Show all formulas and steps solving using engineering econom

Show all formulas and steps solving using engineering economics. A new equipment costing $100K is required to manufacture a product that has an uncertain market potential. The marketing department has come up with the following market potential.

                                    Pessimistic       Most likely      Optimistic

                                                            Estimate          Estimate

Probability 0.3                   0.5                   0.2

Annual sales $25K               $50K               $65K

The product may be on the market for 2 or 3or 4 or 5 years with probabilities of 0.2,0.2,0.5 and 0.1 respectively.

a). If MARR is 9%, prepare a joint probability distribution table and compute the Expected Net Present Worth (NPW) for this product.

b). Compute the risk as Probability of Loss and as a standard deviation.

Solution

Annual Sales Probability Expected Sales (a) (b) sum of (a)*(b) 25000 0.3 7500 50000 0.5 25000 65000 0.2 13000 Expected Annual Sales 45500 Number of Years Probability Expected Life of Market (a) (b) sum of (a)*(b) 2 0.2 0.4 3 0.2 0.6 4 0.5 2 5 0.1 0.5 Expected Life of Product/ market 3.5 Expected Present Networth Using Probabilities Year Annual cash flow PV Factor @ MARR PV of Cash Flows 0 -100000 1                  -1,00,000 1 45500 0.917431193                       41,743 2 45500 0.841679993                       38,296 3 45500 0.77218348                       35,134 3.5 45500 0.73893156                       33,621 Expected Net Present Worth (NPW) for this product.                       48,795