Facing a Big Decision? Math is Your Friend.
How do you make the big financial decisions in life?
Many people, if not most, can make these decisions by trusting their gut.
If that’s you, well, I envy you. That doesn’t work for me. I will be waking up in the night in a panic with my heart pounding, wondering if I’m doing the right thing.
I trusted my gut when I bought my first (and only) house after deciding “It just feels right.” For the next year, I was convinced that when I left for a trip the whole thing would collapse in my absence.
After that, I realized I needed to base my decisions on some reason, weighing the cost against the benefits.
For some things it’s a no-brainer. The benefits of having a car here in Southern California far outweigh the cost, so we didn’t think too much about that one. But what about something that’s no so clear cut? I know I keep blabbing on about solar, but it’s a good example of an expense where the costs are high and benefits are less certain.
It’s time to break out the math. But stay with me. Thinking deeply about money in our daily lives can provide enormous insight into the world around us.
So, we want to be able to compare at the cost of the solar system to what we would be saving in electricity. Here’s what we spent on electricity in the last year:
One way to look at this is to figure out how many years of electricity bills will it take to pay for my solar system. My solar system will cost $14,700 after taxes. I spent $1241 on electricity last year. So my payback will be:
Net cost of solar system/annual electricity bill=12 years
If you want to stop there, fine. But if this strikes you as too simple, good for you! It doesn’t account for change over time. My solar system is supposed to last 30 years and a lot of things will change in that period.
For starters, my utility bill isn’t going to stay the same over the next 30 years. Not a chance! But how much will it rise? The Energy Information Association estimates that residential power bills will rise 2.5 percent a year through 2040. Applying that, my power bill will steadily rise until 2045 when it will be $2,540.
So that $2,540 is money I’m not spending since I’ve gone solar. I can spend it on whatever I want (or save it). So my solar system has freed up cash for my household for the next 30 years. If I were a business, I would call this positive cash flow.
Utility rates aren’t the only thing changing over time. What also will be changing is the value of the dollar. Inflation has been quiet of late but over the next three decades, it will rise again. In fact, there’s a chance it may come roaring back. In 30 years, a dollar will be worth less than a dollar today.
So how do we deal with all this change over time? The answer is a concept known as net present value (NPV). This is a very useful concept because once you understand it, you can use NPV to analyze all sorts of investments like stocks or bonds.
Here is a video that explains the concept in three minutes:
The rule is if your NPV is less than zero, it’s a bad deal. A net present value that is positive means that my solar project or any investment will save me more money than it costs.
It takes a bit of work to figure out net present value. You need to know how to use a spreadsheet, but it gives a much more accurate insight into whether an investment is worthwhile. When I’m spending $21,000 that matters!
Net present value accounts for the changing value of money over time. A dollar is worth slightly less next year than a dollar today. But how how much less? To calculate this, we need a rate of return. I used the 30-year Treasury bond rate, which as of today is 2.8 percent.
NPV is calculating interest in reverse. Let’s start with the interest calculation: If we bought a 30-year bond for $1000 today, next year it would be worth $1000*1.028 or $1,028.
Let’s look at it backwards. How much is a 30-year Treasury selling for $1,028 next year worth today? The answer is $1,028/1.028 or $1,000. Can you guess the NPV of the same bond selling for $1,056 in 2018? It’s $1,028/(1.028*1.028) or $1,000.
Excel and Google spreadsheets have an NPV function that makes calculating this easy. I applied this to my column of electricity bills growing 2.5 percent a year and subtract the cost of my solar and I get a net present value of $19,705. That’s the amount my solar system is saving me over the next 30 years! That’s way above zero, which means it’s a good deal.
There’s still one more way of looking at my solar system. It’s called Internal Rate of Return (IRR). Mathematically, it’s very close to NPV. We assume the NPV is zero and then solve for the rate of return. The IRR for my solar project is 11 percent. An investment that returns 11 percent a year? I’ll take it!
Both net present value and internal rate of return are very powerful tools that allow you to cut through a lot of B.S. Someone offers you an annuity that generates $2,000 a year, guaranteed. Is that a good deal? Renting a house and deciding whether to buy one? Now you can decide with some greater precision.
In fact, net present value is the secret weapon of stock guru Seth Klarman who praises it as a powerful analysis tool in his famous (in Wall Street circles) book Margin of Safety. Klarman writes, “When future cash flows are reasonably predictable and an appropriate discount rate can be chosen, NPV analysis is one of the most accurate and precise methods of valuation.”
How can this be used to pick stocks? We will cover the applications of NPV for stock analysis in
our next a later post.
Is Net Energy Metering a Subsidy for the Rich?
Benjamin Zycher at Forbes thinks so.
So what’s the problem? First, the credit paid in California for the excess solar power is far higher than the cost of alternative electricity sources, usually from utilities or from the spot power market. Consumers without such solar installations have to finance that excessively expensive electricity, so that overall power prices are forced above the level that would prevail in the absence of the net metering system. This system, by the way, subsidizes the affluent (median income of those installing solar systems: $91,210) at the expense of all other power consumers (median of $67,821), an embarrassing reality from which the supporters of the net-metering system prefer to avert their eyes.
