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I use a number of methods to overcome this challenge.
1. If the software is off-the-shelf, obtain quotes from 2 or 3 vendors.
2. Base estimates on previous projects that were similar in size and function.
3. Allow lots of contingency in your budget.
4. List the assumptions that you made in order to calculate the estimate.
5. Ensure that the risks to the budget are clearly articulated - ie there's a risk that the budget will increase once you know the final requirements.
And finally, ensure that the proposal states clearly that the estimates are just that - estimates - and are subject to change once the detailed requirements are finalized. This communication is vital, so that expectations are set.
Hope that helps...
Elaria, you can use estimating methods like three points or PERT and make business case calculating IRR, Payback period and NPV then you can add contingency percentage for example 10 % easiest way otherwise there are more calculations for contingency with different probability
Before you have a detailed understanding of the "what" and the "how", remember that you will be making a Rough Order of Magnitude or similar level of (low) confidence estimate. Top-down approaches such as analogous estimation or using software estimation models such as COCOMO or QSM Slim will give you a range to work with.
What you state is a business analsys phase named "needs analysis" or "strategy assessment" depending on you take PMI or IIBA guidelines. The outcome is the business case but perhaps you are working on feasibility study which is before the business case. What I am using from years is the Vision Document. Two key things are critical to remember: 1-you are working on defining a solution. Solution is equal "the thing" to be created plus "the process" to create it. Business analyst is accountable for the first while project manager is accountable for the second. You need to work with a project manager no matter if the project is approved she/he will not be the assigned project manager. 2-take into account Barry Bohem´s Cone of Uncertainty when you work with estimation.
BUT the key thing is: business analyst must do stakeholder analysis to take into account all people that can help her/him to create all the deliverables.
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