Buying stock at discount yields unintuitive rate of return

Question

My employer offers an Employee Stock Purchase Program (ESPP). Long story short, worst case scenario is that they will purchase stock on my behalf at a 15% discount and then I will immediately sell it. I am confused as to why my gain is 17.65% as opposed to 15%. Where does the number 17.65% come from? It is not intuitive to me. Example calculation:

On purchase day stock price is 10 USD. I get to buy it using my discount so, I buy it at (.85*10) = 8.50 USD I then immediately sell it for 10 USD.

So my gain is (10-8.50)/8.50 = 17.65%

Because your gain of 1.5 is not compared to the "theorical" cost of 10 but to the effective cost : 8.5 — Mauro ALLEGRANZA, Jul 29 '19 at 14:11

score 0 · Accepted Answer · answered Jul 29 '19 at 14:14

The $15\%$ discount is multiplied by the market price to give your purchase price. The gain is calculated as a percentage of the discount price, which is lower. As the absolute discount is the same, the gain on sale must be a higher percentage.

The effect is general and gets larger as the discount percentage increases. If you get a $50\%$ discount you would buy the stock at $5$. The immediate profit would then be $100\%$ because you can sell it at $10$. If your discount is $x$, you buy the stock for $1-x$ and sell it for $1$, so the profit is $\frac x{1-x} \gt x$ because the denominator is less than $1$.

Buying stock at discount yields unintuitive rate of return

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