Second, reliability is a hugely valuable attribute of power systems; no one likes blackouts. Electricity bills reflect the cost of that reliability in the form of “capacity” charges, that is, the part of the bill covering the cost of the physical system and its spare capacity, before fuel expenses and other such generation costs. People who install solar systems benefit from the reliability provided by the grid–they consume conventional power at night and at other times that the sun fails to shine–but because they pay only for their “net” power consumption, they get a free ride on the cost of the generation equipment and other capital that yield the reliability upon which they depend. The problem is that the free ride is not free: Other consumers have to pay for it.
Let’s take those one by one.
The idea behind net energy metering is that my demand for electricity and the solar electricity I supply to the grid cancel each other out. During the day, the power generated by my rooftop panels that I don’t use flows into the grid. At night, I am given a credit for the electricity I supplied during the day.
Perhaps Dr. Zycher has forgotten that solar panels are a source of energy that the utility has paid nothing to produce. Here in San Diego, solar panels generate more than 500 megawatts of electricity. In all of California in 2014, solar generated 10,557 gigawatt hours of electricity.
Would Dr. Zycher have me pay for the privilege of supplying electricity into the grid?
If my solar panels generate more power than I consume, I am paid at the wholesale spot market electricity price. I fail to see how this is “excessively expensive” and drives up power prices, as Dr. Zycher asserts. If anything this power is significantly less expensive for the utility, since the power is instantly in the grid, and the utility does not have to haul this energy long distances as it does with other sources of power.
The second point Dr. Zycher makes about reliability is more grounded in fact. It is true that under net metering, solar users don’t pay the full costs of maintaining the grid. This cost is passed along to other non-solar customers. Dr. Zycher is correct in pointing out that is unfair, and the costs should be borne equally by all grid users. San Diego Gas & Electric has estimated these costs at $100 per year. It would be a simple matter to pass this fee along to solar users.
There are genuine subsidies in solar. The cost of installing solar panels is subsidized by U.S. taxpayers, and we can debate this all day. Do we really need solar subsidies? I believe that all subsidies distort price signals. Watch what happens to solar when the tax credit goes away.
Net metering, however, is no subsidy. Rather it is an accounting system that balances supply and demand. Solar may not work everywhere, but it sure makes sense in California. Doing away with it will unfairly doom a pollution-free source of energy that is delivering a reliable supply of power on sunny days when demand in the Golden State is at its peak.
Going Solar, Part II
Another factor pushing me toward solar was net metering.
Net metering is a billing system that credits solar homes for the electricity they produce. If the solar system was properly designed the inflows and outflows will balance.
There is a misconception that people who install rooftop solar panels go “off the grid.” Unless you are willing to pay the extra expense for an array of massive batteries, that’s not true.
When the sun is up my solar panels generate electricity. They generate more power than I can use, and the excess is fed back in the electric grid.
At night, the situation is reversed. My solar panels generate no power. But I keep the lights on, cook dinner, watch TV, and so on. That power comes from the grid.
The catch is that, under California’s net metering law, solar homes are credited for excess power at the retail electricity rate. My average retail electricity rate in 2015, if you recall from the previous post, was 20 cents per kilowatt hour — among the most expensive in the United States.
The wholesale cost that my utility pays for power, according to the U.S. Energy Information Administration (side note: do we really need another government bureaucracy for this?), is around 4 cents per kilowatt hour.
That 16 cents per kilowatt hour difference covers San Diego Gas & Electric’s costs for generating electricity, transmitting it, distributing, and maintaining the grid. Some of it goes to SDG&E’s $500 million annual profit (in 2014).
This is a good deal for me. But it’s a bad deal for the utility’s non-solar customers. They are subsidizing my cost of maintaining the electric grid. SDG&E estimated that families without solar panels pay an extra $100 per year to cover the costs of solar homes.
California’s net metering law capped the number of solar homes at 5 percent of a utility’s aggregate peak demand. Here you can see how close we are to the cap in San Diego. The limit will probably be reached sometime this year.
What happens then? Right now it’s unclear. But my guess is that new rooftop solar customers will eventually have to buy solar at retail rates and sell it at wholesale rates. If you get in under cap you get a 1-to-1 credit for 20 years.
So there was another reason for going solar.
Going Solar, Part I
My wife had been urging us to go solar for years.
She saw it as a way to send a message to our community and ourselves that we care about the environment and the future of our planet. We live in sunny San Diego, so it made total sense.
Looking back, I can’t exactly say why I was reluctant to agree. We had the money. I don’t believe that global warming is some giant hoax. I was just … apathetic.
When panels started to pop up everywhere, I decided to run the numbers. As you can see below, I paid an average of 20 cents an hour per kilowatt/hour of electricity.
To put this in perspective, 20 cents per kilowatt hour is about as expensive as it gets for electricity in the United States.
How did this compare to solar?
First off, I wanted to buy my solar panels outright. We had the money to do this and it was a far better investment than leasing. Most people in California choose to lease, which is the most expensive way to go solar. Buying panels outright locks in electricity at a low price, while leasing panels leaves you vulnerable to rising rates, just like with your utility.
I was budgeting about $21,000 for my 4.73kw solar system (including a new electric panel). The U.S. government’s 30 percent tax credit brought the total cost down to around $14,700.
That’s a lot of money but buying a solar system is essentially paying for power up front.
Over 20 years at 20 cents/kWh I will hand over $24,820 to my utility, San Diego Gas & Electric. Running my solar system for 20 years would save me $10,000.
And that’s assuming that rates don’t change (unlikely) and my electric use remains the same (also unlikely).
Solar was starting to make sense.