Anyone here good with numbers?

[andrewducker]

I'm currently looking at the difference in price between going to a Samsung Galaxy Nexus by getting a contract (£35-ish/month) or by buying up front (£480+10/month). This works out to about £120-£140 cheaper by buying the phone myself, depending on exactly how I do it.

My question, then, is about discounting future costs. If I spend £480 now rather than in chunks then I lose the utility of that money over the next two years. How does one account for that?

I assume there's a simple equation I could plug in that would tell me to stop being so stupid and just buy the fucking phone, but I'd like to be sure...

Comments

[matgb]

James (magister) says you're better off buying it now for a number of reasons assuming it's money you've got, but he's one of those people that can do the maths in his head without necessarily then knowing the working (he can work out tax due on earnings, including thresholds &c, in his head if given an hourly rate and hours worked, scary stuff).

I think there's another reason. I'm tied to both my phone and my existing contract for another 18 months. Now, I like my phone, and the contract is OK and suits my needs, but if circumstances change, or a new deal is available, I'm stuck with it, but if you buy the phoen outright you can switch deals to get the best data costs &c without any hassle.

Ultimately, money up front plus small monthly fee is probably better, especially given interest rates and similar are very low currently, but I can't do the maths on that.

[andrewducker]

Gotcha. Not that I have £500 right now, but it sounds like any end-of-year-bonus I get ought to be spent buying the phone.

[azurelunatic]

http://en.wikipedia.org/wiki/Amortization_%28business%29 might be of help...

[emceeaich]

What's the other thing you could do with the £480 now? Bank it? Fix something at your home? Lavish your fiancee in jewels? That's your opportunity cost.

[andrewducker]

Yes, but that then means I'd be spending £36/month and not doing something else later. And I want to know the numeric difference.

[rhythmaning.livejournal.com]

I should know this... I spent years doing discounted cashflows (DCF)!

The thing to decide is your discount rate - the value you put on having the cash (all known as the "time value" of cash or - surprise surprise - the interest rate): one would usually use 5% or 10% for simplicity, but when you can only get c 2% interest in the bank that might make more sense.

But it looks like you've already done more or less that calculation - £120-140, you say.

DCF makes more sense over several years - monthly payments complicate it a bit...

[andrewducker]

Well, money I spend in a year will probably be worth 5% less than money I spend now. So in two years it would be worth 1.05^2 less, which actually isn't that much - £50 on the £500, and nowhere near the £120-£140 actual difference.

Not that I have £500 right now, but it sounds like any end-of-year-bonus I get ought to be spent buying the phone.

[octopoid-horror.livejournal.com]

If you have signed a contract to pay £35 a month, the money that you specifically are spending on your contract will not be worth any less, because in the last month of the contract, you'll be spending £35 on exactly the same as you were in the first month, regardless of inflation.

[andrewducker]

That doesn't make any sense to me. £35 in a year and a half will be worth less than £35 now purely due to inflation (unless inflation drops to zero, of course).

[octopoid-horror.livejournal.com]

In month 1 of your contract, £35 gets you a phone handset and a package including however many minutes, texts and whatever amount of data. In month 18, regardless of how much it now costs to buy a loaf of bread, £35 gets you the exact same thing. The month after your contract is up, it's a different matter of course when you have to get a new contract.

That £35 would buy you less of -other- things in eighteen months time compared to what it would buy now, but if you sign a contract for £35 then there will be zero inflation for that product (the product being your phone contract) over the following eighteen months. The contract on my phone costs me the same money each month, and I get the same thing every month, regardless of what inflation is running at in the UK.

I would also argue that if you are considering spending £480 on a phone, I would hope that the effect of inflation or indeed savings interest on £35 a month over eighteen months would not be material to you.

[octopoid-horror.livejournal.com]

Aside from that, is this a very new phone? If it's -not- a very new phone, I would definitely not suggest spending £35 a month for eighteen months, because when it's superseded, it'll be available on cheaper contracts and you'll feel slightly silly in six months when other people signing £35 a month contracts are getting the Galaxy Supernexus which does all that and a bag of chips.

