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.

[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.

[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...

[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.

[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)

[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.

[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.

[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.

[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.

[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...