When does it make sense to buy an annual rather than a monthly pack?
My TV provider offers me a monthly package, but lets me prepay for a longer duration at lower price. Here are the options:
?100 monthly
?567 semi-annually
?1,098 per annum
?2,100 biennial
All these are prepaid, not postpaid.
Assume that I have an investment available that generates a post-tax return of 12%. Which of these options works out to be the cheapest, and in what order do they rank?
Put differently, how much return does my investment need to have for it to be profitable to go for (say) the monthly pack over the annual one?
I understand that by prepaying, I will lose money if I decide to switch providers before the duration I've prepaid for is up.
PS: I googled for "NPV calculator" and "discount rate calculator" but they seem to handle a different situation from this one — they assume that you're investing a certain amount of money in (say) a factory that will generate regular cash flows. That's not the case here. Besides, I never know whether to enter numbers with a positive or negative sign, and they then tell me that at least one of the numbers must be negative, etc.
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A quick Excel calculation tells me that, if you are earning a guaranteed post-tax return of 12% in a liquid investment, then it doesn't matter which one you pick.
According to the following Excel formula:
=PV(0.12/12,24,-100)
You would be able to invest ?2,124 now at 12% interest, and you could withdraw ?100 every month for 24 months. Which means that the ?100/month option and the ?2100/biennium option are essentially the same.
This, of course, is depending on that 12% guaranteed return. Where I come from, this type of investment is unheard of. If I was sure I'd still be using the same service two years from now, I would choose the biennial payment option.
You asked in the comments how to change the formula to account for risk in the investment. Risk is a hard thing to quantify. However, if you are certain that you will be using this service in two years from now, you are essentially achieving 13% in a guaranteed return by pre-paying your fee. In my experience, a 13% guaranteed return is worth taking. Trying to achieve any more than that in an investment is simply a gamble.
That having been said, at the amount we are talking about, each percent difference in return is only about ?22. The biggest risk here is the fact that you might want to change services before your term is up. If these amounts are relatively small for you, then if there is any chance at all that you will want to drop the service before the 2 years is up, just pay the monthly fee.
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