Average Cost Computations

by Victor T. Norton, Jr., Ph.D. - Mathematics

How do you determine the average cost basis and the corresponding gain or loss on shares redeemed from a mutual fund? This is the question addressed in this paper. But first a word of warning. You can only use one method to determine the cost of shares redeemed from a particular mutual fund account. If you use the "first in first out" method on a partial redemption, you can not use the average cost method later, and visa versa.

An Example

Here is a short example that illustrates an average cost computation. The table represents all activity in a particular mutual fund account during the two year period 1994-95.

Trade Date	Transaction	Shares Traded	Share Price	Dollar Amount	Total Shares	Total Cost	Avg Cost	Cost Basis	+Gain -Loss
					0.000	0.00
01/15/94	Initial Purchase	399.361	12.52	5,000.00	399.361	5,000.00	12.52
07/20/94	Purchase	707.714	14.13	10,000.00	1,107.075	15,000.00	13.55
12/15/94	Div Reinvest	9.323	14.25	132.85	1,116.398	15,132.85	13.56
12/15/94	CG Reinvest	13.984	14.25	199.27	1,130.382	15,332.12	13.56
06/13/95	Redemption	-509.554	15.70	-8,000.00	620.828	8,420.70	13.56	-6,911.42	+1,088.58
12/15/95	Div Reinvest	2.631	16.52	43.46	623.459	8,464.16	13.58
12/15/95	CG Reinvest	7.892	16.52	130.37	631.351	8,594.53	13.61

All transactions that occurred during the 1994-95 period are recorded. In particular, all reinvested distributions from the fund must be included. A single redemption, or sale, occurs on June 13, 1995. The redemption data, the shares sold, the amount received, and the average cost basis of the shares sold, appear as negative numbers. Each of the 509.554 shares sold has an average cost of 15,332.12/1,130.382 = $13.56366 to 5 decimal accuracy. The cost basis of these shares is therefor

    509.554 * 13.56366 = $6,911.42

Formulas

The table was generated from the given transaction data with a spread sheet using the following formulas.

Trade Date	date = DATA
Transaction	description = DATA
Shares Traded	shares = DATA
Share Price	price = amount/shares
Dollar Amount	amount = DATA
Total Shares	tot_shares = ROUND( previous_tot_shares + shares, 3 )
Total Cost	tot_cost = ROUND( previous_tot_cost + cost, 2 )  cost = basis IF shares < 0 AND amount < 0 amount OTHERWISE
Avg Cost	avg_cost = tot_cost/tot_shares
Cost Basis	basis = ROUND( shares * previous_avg_cost, 2) IF shares < 0 AND amount < 0
+Gain or -Loss	gain = -(amount - basis) IF shares < 0 AND amount < 0

Most mutual fund companies record numbers of shares to 3 decimal places. In accordance with this practice we continually round the accumulated total number of shares to 3 decimal places. We round the accumulated total cost of these shares to 2 decimal places, a dollars and cents value. Binary computers cannot record decimal data accurately. Without such continual rounding extraneous errors might appear in the accumulated totals. We also round the cost basis of shares sold to 2 decimal places to be assured of a dollars and cents value here.

The average cost per share is not rounded in any way (though it is displayed with 2 decimal accuracy). If the average cost of the 509.554 shares sold were rounded to $13.56, then the cost basis of these shares would be 13.56 * 509.554 = $6,909.55. This figure is simply not correct (though it might well be reported by some fund companies). The last three digits are artifacts of the rounding process and have no relation to the actual cost of the shares sold.

The gain on shares sold is the amount received less the cost basis of the shares. In our example,

    gain = $8,000.00 - $6,911.42 = $1,088.58

We record the amount and basis as negative numbers, however. The leading minus sign in the gain formula is a double negative, so to speak. It serves to render gains positive and losses negative.

Long term and short term gains

For income tax purposes gains must be separated into long and short term. First in first out always applies here. Of the 509.554 shares sold, 399.361 shares were purchased more than a year before the sale; the remaining shares are short term. The gain on the sale must be divided into long and short term in the same proportions:

    $1,088.58 = $853.17 long term + $235.41 short term

Wash Sales

A wash sale occurs when you sell shares at a loss and purchase shares within 30 days before or after the sale. The loss on the number of shares purchased is disallowed for tax purposes, not allowed to cancel gains.

Many bond funds distribute dividends monthly. Any partial redemption at a loss from such a fund automatically incurs a wash sale. Here is a simple example.

A portion of the initial (not accounting for the wash sale) record

Trade Date	Transaction	Shares Traded	Share Price	Dollar Amount	Total Shares	Total Cost	Avg Cost	Cost Basis	+Gain -Loss
	accumulations from previous transactions				2,000.000	19,000.00	9.50
09/30/94	Div Reinvest	13.333	8.10	108.00	2,013.333	19,108.00	9.49
10/25/94	Redemption	-623.441	8.02	-5,000.00	1,389.892	13,191.09	9.49	-5,916.91	-916.91
10/28/94	Div Reinvest	13.400	8.00	107.20	1,403.292	13,298.29	9.48

A portion of the final (accounting for the wash sale) record

Trade Date	Transaction	Shares Traded	Share Price	Dollar Amount	Total Shares	Total Cost	Avg Cost	Cost Basis	+Gain -Loss
	accumulations from previous transactions				2,000.000	19,000.00	9.50
09/30/94	Div Reinvest	13.333	8.10	108.00	2,013.333	19,108.00	9.49
10/25/94	Redemption	-623.441	8.02	-5,000.00	1,389.892	13,191.09	9.49	-5,916.91	-916.91
10/25/94	Wash Sale: Loss Disallowed			39.32	1,389.892	13,230.41	9.52		+39.32
10/28/94	Div Reinvest	13.400	8.00	107.20	1,403.292	13,337.61	9.50

A total of 623.441 shares were sold at a loss. Due to the monthly reinvestment of dividends, however, 26.733 shares were purchased within 30 days of the sale. The loss on this number of shares is disallowed for tax purposes. Since the purchased shares make up 4.28798% of the shares sold, this proportion of the loss, namely $39.32, is disallowed. In compensation, the total cost of the remaining shares is increased by $39.32.

Other Costs

In a wash sale the disallowed loss is accumulated in the increased cost of the remaining shares. The wash sale transaction shows a positive dollar amount though no shares are traded. Other costs--redemption fees, deferred sales charges, closeout costs, service fees, and so forth--can sometimes be recorded in the same way, as positive dollar amounts without corresponding increases in the number of shares. Often, however, a fund "sells" so many of your shares to pay for one charge or another. This type of transaction requires a negative number of shares traded, as in a normal redemption, but no corresponding dollar amount, since you don't actually receive any money.

Fees, disallowed looses, and other costs increase the average cost of your shares. There is another kind of transaction that diminishes the average cost per share, where no shares are traded but a negative dollar amount must be entered. This happens when a fund decides that past dividend distributions were, in part, "distributions of capital." A negative dollar amount, corresponding to the total distribution of capital, serves to cancel the previous, erroneous dividend declarations.

Conclusion

We have attempted to describe how average cost computations can be carried out on a spread sheet. Ideally the average cost of your shares will be much less than the NAV when you decide to sell. Good luck in achieving this ideal!