DCA Calculator: Cost Averaging vs Lump Sum

About the DCA Calculator: Cost Averaging vs Lump Sum

Dollar-cost averaging (DCA) means buying the same amount at regular times, whatever the price. This calculator replays it on prices you supply — typed or pasted with their dates, or a price file you export from your own broker, exchange or charting app — and shows what the plan bought: the average cost per unit, the units, the money put in, the value and the gain, the XIRR of every buy, the deepest fall of the account below the money put in, and each buy in a table.

Beside it, the same money invested all at once at the first buy, and value averaging, which buys enough at each date to bring the holding up to a target that rises every time (and sells when the holding is above it). Buy at every price, once a week or once a month, with a fee in percent or a fixed amount per buy, in any currency and for any market: shares, funds, coins or gold.

The replay is a look at the past prices you gave it. It uses no market data, and nothing you type or load leaves your browser.

Common uses

• Replay a monthly buying plan on the price history you exported, to see its average cost and XIRR.
• Compare regular buying with investing the same money at once, on the same prices.
• See how much cash value averaging calls for after a fall before you choose it.
• Check how deep below the money put in a regular plan went in a falling market.

The formulas

• Each buy: units = (amount − fee) ÷ price, at every price, at the first price of each week (Monday to Sunday) or at the first price of each calendar month.
• Average cost per unit = money put in ÷ units bought. It is lower than the plain average of the prices whenever they vary, because the same money buys more units when the price is low.
• Value = units × the last price (or the price you type), and the gain = value − money put in.
• XIRR: the yearly rate r at which Σ flow ÷ (1 + r)^(days ÷ 365) = 0, counting each buy as money out and the value as money back on the last date, as Microsoft’s XIRR function defines it.
• Lump sum: all the money of the plan at the first buy’s price (less one fee), valued the same way.
• Value averaging: the target after each buy is the target before × (1 + growth) + the amount, so with no growth it rises by the amount every time; each date buys enough to reach the target, or sells the part above it. The method is Michael E. Edleson’s; Hayley’s paper describes it and its returns.
• Deepest fall: the lowest point of the account’s value against the money put in so far, at every price from the first buy.

Reading the results

• Average cost below the average price is the arithmetic of buying a fixed amount, not a sign the plan will make money: it can still be worth less than you put in.
• XIRR counts when each amount went in; for less than a year it is annualised and can look far larger than the gain itself (it is not shown under 7 days, nor above 1,000,000% a year).
• Lump sum against DCA: with the same money, the lump sum is fully invested from the first day, so it gains more when prices rise and loses more when they fall.
• Value averaging puts in more after falls and takes money out after rises, so its money put in changes from buy to buy; the largest single buy shows how much cash it can call for. Hayley shows that its internal rate of return is biased upwards, so compare the values and the money put in rather than its rate.
• Deepest fall says how far below your money the account went on the way; the price’s own largest fall is what a lump sum went through.

What it leaves out

Taxes, the bid–ask spread and slippage, dividends and splits (use an adjusted close if your file has one), currency changes when you buy in another currency, and the cash you keep aside between buys. A replay on past prices is designed with hindsight: a different period gives a different answer, and none of it says what prices will do. For one-off buys, the stock average calculator works out an average price; the XIRR calculator takes any dated cash flows.

Limitations

• Up to 20,000 prices are replayed; a longer intraday file is first reduced to the last price of each day.
• Buys happen at the prices in your list or file: a weekly or monthly buy uses the first price of that week or month.
• Taxes, spreads, dividends and currency changes are left out.
• It replays the prices you supply and uses no market data: past results do not say what future prices will be.

Privacy

Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.