Opportunity Costs: Prices Exist; Interest Rates Don’t – More on Columella

I have a confession to make. I don’t look at bond yields. I invert bond yields to look at bond prices. Always have.

(Price = 1/Yield)

In one article: I multiplied a stock’s free cash flow by the inverse of the 30-year AAA bond yield to get the stock’s intrinsic value. That confused a reader:

“I am still a little confused why the price-to-coupon ratio is used as a multiplier.”

Investors choose between assets like stocks, bonds, and land. If bonds and land are expensive, people buy stocks and vice versa.

Think about Columella and his vineyard. It will cost Columella 32,480 sesterces to plant the vineyard and wait for it to give grapes. In two years: the vineyard will start giving him grapes. Columella will then sell those grapes for at least 2,100 sesterces a year.

His other option is lending the 32,480 sesterces at 6% a year. That would give Columella 1,950 sesterces a year (actually 1,948.8 sesterces; Romans had trouble with fractions).

There are two ways of looking at this choice. You can compare the two options – making a loan and planting a vineyard – in terms of yield: 2,100 sesterces a year is more than 1,950 sesterces.

Or you can compare the two options in terms of value:

2,100 * (1/0.06) = 35,000 > 32,480

I like the value way of looking at things better. It makes more sense to value bonds than discount everything else.

Here is the best thing I’ve read on this topic.

A Roman named Columella wrote a farming manual 2,000 years ago. In it he mentions opportunity costs.

You need to know 3 things to understand what you’re about to read:

1) Sesterces are Roman money

2) A iugerum is two-thirds of an acre, and

3) Vinedressers are slaves.

I…consider a high-priced vinedresser of first importance. And supposing his purchase price to be 6,000 or, better, 8,000 sesterces, when I estimate the seven iugera of ground as acquired for just as many thousands of sesterces, and that the vineyards…with stakes and withes…set out for 2,000 sesterces per iugerum, still the total cost…amounts to 29,000 sesterces. Added to this is interest at six percent per annum, amounting to 3,480 sesterces for the two-year period when the vineyards, in their infancy…are delayed in bearing. The sum total of principal and interest comes to 32,480 sesterces. And if the (farmer) would enter this amount as a debt against his vineyards just as a moneylender does with a debtor, so that the owner may realize the aforementioned six percent interest on that total as a perpetual annuity, he should take in 1,950 sesterces every year. By this reckoning the return from seven iugera…exceeds the interest on 32,480 sesterces…For, assuming that the vineyards are of the very worst sort, still, if taken care of, they will yield…a total of 2,100 sesterces — a sum far in excess of the interest at six percent.

Big, basic ideas last a long time. Opportunity cost is one of them.