The time value of money (or why 25 years of cable TV doesn’t cost as much as you think)

Just after Christmas, Carl Hendley of The Motley Fool wrote about his cable bill and how much lost investment income that money represented. As an economist, I was intrigued by the notion, and couldn't help but run the numbers. (We economists are strange like that.)

Hendley's calculations assume that the average person cares only about nominal, time-insensitive returns. That is, that a dollar today is worth a dollar tomorrow. But we economists know (from all of our fancy-pants research) that, generally speaking, that's not how people make decisions. Instead, when most folks make personal-finance decisions, they take into account the time value of money.

The Time Value of Money

“The time value of money” is a complex term for a simple concept: Any given amount of money is worth more today than the same amount in the future. Assuming a 5% interest rate, for example, $100 today is worth $105 a year from now. (Or, working backward with the same assumed interest rate, $100 in a year is worth $95.24 today. And what, they're not the same? Nope!)

The time value of money has two main components: inflation and personal valuation. While Hendley's main point is correct — recurring monthly charges can be costly in the long haul, and can dramatically affect your retirement savings — the real long-term cost of his cable bill isn't actually $132,683.

Citing research from Good Debt, Bad Debt and other sources, Hendley assumes a 10% annual rate of return on $100 monthly investments made for 25 years. His example assumes that we value $100 invested today the same as we value $100 invested 25 years from now. In reality, $100 today is likely to be worth much more than $100 in the future.

Note: One reason stocks need to show strong long-term growth (and why bonds pay interest) is that investors must be compensated for the time value of money. Otherwise, investors could use that cash for something else.

There's a simple rule to describe the conditions that make investors willing to invest in equities (like stocks) versus, say, TIPS (bonds that automatically adjust for inflation):

Expected Rate of Return >= Expected Inflation Rate + Time Value of Money

In other words, for an investment to make sense, its expected rate of return has to be greater than the total of:

  • The inflation rate. In general, people react to the real (after-inflation) rate of return, not the nominal (pre-inflation) rate of return.
  • Your personal time value of money. What could you do with your money today other than put it in this investment? This is somewhat related to opportunity cost, and is very tough to measure on a personal level. We each have a different time value of money: For you, a 1% high-yield savings account may tempt you to save, but your brother may rather spend the money on a new car instead.

Painful — But Not as Much

Returning to Hendley's cable bill, it's fine to assume constant rates over time to keep things simple. But to show the real cost of paying out for cable television, you have to work some economic magic. Which I've done for you, using a discounting routine (or a net present value calculation).

Note: Though I may be violating the sacred code of magicians economists, you can look behind the curtain to see my calculations with this Google spreadsheet.

What I've done here is take the long-term cost for cable television, and compute a number that tells you what that's worth to you right now if you were to invest the money instead. We need to compare apples to apples. (Or dollars to dollars, in this case.)

Assuming an annual inflation rate of about 3%, the net present value of $132,683 is about $63,250. That is, the $132,683 Hendley could pay toward his cable bill over the next 25 years is actually worth about $63,250 if invested in equities (such as stocks or mutual funds) returning an average of 10% with 3% inflation in today's dollars

And assuming his personal time value of money — what the cash might be worth to him if used elsewhere — is also 3%, real cost of watching cable for 25 years instead of investing is about $30,000. (If you extend the time-frame to 30 years, that estimated cost grows to over $50,000. Your time-frame matters!)

The Moral of Our Story

When you look at savings in nominal terms — when you look at the raw numbers — you over-emphasize the value of future holdings. The future is uncertain. Inflation gnaws at your money, and consuming today is more pleasurable (and more certain) than consuming later.

This is a mistake that many people make when talking about personal finance. David Bach's famous “latte factor” (from The Automatic Millionaire and other books) is perhaps the most notable example of this fallacy. Bach ignored the time value of money.

Still, his primary point — that cutting recurring costs can help you meet your savings goals — is completely valid. Small, easy changes to your habits can have an enormous impact on your future financial status. But it's important to consider all of the factors. One way to do that is to use my spreadsheet (or something similar) to compute the net present value of the proposed savings.

When you do this, you can ask yourself questions like: “Would I rather have $30,000 today or cable television for the next 25 years?” There's no one right answer. It all depends on your time value of money.

More about...Economics

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Kris
Kris
9 years ago

Nice article on personal finance that applies the Austrian Economic Theory on time preference and subjective value in case anyone has heard of these.

dmm219
dmm219
9 years ago

You’re doing it wrong 🙂

You are forgetting to apply the TVM to future price increase. Cable tv will most likely rise in cost along with inflation…therefore, your 30,000 could be more like 60,000.

