* Original specification: A 1964 327 came in various configurations (different camshafts, carburetors, intake manifolds, compression ratios). A base model will make significantly less power than a high-performance version.
* Modifications beyond bore: Simply boring it .040" over only increases displacement slightly. Other modifications like the camshaft, carburetor, cylinder heads, intake manifold, exhaust system, ignition system, and even the valve train will drastically impact horsepower.
* Condition: The condition of the engine (wear on internal components, etc.) will significantly affect power output. A perfectly rebuilt and meticulously tuned engine will make more power than one that's simply bored and slapped together.
* Tuning: Proper tuning of the engine's fuel/air mixture and ignition timing is critical for optimal power.
Estimating Horsepower:
A stock 1964 327ci engine might range from around 210 to 350 horsepower depending on the specific model. Boring it .040" over will increase the displacement by a small amount, perhaps adding 10-15 horsepower *if* everything else is optimized. However, without knowing the specific original specifications and planned modifications, any horsepower estimate is pure speculation.
To get a better estimate, you'd need to provide more details about the engine's specifications and planned modifications. Alternatively, you could consult resources specializing in classic car engines and performance modifications.