A 4-year financial project is forecast to have net cash inflows of $20,000; $25,
ID: 2652475 • Letter: A
Question
A 4-year financial project is forecast to have net cash inflows of $20,000; $25,000; $30,000; and $50,000 in the next 4 years. it will cost $75,000 to implement the project, payable at the beginning of the project. If the requred rate of return is 0.2, conduct a discounted cash flow calculation to determine the NPV.
Now, however, assume that the new cash inflows are probabilistic variables. Further assume that each forecast net cash inflow is normally distributed with standard deviations of $1,000; $1,500; $2,000; and $3,500, respectively. Given a required rate of return of 0.2, find the mean forecast NPV using crystal ball (or Excell). What is the probability that the actual NPV will be positive?
Explanation / Answer
PV Factor Present Year Cashflow at 0.20 rate Value 0 -75000 1.00000 -75000.00 1 20000 0.83333 16666.67 2 25000 0.69444 17361.11 3 30000 0.57870 17361.11 4 50000 0.48225 24112.65 Total 50000 501.54 PV Factor Present Present Value Year Sd at 0.20 rate Value of sd Variance (pv^2) 1 1000 0.83333 833.33 694444.44 2 1500 0.69444 1041.67 1085069.44 3 2000 0.57870 1157.41 1339591.91 4 3500 0.48225 1687.89 2848958.48 Total 8000 4720.29321 5968064.28 Standard Deviation of NPV = square root of 5,968,064.28 = 2,443. Now NPV is normally distributed with Mean of 501.54 and standard deviation of 2443. so z=(0-501.54)/2443 = -0.21 So, area under standard normal cureve between z=0 to z=+0.21 is 58.317 Hence, area under standard normal cureve z=-0.21 and z=0 must be same which is 58.317 Hence probability that NPV >=0 is 58.317