3. You are to conduct an extensive sensitivity analysis on the problem described

Question

3. You are to conduct an extensive sensitivity analysis on the problem described below. The sensitivity approach will consist of two parts: (a) A range approach where the most optimistic, most likely, and most pessimistic values of the dependent variables N PV and IRR are determined. (b) A range approach where the mean value is determined for each independent variable and then each variable is allowed to vary ±20% about that mean while all other independent variables are held constant. Create spider plots for NPV and i RR using the results The project life is 7 years and the MARR is 15%. The initial investment is given by a uniform distribution between $200,000 and $300,000 he annual profit is given by a triangular distribution that has a minimum value of $55,000/year, a mode of S67,500 year, and a maximum valuc of $85,000/year. The salvage valuc of the investment is given by a triangular distribution that has a minimum value of $60,000, a mode of $75,000, and a maximum value of $85,000

Explanation / Answer

The initial investment is uniformly distributed between $200,000 and $300,000 thus the mode of this distribution would be $250,000

Terminal year Cashflow will be salvage value + annual profit thus
Minimum value = 60000+55000 = 115000
Most likely value = 75000+67500 = 142500
Maximum Value = 85000+85000 = 170000

Answer a.
Lets calculate NPV and IRR as below:

Minimum Value

Mode

Maximum Value

Most pessimistic

Most Likely

Most optimistic

Years

Cashflows

Cashflows

Cashflows

0

-200000

-250000

-300000

1

55000

67500

85000

2

55000

67500

85000

3

55000

67500

85000

4

55000

67500

85000

5

55000

67500

85000

6

55000

67500

85000

7

115000

142500

170000

NPV at 15%

$44,677.659

$51,324.878

$74,426.370

IRR

22.480%

21.887%

23.327%

Answer b.
Mean for initial value = 300000+200000 / 2 = 250000
Mean for annual profit = 85000+55000 / 2 = 70000
Mean for Salvage value = 85000+60000 / 2 = 72500
(and final year cashflow = 70000+72500 = 142500)

Deviating each of them by 20% on either side the calculation is as below:

-20%

Mean

+20%

Formula = Mean*0.8

Mean

Formula = Mean*1.2

Years

Cashflows

Cashflows

Cashflows

0

-200000

-250000

-300000

1

56000

70000

84000

2

56000

70000

84000

3

56000

70000

84000

4

56000

70000

84000

5

56000

70000

84000

6

56000

70000

84000

7

114000

142500

171000

NPV at 15%

$47,641.612

$59,552.015

$71,462.417

IRR

22.988%

22.988%

22.988%

Minimum Value

Mode

Maximum Value

Most pessimistic

Most Likely

Most optimistic

Years

Cashflows

Cashflows

Cashflows

0

-200000

-250000

-300000

1

55000

67500

85000

2

55000

67500

85000

3

55000

67500

85000

4

55000

67500

85000

5

55000

67500

85000

6

55000

67500

85000

7

115000

142500

170000

NPV at 15%

$44,677.659

$51,324.878

$74,426.370

IRR

22.480%

21.887%

23.327%

You can also do this calculation in your financial calculator by inserting respective cashflows as shown in the excel file and by pressing CPT and then 15% and NPV for NPV and I/Y for IRR

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