The average cost of shares or fund units bought at different prices, what averaging down does to your break-even, and why the cost method changes the gain you report on a sale.
Your average cost per share is the total amount you paid, dealing fees included, divided by the number of shares you hold. An investor who bought 50, 30 and 40 units of an index fund at 40, 32 and 25, paying a 5 fee each time, has spent 3,975 on 120 units: an average cost of 33.125 a unit, not the 32.33 you get by averaging the three prices. At today's price of 30 the holding is down 9.43 per cent and needs a 10.42 per cent rise to break even.
Worked in full in Stock Market Investing for Beginners by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Anyone who invests a fixed amount every month, or adds to a holding after a fall, ends up owning one position bought at many prices. The average cost is the price at which that position breaks even, the base for the gain or loss on your statement, and in many tax systems the base for the gain you declare when you sell. Brokers show it, but they do not always include fees, and they do not always use the method your tax authority uses.
| Purchase | Units | Price | Cost | Fee | Total |
|---|---|---|---|---|---|
| First | 50 | 40.00 | 2,000 | 5 | 2,005 |
| Second, after a fall | 30 | 32.00 | 960 | 5 | 965 |
| Third, after a further fall | 40 | 25.00 | 1,000 | 5 | 1,005 |
| Holding | 120 | 3,960 | 15 | 3,975 |
The fund now trades at 30. Prices and fees are illustrative, in any currency.
Average cost = (sum of units × price + sum of fees) / total units
Gain or loss = units × current price − total cost
Rise needed to break even = average cost / current price − 1
In Excel, units in B2:B4, prices in C2:C4, fees in D2:D4: =(SUMPRODUCT(B2:B4,C2:C4)+SUM(D2:D4))/SUM(B2:B4)
Step 1, total cost. 2,000 + 960 + 1,000 = 3,960 for the units, plus 15 of fees: 3,975.
Step 2, divide by units. 3,975 / 120 = 33.125. Without fees it would be 33.000; the fees add 0.125 a unit.
Step 3, compare with the price. 120 units at 30 are worth 3,600, a loss of 375, or 9.43 per cent of what was paid. The price needs to rise from 30 to 33.125, which is 10.42 per cent, for the position to break even. Note that the loss is measured on cost and the recovery on today's price, so the two percentages differ, for the reason worked in how much gain recovers a stock market loss.
It helps to see the average after each purchase, because that is what your statement showed at the time. After the first purchase it was 40.10. After the second, 2,970 for 80 units: 37.125. After the third, 33.125. Each purchase at a lower price pulls the average down, by an amount that depends on how many units it adds relative to the units already held.
The third purchase is the one people agonise over: buy more after a fall, or not? Here is what different sizes of that purchase do, holding the first two fixed and buying at 25.
| Units bought at 25 | Units held | Total cost | Average cost | Rise needed from 25 |
|---|---|---|---|---|
| 0 | 80 | 2,970 | 37.125 | 48.5% |
| 20 | 100 | 3,475 | 34.750 | 39.0% |
| 40 | 120 | 3,975 | 33.125 | 32.5% |
| 80 | 160 | 4,975 | 31.094 | 24.4% |
Averaging down lowers the break-even, but only by committing more money to the same holding: the line with 80 extra units needs a 24.4 per cent rise instead of 48.5, and has 4,975 at stake instead of 2,970. For a broad index fund bought on a regular plan that is simply the plan working, the point made in dollar-cost averaging vs lump sum. For a single company whose price has halved for a reason, a lower average is not a reason to buy.
Averaging the prices. (40 + 32 + 25) / 3 = 32.33 ignores that more units were bought at some prices than others, and ignores fees. It understates the cost by 0.79 a unit, 95.00 on the holding, and makes the position look closer to break-even than it is.
Assuming the average is the tax base. Suppose you sell 60 units at 36, receiving 2,155 after the fee. On the average cost method those 60 units cost 1,987.50 and the gain is 167.50; the 60 units left keep their 33.125 average. On a first in, first out basis the units sold are the 50 bought at 40 and 10 of those bought at 32, which cost 2,326.67 with their share of fees, and the same sale is a loss of 171.67. The two methods differ by 339.17 on one sale.
Which method applies is a matter of local tax rules and, in some countries, of the election you make with your broker. The UK pools shares of the same company at their average cost; US brokers default to first in, first out for shares unless you choose otherwise. Check before you sell, not after.
Stock Market Investing for Beginners makes the case for regular, low-cost buying of broad funds; the free workbook and working documents for the book put figures on its compounding and cost illustrations.
Because each price must be weighted by the number of shares bought at it, and fees added. Buying 50, 30 and 40 shares at 40, 32 and 25 averages 33.000 before fees and 33.125 after 15 of fees, while the simple average of the three prices is 32.33. Using the simple average understates the cost by 95.00 on 120 shares.
Yes, but by putting more money at risk. Before the third purchase, 80 shares cost 37.125 each and needed a 48.5 per cent rise from 25 to break even. Buying 40 more at 25 lowers the average to 33.125 and the required rise to 32.5 per cent, with 1,005 more invested in the same holding.
Under the average cost method, no: the remaining shares keep the 33.125 average. Selling 60 at 36, net of a 5 fee, gives a gain of 167.50 on that basis. Under first in, first out, the shares sold are the first 50 at 40 and 10 at 32, and the same sale shows a loss of 171.67.
This article is one calculation from Stock Market Investing for Beginners. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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