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goods that were bought rst ( rst-in) are the rst goods to be sold ( rst out), and the goods that remain on hand (ending inventory) are assumed to be made up of the latest costs. Therefore, for income determination, earlier costs are matched with revenue and the most recent costs are used for balance sheet valuation. This method is consistent with the actual ow of costs, since mer chandisers attempt to sell their old stock rst. (Perishable items and highfashion items are examples.) FIFO is the most widely used inventory method of those that will be discussed. Under FIFO, those goods left at the end of the period are considered to be those received last. Therefore, the 320 units on hand on December 31 would be costed as follows: Most recent purchase (10/4) Next most recent purchase (6/6) Ending inventory 250 units @ $10 = $2,500 70 units @ $ 9 = 630 320 units $3,130

CHAP. 6]

1 We take the absolute values to make sure that the logarithm is de ned. In practice, we shall omit the absolute values when it is clear that the functions are nonnegative.

For the ampli er of Fig. 6-32, nd expressions for (a) the voltage-gain ratio Av vL =vs and current-gain ratio Ai iL =is . Assume that hre hoe % 0. Ans: a Av hfe RC RL =f RC RL hfe 1 RE hie g; b Ai hfe RC = RC RL

CC iL + LL _

and then to differentiate, 1 1 Dx y = 2 y x Therefore, Dx y = y 4 6 2 + x 8x + 5 2x 1 = + 2 4 6 1 1 1 8 3 2 = + 2 8x + 5 2x 1 x 8x + 5 2x 1 4 6 x 2 8x + 5 2 + 8x + 5 2x 1 (2x 1)3 x

Fig. 6-32

Find expressions for (a) Rin and (b) Ro for the ampli er of Fig. 6-32 if hre hoe % 0. Ans: a Rin hie hfe 1 RE ; b Ro RC Suppose v2 is replaced with a short circuit in the di erential ampli er of Fig. 3-22. Find the input impedance Rin1 looking into the terminal across which v1 appears if RB 20 k ; RE 1 k ; hie 25 ; hfe 100; and hre hoe % 0. Ans: 9:11 k For the Darlington-pair emitter-follower of Fig. 6-33, hre1 hre2 hoe1 hoe2 0. In terms of the (non0 zero) h parameters, nd expressions for (a) Zin ; (b) the voltage gain Av vE =vs ; c the current gain Ai ie2 =iin ; d Zin ; and (e) Zo (if the signal source has internal resistance RS ). Ans: a c e

The latest cost of the inventory consists of 250 units at $10. Howev er, since the ending inventory consists of 320 units, we must refer to the next most recent purchase of 70 units at $9. Therefore, you could say that the process for determining the cost of the units on hand involves work ing backward through the purchases until there is a suf cient quantity to cover the ending inventory count. Thus the ending inventory under the FIFO method would be valued and recorded at $3,130. The costs of goods sold can be determined by subtracting the value of the ending inventory from the total value of the inventory available for sale ($6,100 $3,130 = $2,970). Since 320 units remain as ending in ventory, the number of units sold is 380. It should be noted that as a method of assigning costs, FIFO may be used regardless of the actual physical ow of merchandise. Indeed, we might say that FIFO really stands for rst-price in, rst-price out. In a pe riod of rising prices, in ation, the FIFO method will yield the largest in ventory value, thus resulting in a larger net income. This situation occurs because this method assigns an inventory cost based on the most recent, higher costs. Conversely, the FIFO method would produce a smaller cost of goods sold, because the earlier, lower costs are assigned to the cost of goods sold.

This procedure of rst taking the logarithm and then differentiating is called logarithmic differentiation.

0 Zin hie1 hfe1 1 hie2 hfe2 1 RE ;