Debby's Dance Studios is considering the purchase of new sound equipment that will enhance the popularity of its aerobics dancing. The equipment will cost $$20,000.$ Debby is not sure how many members the new equipment will attract, but she estimates that her increased annual cash flows for each of the next five years will have the following probability distribution. Debby's cost of capital is $12$ percent Use Appendix D for an approximate answer but calculate your final answers using the formula and financial calculator methods.

$\backslash$table$[[$Cash Flow,Probability$],[$$$3,850,0\mathrm{.}5],[5,390,0\mathrm{.}2],[7,680,0\mathrm{.}1],[10,530,0\mathrm{.}2]]$

a$.$ What is the expected value of the cash flow? The value you compute will apply to each of the five years.

Expected cash flow

b$.$ What is the expected net present value?

Note: Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to $2$ decimal places.

Net present value