Question

Installing new machinery will cost $170,000. The installation will result in following annual saving: (a) Optimistic scenario: $22,000 annual saving with 22% probability, (b) Most likely scenario: $12,000 annual saving with 48% probability, and (c) Pessimistic scenario: $4,000 annual saving with 30% probability. The interest rate can be 5% or 8% (equally likely) and the machinery should have a useful life of 40 years. i. What is the present worth for each estimated value? What is the expected present worth? (20 pts) Compute the standard deviation of the present worth. (10 pts) ii

Answer 1

Machinery Cost = $ 170,000

Useful Life = 40 yrs

Required rate of return = 5%

Annual Cash Flow under different scenario

a. Optimistic Scenario = $22,000 with 22% probability

b. Most likely Scenario = $12,000 with 48% probability

c. Pessimistic Scenario = $4,000 with 30% probability

Answer to i) So, Present worth for each estimated value under each scenario is as follows -

a. Optimistic = 4840 (PVIFA _{5%, 40}) = 22000 x 17.1591 = $377,500.20

b. Most likely = 5760 (PVIFA _{5%, 40}) = 12000 x 17.1591 = $205,909.20

c. Pessimistic = 1200 (PVIFA _{5%, 40}) = 4000 x 17.1591 = $68,636.40

Expected Present worth = Present worth in each scenario x Probability of each scenario

= 377500.20 x 22% + 205909.20 x 48% + 68636.40 x 30% = $ 202,477.38

ii. Standard Deviation of Present Worth is $154749.335