if i bought a cheap bottle of wine and hung on too it for say 10 years would it go up in value?

No, else everyone would be doing that. Cheap ones are designed to be drunk immediately or at least within a few months. They do not age well.

A lot of the cheaper wines are New World wines which mean they come from places like New Zealand, California or South America, where the climate is different to that in the Old Wine countries (France, Spain etc) The grapes used for making these wines have a different ripening time and tend to ripen earlier which makes them sweeter and results in a stronger wine. These wines have different characteristics.

Most cheap wines are drunk within 2 weeks of purchase and that's why stores have them sitting upright on the shelves. To preserve a good wine it needs to be stored on its side (to keep the cork moist) in a temperature- and humidity-controlled room, preferably a wine cellar.

After a year or so it would be vinegar and worth nothing. Only noble wines get better for storage - and even they have a storage limit which is often less than 10 years.

A cheap wine will always be a cheap wine and would more likely turn to vinegar.

It would have to be in a barrel or perfectly sealed bottle with high quality ingredients. If not then say hello to vinegar.

It would be undrinkable and worthless.