In 1202, the Pisan customs official’s son who has come to be known as Fibonacci gave the world the mathematical tools to calculate the present value of a future stream of money. Now, 816 years later, net present value remains such a foreign concept to most people that it’s deemed too arcane to mention before the general public.
At least, that’s the impression I got after reading through the news coverage of the California Energy Commission’s decision last week to require solar panels on virtually all new houses and low-rise apartment and condominium buildings (those with roofs that are especially tiny or are in the shade most of the time are exempted). I’m not the hugest fan of the move, given that the state’s need for more housing seems to be greater than its need for more solar panels. But that’s an argument for another day. What I’m curious about is whether it’s a good deal for prospective homebuyers in California or a bad one.
The basic numbers on this, provided by the California Energy Commission and cited in multiple news articles, are that the new standard “will increase the cost of constructing a new home by about $9,500 but will save $19,000 in energy and maintenance costs over 30 years.”
OK, $19,000 is twice as much as $9,500. But you wouldn’t be getting all those savings at once, would you? Divide that $19,000 over 30 years, and plug the resulting $633.33 annual savings into Fibonacci’s formula, and it’s worth nowhere near twice as much as $9,500. A key element in the formula is the interest rate by which future values are discounted. Use 4.3 percent — the lowest 30-year mortgage rate I could find online — and the net present value is $10,563. That’s not a big savings!
Except … the next line of the energy commission’s FAQ on the new standards says that, if one buys a new solar-equipped house with a 30-year mortgage, the added mortgage cost will be $40 a month and the energy savings $80 a month. If you divide $19,000 by 360 months (30 years times 12 months), you only get $53. So maybe that $19,000 is the net present value of the estimated future savings. Sure enough, after some digging, I found the “PreRulemaking” document for the new solar rule, which indeed makes clear that what they’re talking about are “present-value energy cost savings over the 30-year period of analysis.”
Why didn’t they say that in the documents intended for public and media consumption? I’m guessing it’s because they figured the words “present value” would be off-putting. Or maybe it’s that everybody already knows that solar cost savings estimates are expressed in present-value terms and I’m getting all worked up over nothing, but I don’t think so. I did a search on the phrase “present value” on Google News and all I came up with was a bunch of exercises in corporate valuation from Simply Wall Street, a CFO Magazine article on “The Renewed Importance of Purchase Price Allocations” and a syndicated newspaper column by “The Mortgage Professor.” That last one was the only one aimed at a general readership.
Present value is a concept essential to informed decision-making about the future — and thus to modern life — yet very few people outside the financial sector (and even there I have some doubts) seem to know what it entails. Certainly most journalists don’t. (I didn’t until I went and wrote a book about the history of academic financial theory.) But the calculation is really simple, and it makes intuitive sense.
First, the calculation: The present value of a sum of money to be received n years in the future is that sum of money divided by 1 plus the interest rate (which means 1.05 if the interest rate is 5 percent) to the power of n. So $10 in two years at 5 percent interest is $10 divided by 1.05 squared, which comes to $9.07. If you’re getting $10 a year for a number of years, all you need to do is add up the values for all the years, which is easy enough to do in Excel, Google Sheets, Apple’s Numbers or another spreadsheet of your choice, although you can also just use an online NPV calculator.