Present$$ value: Mixed streams$$Consider the mixed streams of cash flows shown in the following$$ table, LOADING....

a$.$Find the present value of each stream using a $6\%$ discount rate.

b$.$Compare the calculated present values and discuss them in light of the undiscounted cash flows totaling $$$$70$ comma $000$ in each case. Is there some discount rate at which the present values of the two streams would be$$ equal?

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Part $1$

a$.$ To calculate the present value of the mixed stream of cash$$ flows, find the present value of each cash flow for years $1$ through $4.$ Then, add all the computed present values$$ together, along with the cash flow from year $0$ to find the total present value of the stream. The present$$ value, PV$,$ of some future$$ amount, FV Subscript n$,$ to be received n periods from$$ now, assuming an interest rate$($or opportunity$$ cost$)$ of r$,$ is calculated as$$ follows:

PV equals StartFraction FV Subscript n Over left parenthesis $1$ plus r right parenthesis Superscript n EndFraction

$.$

$$Alternatively$,$ you can find the present value using a financial calculator or an Excel spreadsheet. When solving for the present value of a single cash flow using a financial$$ calculator, you will need to input the values of $$N$,$ I$/$Y$,$ PMT$,$ and FV$.$ Make sure you enter a zero for PMT$,$ which is not used in the problem. When solving for the present value of a single cash flow using an Excel$$ spreadsheet, you will need to enter the values of$$ Rate, Nper,$$ Fv$,$ Pmt$,$ and Type into the present value function.

Keep track of the individual present values as you$$ go; the sum of these values will be the present value of the stream.

Part $2$

The discount$$ rate, $$r$,$ is

$$

enter your response here$\%.($Type a whole$$ percentage.$)$

$0-52,50017,500$

$143,75026,250$

$235,00035,000$

$326,25043,750$

$417,500-52,500$

Totals $70,00070,000$