How do we develop a business case that would recieve Stakeholder approval the first time?

First of all, try to learn as much as possible the stakeholders' interest in the case, for instance, project completion time or minimal cost or minimal disturbance etc...

Hence, build your case as follows:

1- Highlight the most important goals the project will achieve (relative to stakeholders' interest).

2- Mention the requirements (time, cost, ) and briefly relate to the benefits.

3- Finally, close with problems and risks if the project is not carried out, i.e. downsides of the current situation. Add a chart/graph to compare current performance with futrue performance after project completion. This will highly help with visual understanding the project's importance.

If you cover the vitals of the project as mentioned by Mr. Walid it will help you however every stakeholder is interested in followings :

a) ROI , Returns on Investments.

b) Value addition.

c) Key benefits.

d) Risk factors and risk coverage

Apart from above, some other vitals are : Proper road map, project duration, budget, execution plan, major milestones etc.

It will be very very difficult since the stakeholders range is huge. It can from owners(shareholders and their families), officers (directors, managers and their families), employees and their families, customers & suppliers and their families all the way to the government.

If what you mean is the share holders, then simply follow the sensitivity of the owners in exact order and you can instantly get their attention.