I graduated from
NTU Aero Eng last year. Most of my friends got into ST Aero and SIAEC (if I rmb correctly around 5-6 guys each). Those with 1st class hons went into banking, or became researchers in
DSO/
DSTA. One or two went to Changi Airport Group, I think because he interned there last time. As for big MNCs: RR recruited less than 5 fresh grads I believe? And those grad positions are not aero-exclusive, meaning students from other programs, mainly mech engs, have the same chance as us. P&W even did not recruit any freshers. If your long term ambition is to become a specialised, 'hardcore' engineer then I'd suggest going overseas, and if possible take a Master's. Singapore is more a financial hub, not manufacturing/engineering.
As for prospects, we've seen it in the news... Aero industry is still largely affected by crises in the USA & Europe. Yes, low-cost carriers are expanding like crazy but the two biggest LCCs out there, Air Asia and Lion Air are not local-based. I don't know whether they are open to international recruits. Also, their openings are mostly for LAEs, technicians and flight attendants. Hardly a position for degree holders, no?
However, since you're just going to enter the industry in 2018, have faith! A lot of things can happen in 4 years, hopefully the economy has picked up by then
As for biz degree, I can't comment much but what I observe is this: engineering degree holders can always jump to biz world later, with or without MBA, but the opposite direction is very rare and unlikely, because engineering is a very specific field while biz is very general (each with its own pros and cons). But then again, if your passion is in biz in the first place, why study engineering and graduate 1 year later?
All the best for your studies! feel free to PM me if you want to ask more about aero stuff

(yes, I know there are definitely other more senior aero people in this forum, but until they come and share their knowledge here, I am happy to offer what I know)