Economist Writing Every Day

Recently, I’ve been buying a lot more non-durable goods when they are on sale. Whereas previously I might have purchased the normal amount plus one or two units, now I’m buying like 3x or 4x the normal amount.

What initially led me here was the nagging thought that a 50%-off sale is a superb investment – especially if I was going to purchase a bunch eventually anyway. I like to think that I’m relatively dispassionate about investing and finances. But I realized that I wasn’t thinking that way about my groceries. The implication is that I’ve been living sub-optimally. And I can’t have that!

If someone told me that I could pay 50% more on my mortgage this month and get a full credit on my mortgage payment next month, then I would jump at the opportunity. That would be a 100% monthly return. Why not with groceries? Obviously, some groceries go bad. Produce will wilt, dairy will spoil, and the fridge space is limited. But what about non-perishables? This includes pantry items, toiletries, cleaning supplies, etc. 

Typically, there are two challenges for investing in inventory: 1) Will the discount now be adequate to compensate for the opportunity cost of resources over time? 2)  Is there are opportunity cost to the storage space?

For the moment, I will ignore challenge 2). On the relevant margins, my shelf will be full or empty. I’ve got excess capacity in my house that I can’t easily adjust it nor lend out. That leaves challenge 1) only.

First, the Too Simple Version.

Say that I spend and consume $100 of product per month for a total of $1,200 per year. But then, I see a bogo sale (Buy one, get one free). That’s equivalent to 50% off for even numbered quantities. How much should I purchase? If the time value of money is irrelevant and I am constrained to a year, then the answer is that I should immediately purchase a year’s worth at a total cost of $600. The maximum that I’d be willing to pay is $1,200 today, but I only have to pay $600. The net present value (NPV) is $600 and the internal rate of return is 12.69% per month. It’s a no brainer.

The Appropriately Simple Version.

What about opportunity cost? Surely, I could be doing something else with all of that money that I’m forgoing in order to take advantage of the bogo sale. Indeed! Let’s say that, due to liquidity constraints, I forego my monthly savings contribution in order to take advantage of the sale. Now the decision is not so clear. I have to ensure that my bogo purchase yields me a better return than does my savings account (my opportunity cost of resources). Say that my savings account has a 10% annual return, or 0.8% monthly. That’s the time value of my money.  Even now, the bogo deal is a great deal. I’d be willing to pay is $1,140.05 today, but I only have to pay $600. The net present value (NPV) is $540.05. It’s still a no brainer.

Just so we are clear, my savings might earn 10% per year and I am finding a grocery deal that earns more than that over each month. How are we not all packing our homes and apartments to the gills with groceries and such for future consumption?! With rates of return like these, I feel like an idiot if I don’t purchase a year’s worth.

Not so fast.

The Appropriately Complex Version

The two challenges listed above are great for businesses. But individual consumers are different. We have warm-and-fuzzies that get in the way of our inner Spock that is quietly judging our poor grocery habits. Consumers face a third challenge. For many goods, we tend to consume more when we have more on our shelf. This is a version of the wealth effect.

“Do you wanna beer? After all, we have plenty.”

“I thought that ice cream was for special occasions. Yes, but we have so much.”

“Oh shoot! We’re out of napkins. Go ahead and use a paper towel – we’ve got a life-time supply.”

Clearly, the wealth effect matters for some items more than others. I’ll probably drink more beer if I have it. I will probably not use more bathroom tissue or face wash just because there is more in the closet. The wealth effect on our consumption is different from good-to-good. Let’s define the wealth effect on consumption as multiplicative:

Such that:

The above equation says that the wealth effect grows with our current stock as a fraction of our typical monthly consumption. β is just a parameter that describes our consumption sensitivity to our current stock-to-typical-consumption ratio. β is bigger for things like beer, wine, chocolate, and paper towels. β is smaller for things like laundry detergent, shampoo, and tooth paste.

Depending on our sensitivity, we will consume greater amounts of groceries when we have a large cache hidden away in the closet. How does this change the investment decision? Well, it depends on how you respond when you run out. If you consume $100 worth of the good each month once you’ve consumed your stock, then that’s going to begin tp increase the total annual cost. This last part is a judgement call. Where does the future expenditure come from once you run out of stock? I’m going to assume that it comes from savings (since it is beyond the typical budget).

With any β>0, we end up consuming more of the good over the entire year than our typical monthly consumption would have predicted. That is, we may go over budget. But, going over budget isn’t necessarily a bad thing! The NPV could still be positive even so.

So what?

The advantage of this model is that it makes clear when we should take advantage of a sale. It depends on the magnitude of the sale, our opportunity cost rate of return, and our consumption sensitivity to having a large stock. Given that the first two items are largely predetermined when you make your bogo purchase decision, then the only remaining variable is the magnitude of the wealth effect. For each person and good, that effect will be different. Effectively, a larger β implies that you will consume greater amounts sooner in time and throughout the entire year than you had budgeted. With a little introspection and honest reflection, we can try to make purchases prudently taking our wealth effect into account.

Bottom line: Buying in bulk is a great investment if your self-control can handle it.