6,200 Closing cash balance 1,500 2,200 2,900 Closing inventory 10,000 9,000 8,000 Inventory purchases 18,000 18,000 18,000 Table 5: Completed table for Question 3. 8

9 Answer: Under the FIFO method, COGS is COGS F = COGS L Change in LIFO reserve = 3, 800, 000 4, 000 = \$3, 796, 000. Since Net income = (1 t)(sales COGS), sales in 20X4 are Sales = Net income 1 t + COGS = 340, , 800, 000 = \$4, 323, 077 and thus NI F =.65 (4, 323, 077 3, 796, 000) = \$342, 600. Note that the change in net income is given by (1 t) COGS =.65 4, 000 = 2, 600. (b) Calculate the company s inventory turnover ratio on both a FIFO and LIFO basis. Answer: Under the FIFO method, the inventory turnover ratio is 3, 796, 000 (794, , 800)/2 = Under the LIFO method, the inventory turnover ratio is 3, 800, 000 (748, , 800)/2 = (c) Calculate Zeta s return on equity on a FIFO basis. Answer: ROE under the LIFO method is 4.6% and thus average equity under this method is AE L = NI L.046 = 340, = \$7, 391, 304. If the FIFO were used by Zeta, its shareholders equity in each year would be greater by an amount equal to the after-tax value of the LIFO reserve and thus 9

10 average equity under the FIFO method is given by and thus (1.35) (46, , 000) AE F = AE L + 2 = 7, 391, , 200 = 7, 422, 504 ROE F = 342, 600 7, 422, 504 = 4.6%. (d) Discuss the usefulness of the adjustments made in parts (a), (b) and (c) to a financial analyst. Answer: The main objective of these adjustments is to allow better comparisons between different companies. (e) Describe alternative measures of inventory turnover and return on equity that would be more useful to assess Zeta s operating performance. Answer: The current cost method. That is, COGS and net income measured under the LIFO method and inventory and shareholders equity measured under the FIFO method. 5. The data in Table 10 were obtained from annual reports of Stride-Rite [SRR], a shoe manufacturer and retailer. (a) Compute the gross margin percentage for each year. Answer: Gross margin is 36.37% in 1997, 35.38% in 1998 and 36.77% in (b) Stride-Rite disclosed the effect of LIFO liquidation net of income tax. Asssuming a tax rate of 35%, recompute Stride-Rite s gross margin for the years after removing the effect of LIFO liquidations. Answer: LIFO liquidation being recorded on an after-tax basis, LIFO before liquidation is 3, = 5, 198 in 1997, 1, = 2, 666 in 1998 and 0 in

11 Cash 2,900 Common Stock 10,000 Inventory 8,000 Retained earnings ,900 10,900 Table 6: M&J s LIFO balance sheet. Cash 2,200 Common Stock 10,000 Inventory 9,000 Retained earnings 1,200 11,200 11,200 Table 7: M&J s weighted-average balance sheet. Cash 1,500 Common Stock 10,000 Inventory 10,000 Retained earnings 1,500 11,500 11,500 Table 8: M&J s FIFO balance sheet. 20X3 20X4 Raw material 392, ,725 Finished products 401, ,075 Inventory on FIFO basis 794, ,800 LIFO reserve (46,000) (50,000) Inventory on LIFO basis 748, ,800 Table 9: Data for Question Sales 515, , ,696 COGS 328, , ,108 Gross profit 187, , ,588 LIFO liquidation (net of taxes) 3,379 1,733 0 Table 10: Data for Question 5. 11

12 LIFO liquidation being 0 in 1999, the gross margin is the same before and after adjusting for LIFO liquidation. For the two previous years, however, adjusted gross profit margins are 187, 556 5, , 728 = 35.36% in 1997 and 190, 826 2, , 413 = 34.88% in (c) Explain why the trend in gross margins shown in part (b) is a better indicator of Stride-Rite s performance than the reported gross margins. 12

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