Dollar-cost averaging results in an average cost per share that is lower than the average price per share when the price of stock has:

Dollar-cost averaging is an investment strategy where an investor regularly invests a fixed amount of money into a particular stock or fund, regardless of the share price. This method has the effect of purchasing more shares when prices are low and fewer shares when prices are high. Consequently, when the prices fluctuate, resulting in both higher and lower share prices over time, the average cost per share tends to be lower than the average price per share.

This phenomenon occurs because when prices are low, the fixed investment amount allows the investor to acquire more shares, effectively reducing the average cost per share. If stock prices randomly increase and decrease, the strategy capitalizes on market volatility, capturing low-priced shares that help lower the overall average cost.

In contrast, if the stock price increases steadily, the average cost per share would likely approach the average price per share, and the same holds true if the price decreases steadily or remains constant. In those scenarios, there wouldn't be the same advantage provided by the range of prices that dollar-cost averaging exploits when the price fluctuates.