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An investment that requires $1,000 initial investment will return $600 at the end of the first...

An investment that requires $1,000 initial investment will return $600 at the end of the first year and $650 at the end of second year. Assume the discount rate is continuously compounded at 8%. What is the Net Present Value of the investment?

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Answer #1

Net Present Value (NPV) is the sum of present value of cash inflows less present value of cash out flow.

NPV for continuous compounding = C/ert

C = Cash flow

r = Rate of discount = 8 % or 0.08 p.a. continuously compounded

t = time period

e = Euler's number (approx. value = 2.718281828)

NPV = $ 600 /e (0.08)(1) - $ 650 /e (0.08)(2) - $ 1,000

         = $ 600 /e (0.08) - $ 650 /e (0.16) - $ 1,000

       = $ 600 /(2.71828183)(0.08) - $ 650 /(2.71828183)(0.16) - $ 1,000

       = $ 600 /1.083287068 - $ 650 /1.17351087 - $ 1,000

        = $ 553.8698078 + $ 553.8934628 - $ 1,000

        = $ 1,107.76327 -1,000 = $ 107.76327 or $ 107.76

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