If a company's stock is over-valued, why would they issue more stock?

Issuing more stock isn’t really related to being “over-valued” (or even under valued). The companies issuing more shares need additional capital to grow, so they sell more shares. Being over/under valued doesn’t make a difference in your question.

Let use Shopify ($SHOP) or Tesla ($TSLA) as an example, both have revenue growth > 75% YoY (year over year) and are BOTH losing cash — by design — intentionally. Imagine a scenario where Shopify slows its growth (by not aggressively investing in sales & marketing) and is now profitable — assume Shopify makes a $25m profit with 30% growth, are investors happy?

Shopify has CHOSEN to take the profits they would have made (with a slower growth scenario) PLUS as much money as they can use to “ramp” the 35% growth to 75%+ growth (which is exactly what they are doing now) to fuel the growth engine they have created by investing AGGRESSIVELY in sales & marketing.

Because they are “valued” as a growth stock/company off P/S or the “revenue multiple”, they LOSE CASH every quarter to fuel faster growth — their faster revenue growth makes their valuations increase. So, it goes like this > spend lots of cash on sales & marketing to fuel revenue growth > the revenue growth determines the revenue multiple (the higher the revenue growth, the larger the multiple) > the revenue multiple determines market cap > the market cap is derived by the share price * outstanding shares. At some point, their cash burning accounts need to be refilled to continue fueling growth, so they sell more shares. They are currently valued at almost 18x’s revenue and growing revenue around 85% average in the most recent 4 quarters. Make sense?

Inversely, companies can buy back their own shares if they have excess capital that isn’t being deployed. Sometimes this works out — sometimes not — as GoPro ($GPRO) did this Oct 2015 — not so good for them today.