| This is not a paid endorsement. I recommend this company because I use its service, and have found it to be superior to many common alternatives. I am not affiliated with this company in any way other than being their customer. |
If you're looking for an inexpensive, high-quality long distance telephone service provider, I would highly recommend OPEX . Their rates are the lowest available for most subscribers in California, and are probably at least similar to the lowest rates across the country. I have been using them since September, 2001, and have never experienced a problem with call quality, reliability or availability.
There are no minimums or monthly fees (unless you want them to bill through your local phone company, in which case OPEX passes their $1.99 fee on to you).
The second option, called "auto-pay," deducts charges from your bank account every month. The third option, called "pre-pay," deducts an amount that you specify from your credit card or checking account every time your OPEX account balance reaches 10% of your specified amount. You get an 8% discount to compensate you for keeping some of your money in their bank account.
In order to determine whether you should prefer "auto-pay" or "pre-pay," I recommend using the following analysis.
| M | Maximum specified balance (exogenous, i.e. you can pick its value) |
| m | Minimum balance (1/10 × M) |
| r | Investment return (per year) [about 0.05] |
| C | Transaction charge ($0.99) |
| V | Usage volume ($ / year) [multiply monthly minutes by 12 × (OPEX rate, e.g. $0.049)] |
| D | Discount (0.08) |
| B | Net yearly benefit from pre-pay over auto-pay. |
Assuming that the yearly opportunity cost of having money not earning interest is approximately given by r × (M + m) / 2, then we have:
| B ~ D × V - r × (M + m) / 2 - C × V / (M - m) |
| = D × V - 11/20 × M × r - 10/9 × C × V / M |
Taking dB/dM and setting it to zero, we get the optimum as
| M* ~ sqrt(200/99 × C × V / r) |
| B* ~ D × V - sqrt(22/9 × r × C × V) |
If B* is negative, then opt for auto-pay. If B* is positive, then opt for pre-pay, and set your pre-pay amount to M*. If M* is less than the minimum M allowed ($20 for residential, $50 for business), then plug the minimum M into the equation for B, and opt for pre-pay if the result is positive.
Enjoy!
Anders Johnson, last modified $Date: 2002/02/20 $