Innovative Industrial Properties (IIPR 0.88%) is a smart passive income stock thanks to its ever-growing empire of marijuana cultivation real estate. But as all investors know, building up a significant amount of dividend income typically requires a lot of money or a lot of patience, if not both.

In fact, with a relatively small weekly commitment, you could build up a pretty decent haul of dividends annually, and it wouldn't even take you that long to do so in the grand scheme of things. Before we go over the details of how to do that, let's start by taking a minute to appreciate why this real estate investment trust (REIT) is such a passive income machine in the first place.

This company plays the long game, and so should you

Innovative Industrial has a strong business model based on sale-leaseback transactions that enables it to pay a juicy dividend while growing its revenue, earnings, and its base of assets under management. In short, it exchanges lump sums of cash for cannabis cultivation, manufacturing, distribution, or retail facilities, which it purchases from marijuana businesses that need capital for growth. After the trade, the capital-hungry companies become rent-paying tenants for the duration of their lease; most of Innovative Industrial's leases are for terms of 15 to 20 years.

The relationship with its tenants works because cannabis operators in the U.S. can't access traditional sources of capital, like investment banks, as marijuana remains illegal at the federal level. But state laws still allow them to buy real estate, so as long as IIP is around to be a buyer, they still have a chance at raising money.

And that's how the business came to own 110 properties across 19 states since its initial public offering (IPO) in late 2016. For reference, the rental income from those properties made it trailing-12-month (TTM) revenue of $264.8 million, which worked out to TTM funds from operations (FFO) of just under $199 million. 

Weekly contributions could make for robust passive income

Now that you're up to speed on how this stock can afford to pay a dividend, let's get down to brass tacks about what you'll need to do to get it to pay you a couple of grand each year.

IIP's forward dividend yield presently sits at a smidgen over 8.3%. At that rate of return, you'd need to invest somewhere in the ballpark of $24,100 to get $2,000 in annual dividend revenue.

That's a lump sum far beyond what most investors have sitting around in their bank account, obviously. So, it makes more sense to gradually build up a position by dollar-cost averaging, which entails buying a small number of shares each week as you have the money to do so. If you spread the investments out over five years by making 260 weekly purchases of around just $93, in theory, you'll reach the target level of income.

In practice, this calculation is quite fuzzy, and the details of the fuzz could easily turn in your favor -- or potentially against it. For example, it's unlikely that this company's dividend yield will remain exactly at its present level in the medium term. IIP has a history of hiking its dividend each year, which would let you accumulate enough shares to get the passive income you want before five years elapse.

In the last three years, its payout rose by 80%, so similar growth moving forward, while not guaranteed, would dramatically speed up the process and reduce the total investment required to get $2,000 annually. Similarly, its share price could drop, driving yields upward and giving your weekly purchases more bang for the buck. 

In contrast, sharp rises in its stock price caused by positive catalysts, like perhaps marijuana legalization, would make your dividend income project take a bit longer, as yields would drop. Although IIP is a REIT that is required to return at least 90% of its FFO to shareholders, there's the obvious risk of the dividend getting trimmed if times get tough -- and they're getting tough right now. 

At present, IIP is dealing with a trio of tenants that are late paying rent, so that isn't an idle concern, especially if conditions in the cannabis industry continue to deteriorate over the next year or so, which they might. So regardless of whether you decide to actually try to implement the plan by buying shares each week, you'll need to stay abreast of what's going on with the company and its operating environment to make sure that you're not accumulating too much of your money into a stock that's too risky for your taste.