About $65 in hardware
An RTL-SDR dongle, a balun, coax and some wire. No proprietary decoder box.
Build a complete RC lap timing system from an RTL-SDR, a wire loop, and free software. Compatible with OpenStint, RC3, RC4, MRT and other transponders.

OpenStint is a free, open-source lap timing decoder for motorsport racing. It uses the same technology as professional timing systems (from club events to Formula 1): each car carries a small active transponder, and a wire loop laid across the track picks up its signal as the car passes.
The difference is the decoder. Instead of a dedicated, expensive decoder box, OpenStint uses an inexpensive software-defined radio (SDR) plugged into a computer. The software demodulates the transponder signal, identifies the car, timestamps the passing, and hands the result to your lap counting and race management software.
It is aimed at clubs, private tracks and anyone who wants reliable transponder timing.
OpenStint decodes several transponder families, so drivers can usually keep what they have:
Different transponder types can be mixed in the same race.
The decoder running on a Raspberry Pi with a HackRF One, reading transponders from the loop:
Order the parts and lay the loop, then install the software and point your scoring program at it. The step-by-step guide walks you through all of it.