A cheap HRM (or anything else) gets expensive after you have tried a few that don't work well or at all. I had a cheap wrist unit that was supposed to read the ulnar pulse but it didn't work for me. It turned out to be a complete waste of $29.95. I then bought a Polar F6 at REI and it works flawlessly. It was about $100.00 but you can find it for less on ebay, etc. The most basic Polar, the B1, is about $45.00 and it is what one of the personal trainers at my gym recommends for folks who want a lower priced unit.
Here is a link to the Polar site for a comparison of all their models:
Polar HRM