DCA vs Lump Sum Calculator

How the Two Strategies Differ

Someone holding a lump sum can put it into the market all at once, or spread it across several months, an approach known as dollar-cost averaging (DCA). The two end at different values because they hold different amounts of capital in the market at different times. Lump sum puts the whole balance to work immediately. DCA leaves part of the balance uninvested through the averaging window and buys at whatever prices arise along the way. This calculator models both paths over a window you set, at a return rate you set, with an optional market dip you set, and reports the gap between the two final values.

Why Time in Market Widens the Lump Sum's Lead

With the dip left at zero, the lump sum ends ahead at every positive return rate. The reason is structural rather than historical: capital compounds for as long as it is invested, and DCA holds a shrinking share of the balance in cash across the window. The first tranche compounds for one month short of the full window, the last for none at all. Time-weighted across the whole window, DCA keeps a little under half the balance invested, and less than that at short windows: 45.83% over 12 months, 47.92% over 24, but only 33.33% over three.

That gap widens with both the window length and the return rate, and it is a property of the arithmetic rather than a claim about any particular market. At a zero return rate with the dip also at zero, the two paths end exactly level, since there is no growth for the idle cash to forgo. At a zero rate with a 10% dip applied, DCA ends ahead by 4.87% of the amount invested, because the discount on the below-trend tranches is then the only thing separating the two. The no-dip case is a useful reference point to read before any market-path assumption is layered on top.

Where the Dip Assumption Changes the Answer

The Expected Market Dip input overlays a V-shaped price path on the averaging window. The index falls from trend to a trough at the midpoint, then recovers to trend by the end. A lump sum bought before the fall is unaffected once the path recovers, because it is measured at the end. DCA tranches bought while the index sits below trend acquire more units for the same money, which lifts the DCA final value. The deeper the modelled dip, the larger that effect.

Worked Example

Take 100,000 spread over a 12-month window at an 8% expected annual return, with the dip set to 0%. Lump sum ends at 108,299.95 and DCA at 103,749.38, a lump sum advantage of 4,550.57. That is 4.55% of the amount invested, or 4.20% of the lump sum's own final value. The gap is the growth earned by capital that DCA was still holding in cash.

Widening the DCA window to 24 months takes the lump sum advantage to 9,233.84, though the two figures answer different questions. The model measures both strategies at the end of the DCA window, so a 24-month window also gives the lump sum 24 months of compounding rather than 12. The larger number reflects a longer horizon as well as a longer averaging period.

Setting the dip to 20% instead reverses the sign. DCA ends at 114,659.49 against the lump sum's 108,299.95, a DCA advantage of 6,359.54. For this 12-month, 8% scenario the crossover sits at a 9.06% dip: below it the lump sum ends ahead, above it DCA does. The tool opens with the dip at 10%, just past that crossover, so the default view lands on the DCA side; entering 0% shows the no-dip case described above. The crossover shifts with both the window length and the return rate, so it needs recomputing for any other combination.

What Moves the Modelled Gap

Three of the four inputs move the result in one direction throughout the range the tool accepts. A higher return rate moves the result toward the lump sum, since idle cash forgoes more growth. A deeper dip moves it toward DCA, since more tranches buy below trend. The amount invested scales the gap proportionally without changing its sign, so halving the amount halves the advantage and leaves the direction untouched. That last property is why the comparison reads identically in every currency, and why the crossover sits at the same 9.06% dip whatever the amount.

The DCA window is the lever that does not move in a single direction. Above a boundary set by the other two inputs it behaves as expected: a longer window moves the result toward the lump sum, because more capital sits uninvested for longer. Below that boundary, two features of the model interfere with each other. The dip does nothing at one or two months, since every purchase lands on an endpoint of the V-shaped path where the price factor is 1, so the result jumps toward DCA at three months when the dip first bites. Separately, an odd month count lands a tranche exactly on the trough while an even count straddles it, so stepping from four months to five also moves toward DCA.

The boundary sits at five months for the 8% return and 10% dip the tool opens with, and it moves with both. A deeper dip pushes it out: nine months at a 20% dip, seventeen at 40% and thirty-three at 60%, all still at 8%. A lower return rate pushes it out further. At a 10% dip the boundary reaches eleven months at a 2% return, twenty-five at 0.5%, and the whole 60-month range at 0%, where there is no compounding drift for the alternation to sit on top of. A higher rate pulls it in, to three months at 20%. The five, nine and seventeen figures describe the 8% case rather than the model generally.

What the Model Does Not Capture

Returns here follow a smooth monthly trend with a single symmetric dip. Real price paths are irregular, and a window that rises first and falls later, or one that falls without recovering, would produce an answer this model cannot show. Since the modelled dip always recovers by the end, there is no setting at which the assumed path works against DCA, which makes the dip input a one-directional lever rather than a balanced scenario range.

Costs sit outside the model. DCA involves more transactions than a single purchase, so dealing charges and bid-ask spreads apply more often to it. Tax treatment is excluded as well, and it varies by jurisdiction and by account type. The model also assumes each schedule runs to completion; a DCA plan paused partway through follows neither of the two paths shown here.

The dip is an assumption rather than a measurement. No price history supplies it in advance, so the figures shift with whatever value is entered, and the output describes that assumed path rather than a forecast.