[andrewducker]

It's the newest pure Google Phone. It will be superseded in approximately 12 months, and again 12 months after that.

It's most definitely the phone I want (I did a post, and nobody could recommend an alternative that fulfilled all of my requirements).

Buying it outright does give more possibilities for selling it on and getting another one though in a year if I'm staggeringly rich at that point, which is even better.

[autopope.livejournal.com]

It also gives you the flexibility of not being locked in with a carrier whose quality of service may take a dive in the next year (this is unknown but possible).

That's why I am now buying unlocked iphones at full retail price direct from Apple. Combined with a SIM-only monthly contract it works out about the same price as a two year contract, but if my carrier goes pear-shaped I can walk at a month's notice. (Oh, and I'm choosing to buy alternate iPhones, i.e. I started on a 3G, skipped the 3GS, am now on a 4, am skipping the 4S, will probably upgrade to an iphone 5 a month or three after it comes out ... unless Apple piss me off in the mean time.)

[andrewducker]

Yeah, that's basically what I'm doing. Which gives the options of selling it after a year if the next one is so awesome that I have to have it (unlikely), and more freedom. It seems like a definite winner so far.

[undeadbydawn.livejournal.com]

I went 1G to 3G to 4S.
The 4S is a fucking fantastic phone, but I don't love it in the same way as I did the 3G. This is entirely down to form factor: I did not and still don't like the 4 design, though it is growing on me daily. As a device to use, it is quite wonderful.

I will be sorely tempted by the 5, assuming I can afford it. The mock-ups posted based on 'insider info' were stunning

having now played with a Galaxy S II, I'm very happy to stick with iPhone. It just feels better to use - and saved my life countless times in Moscow.

[andrewducker]

It's as you say - I lock myself in to a contract, and thus give up the opportunity costs of that money - it's exactly the difference between the two amounts that I was asking how to calculate!

It's 24 months, and over that time, 10% of £the 840 is 1/6 of the original cost of the phone. That's certainly big enough to be worth taking into consideration.

[cairmen.livejournal.com]

If you would otherwise be saving the money, you need to consider interest rates too. That'll add about another 3% on to the "cost" of buying now.

[ciphergoth.livejournal.com]

I don't think it adds another 3% - I think it might mean that 3% is the least it can be

[cairmen.livejournal.com]

True. My brain is too fuzzy right now to figure out how the interest and inflation will work together.

[andrewducker]

Interest will give you more money, inflation will make it worth less. The difference in the value of the money you have will be interest-inflation (well, not quite).

If I have £100, and there's 5% inflation and 4% interest, then one year from now I'll have £104 and that will be worth £99.04 in today's money.

[rhythmaning.livejournal.com]

Sorry, formatting didn't work... I hope that makes sense!

[andrewducker]

Hang on, if I spend £420 next year doesn't that mean that it would be worth less than £420 spent this year? Because next year's money is worth less than this year's money.

[rhythmaning.livejournal.com]

Sorry, so long since I'd done it that I got it back to front. Ooops.

[andrewducker]

I'm holding you responsible for the collapse in the economy.

[allorin.livejournal.com]

Where's the 'like' button when you need it? ;+)

[charleysjob.livejournal.com]

http://en.wikipedia.org/wiki/Time_value_of_money#Present_value_of_an_annuity_for_n_payment_periods

Your looking for the present value of future cash flows. In your case, with monthly payments, take your interest rate and divide by 12, and do it for 24 periods.

In excel or something similar, copy "25" in a row 24 times (the difference in monthly payments), then somewhere over on the left type "=NPV((5%/12), A1:X1)" and see if that's more or less than the difference in price.

(obviously, "A1:X1" should be replaced by wherever your string of 25s is)

[charleysjob.livejournal.com]

Shit wrong "you're". Going to self-flagellate now.

[poisonduk.livejournal.com]

One thing you haven't factored in is that the phone you buy is unlocked from day One. Financially ths is worth a lot if you intend going to the USA during the lifetime of owning the handset. I bought a PAYG SIM in NY, which I could use in my phone and thus not rack up my UK data charges yet have full access to email and Internet whilst there.

