Last month, we gave you $100 to start a farm, provided the below list of potential crops to plant and sell, and asked how much you could earn selling your crops in 5 years.
The trick was to transform the cost, selling price, and time to grow into a rate of return on investment. Through this lens, it was clear that saffron is the ultimate crop and should be grown as soon as possible. But to do so, sub-optimal crops had to be grown first.
Before we get started, we’d like to acknowledge last month’s winner—Serge Éthier, who was able to realize a profit of $2,314,067 by optimizing their investments every 2 months. May bountiful harvests lie in your future, Serge!
To make as much money as possible, we want to grow whatever crop makes the best return on investment as early as we can manage.
The way to do this is to look at the fractional return projected out over a year. For example, saffron returns $\$500$ on a $\$175$ investment, giving a fractional return of $\$500/\$175 \approx 2.86.$
Because saffron takes 6 months to grow, we can fit two cycles into a year, making the annual return $2.857^2 \approx 8.163.$
Calculating this for each crop, we can compare apples to apples:
| Crop | Cost | Revenue | Time to grow | Annual rate of return |
|---|---|---|---|---|
| Peas | $10 | $12 | 2 mo | ~300% / yr |
| Potatoes | $5 | $8 | 4 mo | ~410% / yr |
| Raspberries | $15 | $25 | 4 mo | ~460% / yr |
| Saffron | $175 | $500 | 6 mo | ~816% / yr |
Through this lens, it’s clear that we should try to grow saffron as soon as possible.
A precise strategy requires some bookkeeping, so first we’ll develop the spirit of the strategy, and make a back-of-the-envelope estimate of the profit we can expect.
Saffron’s startup cost is more money than we have to start, so we simply can’t afford it. Ever the pragmatic farmers, we can compromise and go with the next most profitable crops.