The mistake that many make with TVM is that they forget to apply it to both sides of the ledger.

Amanda
Amanda
9 years ago

@2. We don’t know that cable will go up. It might go down because of becoming an “old technology”.

Noadi
Noadi
9 years ago

Don’t forget to add into calculations like this the impact removing something from your life would have (or not have). I use netflix’s streaming only service instead of cable, it’s $7.99 a month. I watch at most 5-6 hours of tv a week. If I had cable I’d be paying somewhere around $4 for every hour of tv I watched which isn’t worth it for me.

A household of more people who watches 40 hours a week of tv cable may be of far more value. Each hour of tv watched would be closer to $0.80.

Pat S.
Pat S.
9 years ago

The other factor is the individual’s personal valuation of their cable television service. If cable t.v. is an essential part of their social, home or family life then the service may very well be worth 30k to the individual.
Pat
http://compoundingreturns.blogspot.com

Sakoro
Sakoro
9 years ago

This is really thought-provoking! I was an econ major in college and had never really considered TVM in reverse like that.

fetu
fetu
9 years ago

How much more is your time worth if you do not watch TV apart from the cable cost?

Just asked my cable company today ( Oceanic in Hawaii) how much a local stations only basic cable would cost a month. $13 Where we live we need cable to get TV snow free but I am thinking of ditching all the extra channels.

jdmitch
jdmitch
9 years ago

Yup… with many of these “wants” you aren’t chopping as much out of your future earnings as you might think. The key for my family is reducing outgoing cash flow and the potential impact on financial security. Either a) you have a higher free cash flow every month or b) you can accelerate debt reduction.

El Nerdo
El Nerdo
9 years ago

@3 Amanda dmm219 is correct. The article says “Assuming an annual inflation rate of about 3%…” — Per your logic (“We don’t know that cable will go up”), we also don’t know that inflation is going to be 3%– we could have deflation, we could have hyperinflation, we could be invaded by China, but this is a simple calculation, not a crystal ball. If we are assuming 3% inflation (even though “anything could happen” ) it’s also reasonable to assume a corresponding rise in cable prices. Otherwise formulas would make no sense since we don’t know what the future will… Read more »

Jerichohill
Jerichohill
9 years ago

@El Nerdo

Jerichohill
Jerichohill
9 years ago

@El Nerdo & dmm

Please note that there is only so much abstraction I can do in any discussion on the time value of money given a set word limit. Obviously, I made some assumptions.

Samantha
Samantha
9 years ago

Two regular typos and what looks like one BIG typo.

Nicole
Nicole
9 years ago

@12… Samantha, no need to be so wroth with him… (or was that worth?)

Joe M
Joe M
9 years ago

Anyone want to proof read this article and fix the typos?

Jerichohill
Jerichohill
9 years ago

Considering this is a labor of love, joe, nicole, and samantha, i figure two typos is pretty good for free labor.

razmaspaz
razmaspaz
9 years ago

I’m not following all of that, but I think I got the main point, money isn’t worth as much in the future because of inflation so assuming you will be 10% richer in a year is a mistake. Where I run off course though is the $30000 today. If I stopped paying for cable I would not have $30000. If I did have 30,000, I could put it in a bond fund earning 3.3%, beat inflation by .3% and use the proceeds to pay for my cable again. I think what you really did was calculate the value of the… Read more »

Bill
Bill
9 years ago

TVM is great for pointing out the flaws in the 0% interest deals for new cars.

El Nerdo
El Nerdo
9 years ago

@ Jerichohill Thanks for your work, we all appreciate it, and the spelling nazis contribute nothing to the discussion. I do think however dmm’s suggestion is simple and abstract enough to work into the formula while making it more accurate. The $100 at 3% annual price increase over 25 years ends up as a $209.38 monthly fee. That’s more than double today’s price, so it’s not a trivial factor in the calculation. I think the article you refute fails to account for that also (not sure). But if the price of cable goes up from $100 to $105 in a… Read more »

Bill in NC
Bill in NC
9 years ago

Cable prices historically have increased faster than the overall rate of inflation.

Here what used to be 40 channels for $15/month is now 70 channels – for $60/month.

I would expect that trend to continue.

A year ago I chose to hang an outdoor antenna indoors, simply pointing out the window, and I now get all locals plus a couple of stations 60 miles away.

