Please answer and provide a numerical example for each following question:

Explain the difference between pre$-$money valuation and post$-$money valuation.

Discuss what is meant by a capitalization $($or cap$)$ rate in reference to calculating a terminal value.

What other types of terminal values might be appropriate $($i$.$e$.,$ other than smooth growth procedures$)?$

Describe the process for estimating the percentage of equity ownership that must be given up by the founder when a new equity investment is needed.