You can do this by creating three calculated fields, one for New, Existing and Total. They would look similar to the following:
if [Customer Type]='New' then [Income] end
if [Customer Type]='Existing' then [Income] end
sum([New]) + sum([Existing])
Then, remove Customer Type and Income from your view. Place Measure Names where Customer Type was and place Measure Values on the text shelf with only the above 3 calculations on the Measure Values Card. Finally, turn on the grand total by going to Analysis>Totals>Show Column Grand Totals.
Hope this helps!
Thanks for posting this. It works great for 1 Measure. How can this be accomplished for multiple Measures? For example add 2 columns to the right of Income in Paul's example called Cost and Profit.