A firm is considering an unusual project of the selling of a machine today that

Question

A firm is considering an unusual project of the selling of a machine today that will result in an immediate inflow of S530. Without the use of the machine the firm will ncur an annuity of outflows of $75 per year that begin at the end of year one, and continue for 6 consecutive years. The required rate of return is 8.30%, what is the project's net present value (NPV)? Place your answer in dollars and cents. If your answer is negative, then indicate this by placing a "minus" sign before the number. Do not use a dollar sign or comma. For example, an answer of negative one thousand one hundred and eleven dollars as 1111 Work your analysis using at least 4 decimal places of accuracy

Explanation / Answer

NPV is the difference between cash inflow and cash out flow

Let’s consider cash out flow as annuity, we need to find the PV of that annuity

Present value of annuity is the present worth of cash flows that is to be received in the future, if future value is known, rate of interest in r and time is n then PV of annuity is

PV of annuity= P[1- (1+ r)^-n]/ r

= 75[1- (1+ 0.083)^-6]/ 0.083

= 75[1- (1.083)^-6]/ 0.083

= 75[1- 0.619768158912342]/ 0.083

= 75[0.380231841087658/ 0.083]

= 75[4.58110651912841]

= 343.582988934631      

NPV = Cash inflow – PV of cash out flow

           = 520 – 343.5829

            = 176.41171                                                                                                                                                                                                                                                           

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