There are two issues with the articles calculations, that end up making the already bad payback time even worse, before considering opportunity costs. Numbers are for Germany since that's the more favorable case:

1 - degradation: assuming the 15 years battery life / 10.000 cycles number from the datasheet is accurate, and that the manufacturer considers 70% capacity end-of-life, this pushes the payback time from 11.1 to 12.7 years.

2 - The article calculates the savings with:

> daily saving = 4.5 × expensive price − 5 × cheap price

but this is wrong because it assumes that grid charges fully cancel out. The article generally does a poor job at explaining this, but essentially it proposes you overbuy electricity when it's cheap and use it when it's expensive. The difference of those two, €0.133/kWh - €0.041/kWh is much smaller then the average electricity price of €0.3869/kWh because the latter also includes taxes and grid charges. So with 90% efficiency they end up with the formula above, but completely ignore the fact that from the grid's point of view, the total electricity consumption increased. On the flipside, it's also taking EPEX prices directly, pre-VAT, so you actually save 19% more then the difference 0.133 - 0.041 = 0.092. So the actual formula should be:

> daily saving = 1.19 × (5×0.9 × expensive price − 5 × cheap price) − 5 × (1−0.9) × grid charges

At a average rate of 21 cents/kWh for total grid costs (including VAT) that comes out to a payback time of 13.71 years.

So yeah, buying batteries alone doesn't make sense. You need solar or wind to charge them, so you actually avoid the grid charges. So that instead of saving 10 cents you save 40.