If a better motor fluid is used, the capital cost will increase by 350, but flui
ID: 2649746 • Letter: I
Question
If a better motor fluid is used, the capital cost will increase by 350, but fluid losses will be reduced through the 30 year life of the project. The optimistic, most likely, and pessimistic projections are 35, 30 and 23. All estimates are inflation adjusted and the real MARR is 4%.
a. What is the NPV under the "most optimistic" projection of annual savings? Under "most likely" projection savings? Under "Pessimistic assumption"?
b. Does the expected value of the NPV equal the NPV for the most likely outcome? why or why not?
c. Using the beta probability distribution to calculate the expected value of NPV. Attach a probability of 2/3 to the most likely outcome and a probability of 1/6 to both the pessimistic and optimistic outcomes.
Explanation / Answer
Answer:
a.
Increase in capital cost due to use of better motor fluid that is $ 350 is the initial outflow.
Annual savings in losses under the three scenarios are the cash inflows for 30 years.
Net Present Value (NPV) = Present Value of Inflow - Present Value of Outflow
here,
Present Value of Annuity of inflows = A{1/(1+r)^1 + 1/(1+r)^2 + ........ + 1/(1+r)^n}
A is the annual saving in losses
r is the MARR that is 4% or 0.04
n is the number of periods that is 30
Also, Present Value of Annuity Factor for 30 years at 4% is 17.714
Now, let us calculate NPV under the three scenarios:
b. To answer subpart b we need to solve subpart c for expected NPV.
c. Calculation of Expected NPV using given probability multiples and the formula as used in subpart a;
Present Value of Outflow = $ 350
Expected Inflows with Probability multiples = ($ 35 x 1/6 + $ 30 x 2/3 + $ 23 x 1/6) = $ 29.667
Present Value of expected Inflows = $ 29.667 x 17.714 = $ 526 (rounded off)
therefore Expected NPV = $ 526 - $ 350 = $ 176
b. Yes, the Expected NPV that is $ 176 is very close or we can say it is equal to NPV for the most likely outcome that is $ 182. This is so because the probabilty is happening of most likely outcome is given the maximum weightage under the beta probability distribution while calculating the expested value of NPV.
Particulars Optimistic Most Likely Pessimistic Present Value of Outflow ($ 350) ($ 350) ($ 350) Annual inflow for 30 years $ 35 $ 30 $ 23 Present Value of Annuity Factor for 30 years at 4% 17.714 17.714 17.714 Present Value of Annuity (rounded off) $ 620 $ 532 $ 408 Net Present Value $ 270 $ 182 $ 58
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