Tag Archives: time value of money

Plug-in Prius payback period…

I’ll start with a preamble, expressing hope that the tragedies and suffering from Hurricane Sandy can be limited to a minimum.  And, recognizing that there are undoubtedly other tragedies I’m unaware of, whose victims are just as deserving of such hopes — I wish them the best as well.

I’ll also note that the Red Cross has a variety of apps available for emergency situations, including an earthquake app where you can sign in after a disaster, so that concerned friends and relatives visiting the Red Cross website can find out if you’re safe.  (The chances of them reaching you by phone are slim, given how phone lines overload in emergencies.)

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The inevitable question was asked about the payback for our Plug-in Prius purchase (versus a different vehicle), using time-value-of-money, assumed electric and gasoline costs, and so forth.

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1.  I’m going to argue that this is the wrong question.  The Plug-in Prius isn’t an attempt to save money, it’s the end result of having saved money.  By “delaying gratification” for various things (most specifically, the gratification of owning a house) we were lucky to wind up able to afford the vehicle.  (We also contented ourselves with a very old car, and managed to avoid acquiring a taste for cigarettes, alcohol, or fancy cuisine.)

Consider that many couples go out for a fancy dinner on their anniversary: perhaps they go to a nice steakhouse, order three courses, and enjoy some red wine as well.  From a purely financial perspective, that’s nuts because McDonald’s is way cheaper, and there’s no way to achieve net savings on the fancy dinner.  Well, unless one considers the certainty of divorce by a spouse who realizes they’ve married someone who sees relationships as an accounting entry:

 “Honey, by eating at McDonald’s instead of a fancy restaurant for our anniversary for the next twenty-seven years, and investing the roughly-$100 difference in a no-fee mutual fund compounding at 8% per year… we’d have $10,000!”

In a similar way, we could have purchased a nice used car, or even a new but much less expensive non-hybrid vehicle.  But since we could afford it, we chose a car which would benefit our son, in much the same way that married couples who can afford it, spend a bit more money to celebrate their anniversary — which presumably benefits their relationship.

As a side note, here’s a recent study arguing that small-battery PHEV’s (such as the Plug-in Prius) and regular hybrids (such as the regular Prius) are the most cost-effective way of reducing societal gasoline consumption… and by extension, of reducing transportation-related GHG emissions.

All of which is to say that the Plug-in Prius wasn’t bought as a cost-saving measure so much as a conscience-saving one; and it was paid for by previous cost-saving measures.  :)

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2.  Payback questions are highly influenced by one’s assumptions about the (uncertain) future

In the article, I estimated that the Plug-in Prius would prove cheaper than the regular Prius, after about 150,000 electric-mode km.  This was based on several assumptions:

– the Plug-in Prius’ premium over the regular Prius was $8000     (safe assumption, I checked it)

– electric prices of roughly 7 cents / kWh from BC Hydro       (reasonably safe assumption: BC Hydro has a record of keeping rates low, despite the fact that raising rates would spur conservation.)

– all-electric distance of 20 km for 3 kWh, or about 20 cents, of charge    (safe assumption, based on personal experience)

– gasoline consumption of 1 L per 20 km    (reasonably safe, based on personal experience; there’re a lot of hills where we live)

– gas prices of roughly $1.40 per L     (extraordinarily risky assumption, given how the price of oil has fluctuated over the past decade!)

The calculation therefore works out to a savings of $1.20 per 20 km (6 cents per km) in electric mode, so the number of electric km required to save $8000 equals:  (8000/ 0.06) = 133,333 electric km.  Since I was being quoted, I added a safety factor to come up with the 150,000 km.  Which is probably the equivalent of about ten years’ driving.  Good thing we plan to own it for twenty!  ;)

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I could get very different numbers, depending how I chose my gas price assumption!  And choice-of-assumption is often how people on different parts of the political spectrum can come up with wildly-diverging results on various issues.  As an example, supporters of Public-Private Partnerships (P3’s) claim they’re cheaper than government projects.  Opponents argue that this is due to flimsy assumptions (here’s a paper a Canadian union wrote up) and that other arrangements are more economical.  I don’t know enough about the nuances to know which is more correct, but given how the fantastically wrong assumptions of the right-wing deregulation faction caused the 2008-on-and-lingering financial crisis, I doubt the benefits are quite as extensive as proponents claim!

Similarly, there’s been noise about how the US could surpass Saudi Arabia in the carefully-chosen category of “liquid hydrocarbons” production.   I want to devote a separate blog entry to this fallacy, but suffice to say that Saudi oil production is about 10 million barrels per day, and American oil production is… 6 million barrels per day, and barely climbing.  The balance largely consists of about 1 million barrels per day of biofuels (a ridiculously roundabout way of turning natural gas based fertilizer and coal-based electricity into a liquid fuel) … and natural gas liquids and condensate, none of which are practical for running vehicles.  True, they could be refined into gasoline — but you’d have to build or retrofit an existing refinery first!  Here, the silly assumption is that all liquid hydrocarbons are equivalent to oil.  They’re not.

All of which is to say that payback calculations often give a false certainty to decisions built on a foundation of fluid variables.

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3.  Opportunity cost for companies is different than opportunity cost for individuals

It’s common in industry to assign a time-value-of-money, when deciding whether to move forward with capital expenditures.  This is tied in with the opportunity cost of a spending decision: the lost benefit of not doing a different project which would have also saved money in the long run.  A related metric is the payback period, being the time it takes for the savings to offset the up-front cost.  That’s the easiest to discuss without getting into detailed math, so I’ll focus on that.

A chemical plant has a zillion ways of reducing processing costs, so it’s not uncommon for spending decisions to have to pay for themselves in two years.  Other businesses might be a bit more lenient, but from what I’ve seen, three years seems to be a common cutoff.  Companies can’t afford to spend money on a project with a ten-year payback, because there are so many other projects which are more cost-effective.

Unfortunately for Mitt Romney, corporations aren’t people.  Unless a person is speculating in real estate or fad collectibles, there aren’t many purchases they can make, which will pay themselves off in a two- or three-year period!  As for the time-value-of-money, ING’s high-interest savings account currently offers a whopping 1.35%.  As for those who might be tempted to use the stock market’s historical average of 8%-per-year as a time-value-of-money metric… that hasn’t really (or should that be, “really hasn’t?”) worked for the past decade.

All of which is to say that business-type financial measures lose their meaning when applied to personal spending decisions.  Transposing them from the business context to the personal-finance context, is one of the dubious assumptions noted in (2) above.  :)