## Opportunity Cost Calculations

One of the outcomes of my recent bill were the articles written. Lindsay Handmer over at Gizmodo wrote an interesting piece about opportunity cost.

For those playing at home, “opportunity cost” is an economic term, defined as follows:

…the loss of other alternatives when one alternative is chosen.

In particular, looking at my statement about leaving the money in the mortgage offset account, versus buying the system.

I had confidently stated my preference for the financial outcomes of the system early on. As it was likely to save me (at least) double the value of my offset in terms of electricity savings, it looked like an easy choice.

Honestly, opportunity cost was not something I gave much thought to. I decided to invest the money in acquiring a hybrid solar system. I wanted to save on electricity bills, and the money looked well-spent.

What some may not know is Lindsay and I had a fairly long email discussion about the direction of the article. We checked facts and figures,and compared notes in terms of thought process.

The ultimate conclusion is the one that most basic analyses have come to; the Powerwall is not yet considered financially sound in terms of payback, against its warranted 10 years.

Estimates for payback vary widely on how you analyse it, and individual circumstances. I had calculated mine at around 8-10 years, and that looked good after the first bill produced savings of ~ $450 compared to same quarter last year (or about $1800 per annum).

#### OPPORTUNITY COST

I got to thinking about my financials, since Lindsay’s article. During a subsequent proof read for another article I’ve written (to be published in the near future), I decided to go back and review “opportunity cost” as a thing.

I wondered if I’d made the right decision.

The article on gizmodo was right: while I was going to save on electricity bills, that money would no longer be helping slaughter my loan. By sticking it to the power company, I’d lost the chance to stick it to the bank!

What a conundrum…

I should mention that in the weeks before the install, I’d moved my mortgage to a product *without* an offset. I still could have dumped the lump sum it the mortgage directly, and let it ride.

But would I? Really?

Even in Aussie dollars, $16k is non-trivial amount of money to the average family. Maybe it was time to have a family holiday? Pay off some other debts? Do some enhancements around the house? Buy a GoT-themed jumping castle? _{Wait. What?}

The point is, while its all well and good to say “stick it in the offset”, there are no guarantees that it would stay there. The problem with ready cash is that there are always things for which it could otherwise be used. Life happens.

#### DOING THE NUMBERS…

For the sake of this discussion, let’s say the money went into the mortgage, for the Powerwall’s warranty period of 10 years.

Assume the interest rate stays at 4% (unlikely), and we keep any benefits in the mortgage. Under the principal investment of $15,990 the interest saved is $639.60 over the first year. Second year is principal $16,629.60 (adding the savings), which saves $665.18 and so on.

Now, based on rolling the principal + interest over every year, after 10 years we arrive at … _{carry the three … square the hypotenuse … divide by the tangential inverse of pi …}

A total interest saved figure of $7,679.11 from my investment of $15,990.

Not bad!

I’ve continued to pay electricity bills during that time, of course.

Starting with my base usage costs of $1920 from the 12 months leading up to Powerwall, let’s be *extremely* generous to the retailers, and flag an upward move of 0.5% per year, on average.

That means in the first year the new usage costs are $1,929.60. Second year $1,939.25 – and so on.

Over 10 years, that little hike makes for a total electricity bill of $19,736…

Therefore, despite saving money in my offset, I’m still down by a figure of just over $12k. If the price rise was just 2% per year on average, its more like $21,443.93 paid to the electricity retailer (loss of nearly $14k).

Just for reference, 2% increase on usage costs, for the average of 25 cents per kilowatt hour in these parts, is half a cent.

If the increase was 4% (1 cent per kWh), I’m paying out nearly $24k in electricity. That’s enough to cancel out the interest savings AND put me in the hole for the value of my system!

#### NOW FOR SOMETHING COMPLETELY DIFFERENT

Man. Who knew an increase of 1 cent could hurt that much?

Let’s take another tack, and look at using the money I save on electricity against the mortgage.

Again, we need to make some assumptions:

- mortgage interest rate will be 4% ongoing
- $450 saving on the first quarterly bill extrapolates to $1800 per annum
- degradation in Powerwall is cancelled out by increases in electricity price
- money saved on bills will be put back into the mortgage*

_{* Again, it probably won’t, but given the opportunity cost matrix assumes that all monies stay dedicated to the mortgage, I say game on!}

Starting at Year Zero with a capital position of negative $15,990 we can compound all our numbers moving forward. Remember, we’re adding $1800 into the pot every year from bill savings, as compared to my old provider.

Therefore in the first year, we subtract $639.60 in lost interest from the starting capital position, but add $1800 per year in bill savings. That rolls over to the new amount for calculating the offset in the next year.

Year |
Lost offset |
Bill Savings |
Capital Position |

0 | n/a | n/a | -$15,990.00 |

1 | -$639.60 | $1800 | -$14,829.60 |

2 | -$593.18 | $1800 | -$13,622.78 |

3 | -$544.91 | $1800 | -$12,367.70 |

4 | -$494.71 | $1800 | -$11,062.40 |

5 | -$442.50 | $1800 | -$9,704.90 |

6 | -$388.20 | $1800 | -$8,293.10 |

7 | -$331.72 | $1800 | -$6,824.82 |

8 | -$272.99 | $1800 | -$5,297.81 |

9 | -$211.91 | $1800 | -$3,709.72 |

10 | -$148.39 | $1800 | -$2,058.11 |

11 | -$82.32 | $1800 | -$340.44 |

12 | -$13.62 | $1800 | $1,445.94 |

This indicates that some time very early in the twelfth year is when I hit payback, under the opportunity cost calculation. That would be the system paying itself off in full, and accounting for the mortgage offset.

#### DOES IT REALLY MATTER?

Really, these numbers are just an exercise in maths. And a bit of fun.

It would be highly unlikely in either scenario, that spare money would sit in the mortgage that long. There are things to *do*, and locking up a bunch of money for a few percent interest until I’m in my 50s? Sounds like wasted beer money, or holiday money, or holiday beer money.

Beyond the first year will I really save $1800? What happens when the interest rate on my mortgage shifts?

Trying to cater for all these factors could drive a bloke crazy.

Looking at the opportunity cost is an interesting exercise, but it won’t keep me up at night. I’m hardly tying myself in knots with post-purchase cognitive dissonance either. I have a power bill that makes me smile.

There are also intangible benefits I’ve had on a personal level.

My rough biscuit has been on TV a few times, and across other media, which was a bit of fun.

I have created a little corner of the internet to blather my thoughts into the ether, and I’m flattered that people read it!

One of the best parts has been meeting with switched-on people, who want to make a real and positive change. They have a lot to teach, and I am in awe of the chance to learn from them.

You can’t put a price on that.