How can a variable follow normal distribution with varying skew??? If the distribution is normal, then the skewness cannot be varying. If the skewness is varying, then the distribution is not normal.

The connection between any continuous distribution (for example normal) distribution and uniform distribution is very simple:

https://en.wikipedia.org/wiki/Inverse_transform_sampling

 if is a continuous random variable X with cumulative distribution function F, then the random variable Y=F(X) has a uniform distribution on [0, 1].

Peter,

Thanks for the reply including the reference link.

My reference to varying skew is that since the cash flows will vary over time depending upon the progress of the project, in order works, the peaking of the cash flow pattern over the period of time is subject to change. I am not sure whether i can refer to the same as a skew. 

Best Wishes,

Sarosh

Use norm inv in excel with rand as the param. Rand() is already set as uniform and you can get the answer you need in a defined number of simulations. This pertains only the stated maths of the question. Skew param needs to be separately set . I don't see that available as a std function in excel. 

I could be off the mark here.  If I understand the question, you may find probability density function, and its analogues, appropriate analytical methods.  

Try this relation x = [-2ln(n1)]^(0.5)* Sin(2*pi*n2) where n1 and n2 are from U(0,1).

mu+sigma*x gives normal distribution. I hope this may help you.