You are going to hit a huge CPU bottleneck pairing a 7870 with any Pentium D. Pentium Ds are very, very slow CPUs by today's standards, honestly, anything higher than a Radeon HD 7750 is likely to be held back by your CPU. It is probably time to look at a new CPU/Mobo/RAM combo, or at the very least a new CPU. If your motherboard supports a fast Core 2 Duo or the Core 2 Quads, that might be a cheap upgrade option for you. As for the 7870, there is little sense in buying it unless you get a much faster CPU, you'll be lucky to get 50% usage out of the card when using it with a Pentium D. Battlefield 3 and DayZ can also be rather CPU heavy, so that further exacerbates the problem.
Depending on what your old graphics card is, your best option may be to split your budget, and spend some money on a CPU upgrade, and the rest on a lower end graphics card.