[nameandnature]

It's interesting that you phrase it that way: this article talks about working it out in terms of the effective interest rate you're paying to borrow the cost of the phone and the talk plan from the phone company if you take the contract.

[andrewducker]

Thank you - the spreadsheet there gave me my answer - I'm effectively 14% interest for two years, which is way over inflation.

[drdoug.livejournal.com]

The Right Answer is to use the Net Present Value function in your favourite spreadsheet to do the sums for the discounted cash flow of £25 a month (£35-£10) for the length of the contract, and compare that to the £480.

The key question is what to use as the discount rate. This question is at the heart of the current financial crisis!

I reckon it's defensible to use 0% - to say £1 today is worth £1 tomorrow. The big benefit of this is (a) sums are trivially easier, and (b) it's a nice counterbalance to the human tendency to hyperbolic discounting.

Another quick answer is to use 3% because that's what everybody does.

Or you can try to work it out.

You need to job in a guess for inflation (CPI? RPI? whose forecast)?

Then you need your personal risk-free return rate. This is very apropos at the moment, since if you were doing this for finance purposes you'd use the rate on Government debt ... but the consensus that this is a risk-free return rate is dissolving, to say the least.

I'd say the more important factor is what you'd do with the money otherwise - the opportunity cost. If it'd just be in your current account earning 0.1% minus your top marginal rate of tax, that's negligible, but if on the other hand it would save you from taking out payday loans every month, that's well worth taking in to account.

... out of time, sorry, but you get the idea. Every time I do these sums, buying outright wins by such a spectacular margin I think I must have made some mistake, and I can't really understand why so many people buy on a contract. I mean, even credit card debt works out cheaper.

[andrewducker]

See the comment from pw201 - it works out to 14% interest, which is just dumb.

[despotliz.livejournal.com]

Also worth considering: Can you get the contract through a cashback deal, which might close the gap between the two alternatives? And check the small print in case your ~£35/month contract could end up increasing in price during the contract period.

[andrewducker]

Cheers for that - I'll investigate in 10 days time when my contract ends!

[fearmeforiampink]

See, I wouldn't do this in the mathematical way you're approaching it.

I'd look at "Can I afford to pay up front?" and if yes on that, then "What else could I do with that cash sum?" less in terms of interest, more in terms of buying other things you might want or need.

Another question is the difference between the £10/month contract and the £35/month contract in terms of what they give you, free minutes, texts and internet-wise.

I bought my iPhone 3GS on pay as you go, used it on such for a year (spending about £10 every 2-3 months for more credit), when the free internet that came with the phone ran out, I switched to a £10 for 100 texts, 100 minutes, and Unlimited/2GB internet usage. Whilst I went over it a few times during the Yes campaign, outside of that I rarely use up all of my allowance, but I don't think there's any cheaper option that gets me some level of phoning plus what I really want — the internet.

If your usage is similar to mine, then the buy it and pay £10 a month thing is probably a good solution if the cash is viable — I looked at mine and was saving somewhere between £130-200 depending which contract I'd bought it on, I did have the money to buy it outright with, and I had no other things I desperately needed to buy with that cash.

[andrewducker]

There isn't anything that I could do for £500 that I couldn't also do for £x/month, due to the wonderful services of the financial system.

And for £10/month I can get 300 minutes, 3000 texts and a GB of data from 3. Which looks better than what I have at the moment.

[chaos-monkey.livejournal.com]

Late to the party, and from all that it looks very much like buying it outright is vastly cheaper, but just to say...

Never take the contract they advertise. Phone them, and say "I want [shorter contract/ more data allowance/ freebies] for [amount of money]. Or I will go and talk to [other provider] and give them all my money instead. Get back to me if you can't agree that now. You can call me at [convenient time]."

It works most of the time. Unless the phone itself is only available on one network, of course...

[andrewducker]

I'll bear that in mind. Thanks!