$1.$ You are helping a manager calculate the present value a single cash$-$flow at the end of the year. Based

on your conversation with this manager you gather that s$//$he believe the expected cash$-$flow is $$5,000.$

S$/$he also feels that that any $1\%$ deviation of the S&P$500$ rate of return from its mean will cause a

corresponding deviation of $$500$ in the cash$-$flow. The risk free rate is $5\%,$ and the expected rate of

return on the index is $12\%.$ What is the present value of this cash$-$flow?

$2.$For the data of the previous question, what the project cost of capital?

$3.$Consider a project that will have the previous cash$-$flowsevery year in perpetuity,The initial investment is

$$50,000.$ What is the NPV$?$

$4.$Repeat the previous problem, but this time assume that the project will generats only $15$ annual cash$-$ flows.