I buy other shows I want commercial-free via iTunes or from Amazon’s Unbox.

brokeprofessionals
brokeprofessionals
9 years ago

My wife and I have gone off and on cable for the past several years. The real issue with most things has more to do with the value (or marginal utility as economists might say?) than anything else….in most instances. During football season I find cable to be worth the price each month. Otherwise, I generally do not. The only issue for us is that there is no good way to get basic where we live, so if you go off paid tv you pretty much have no television at all. With the internet and some simple wiring that is… Read more »

Nicole
Nicole
9 years ago

I dunno, when I get called on a typo, I just fix it. I don’t really see any need to attack folks who point them out, especially when they’re kind of funny typos.

Thank you for fixing them, btw.

Laura in Cancun
Laura in Cancun
9 years ago

I’ve never seen or paid a cable bill in the US… but do ya’ll really pay $100 a month for cable? Or is that amount just aiming towards the high end for the purpose of the original article?

In Mexico I pay $27 a month for satellite service with about 100 channels.

El Nerdo
El Nerdo
9 years ago

@ Nicole – ok, typos are fixable, but only worth bothering with them when they confuse meaning, and when someone comes on the blog just to scream “Typo!” everywhere without saying anything else (not just in this thread), it’s a little irking, kinda like “cacao!” in Portlandia.

http://www.hulu.com/watch/210891/portlandia-cacao

^^ now that’s funny (parental guidance required)

und heers summ mor tipoz 😉

Chris P.
Chris P.
9 years ago

I didn’t read the original article, but this is still very timely. I just contacted my cable company earlier this week to get rid of the signal I was getting. Currently, I pay 86 a month for cable tv (no digital box) and cable internet. I will drop this by 50 bucks a month by removing the television. In it’s place, I bought an HD Antenna (originally 80, got it for 45 because the box was opened. Lifetime warranty) and netflix with 1 DVD. That’s a savings of $40 a year and $480 a year! Plus, since I live in… Read more »

Samantha
Samantha
9 years ago

Not to hijack this thread, but if at least three people noticed an error, shouldn’t it be pointed out? If it takes just a little bit out of the experience, then shouldn’t it be fixed for later readers?

I freely admit that I have nothing to contribute to this discussion, I found it a little difficult to follow, but if I have something to contribute to readability, then I will.

Again… not trying to say that anything’s bad, just trying to be helpful!

El Nerdo
El Nerdo
9 years ago

sorry if i was harsh, i just felt people were ganging up on the guy and i guess felt compelled to come to his defense (not that he needs it– it’s just an instinct of mine). ok, let’s all be friends again.

TF, Boston
TF, Boston
9 years ago

Rather than considering the PRESENT VALUE, wouldn’t it make more sense to consider the FUTURE VALUE?

Because of the time value of money, that cable TV is likely to take a far bigger bite out of your retirement than the $130k suggests. It could easily force you to work an additional one or two years, or alternatively cut your retirement income by $5k-$10k/year. Try running the numbers on that one?

These monthly bills add up very rapidly.

Samantha
Samantha
9 years ago

Friends 🙂

Jerichohill
Jerichohill
9 years ago

Yeah, to the typo folks (Samantha is one, but there were 3 in a row which was irksome), really folks, as the author I don’t actually post the darn thing. It was submitted and revised by someone who is not me. The typos (which I do not know what they were) may have been my hand or someone else’s. The typo comments added nothing, because they didn’t state where the typo was. Further, while I admin the forums, I have no control over the editing of posts, as is true of my guest authors on this blog. So, yeah. @TF… Read more »

rose
rose
9 years ago

If you just shop around for a good and cheap TV provider you wouldn’t spend more than $45.00 a month. I work for DISH Network and they have their lowest package starting at $44.99 a month, and that’s without any promotional offers. Cable companies are a lot higher in pricing than DISH. That package is 120 channels. So shopping around would make a huge difference in the price you pay for TV.

Leszek Cyfer
Leszek Cyfer
9 years ago

Neat example. Of course all varies depending on your assumptions. Like that 10% return or the 3% rate of inflation. What it all boils down to is one’s awareness of choices. If you “go with the flow” and spend your money with abandon on whatever fancies you (and usually it’s influenced by ads and example of people that surround you) then not knowing how your money go down the drain and you are left with no assets to pursue your own dreams. And the stuff you purchased turns into ash in your hands as it turns out that you don’t… Read more »

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