Its a valuable degree. If you are starting now, by the time you're done perhaps Zim economy will have stabilised to grow you or utilise your skills.
The greatest benefit is that you are globally marketable. If you like the idea of application/software development, that degree gets you a ticket to the industry. If you add more skill to yourself, you will also be able to develop software, web or other applications from Zimbabwe, since you seem to insist on the Zim market. The beauty of software development is that the main artifact you produce(software) can be developed and delivered from a remote location.
Speaking for myself, during the difficult Zim economy (2008), I relied on freelance work to survive. Depending on how hard you work or how fast you learn mainstream development languages( e.g. PHP,C#,Ruby, Python or Java) you can even start making money whilst doing your degree, without leaving Zimbabwe.
Otherwise for now,in Zimbabwe, you are limited in terms of the types of positions you can occupy with your CS degree. If you are happy with the more generic IT Manager/Administrator position, you can get that in Zim. But too much competition because many people opt for that easier way out