Probabilistic Analysis Handout
Important excel functions
=randbetween(bottom, top) might require analysis tool pack add-in
= rand()
=norminv(probability, mean, standard deviation)
=if(logical test, value if true, value if false)
=vlookup(lookup value, table array, column number)
=countif(range, “criteria”)
=count(range)
F9 to execute the rand() and randbetween() functions
Table 1: Using excel to get a random “draw” from a distribution
Common
Excel functions to call a
Examples
distributions random value
uniform
=randbetween(min, max)
uniform
between 2,000
and 3,000
$400 at 25%
$500 at 25%
$600 at 25%
$700 at 25%
normal
=norminv(rand(),mean,std)
normal dist.
with mean =
$500 and std =
$200
discrete (2
=if(rand()<=lower bound,
15 yrs 30%
possibilities)
lower outcome, higher
16 yrs 70%
outcome)
discrete
=vlookup(rand(),lookup table, $120 at 10%
(more than 2 column)
$160 at 30%
possibilities)
$180 at 60%
Example Excel code
=randbetween(2,000,3,000)
=randbetween(4,7)*100
=norminv(rand(),500,200)
=if(rand()<=.3,15, 16)
lookup table
range
Lower
value
bound
0-0.1
0
$120
0.1-0.4 0.1
$160
0.4-1.0 0.4
$180
Note:
lower bound sorted low to
high
Installation of the MCSim add in
1. Get MCSim.xla from the class website or directly from its creators at this address:
http://www3.wabash.edu/econometrics/EconometricsBook/Basic%20Tools/ExcelAddIns/MCSim.htm
2. In excel, go to Excel Options/Add-Ins. Hit “Go” at the bottom. Browse to location.
3. You will from now on see the button for it in the “Add-In” tab of excel.
**1. Do not run the addin from the zip folder. You need to "extract" or "unzip" the folder first.
**2. Do not click on the addin and open it up directly. You must open a separate excel file, and then:
File/Options/Addins/Go/Browse.
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Generate 1,000 simulation runs and calculate (1) mean, (2) standard deviation, (3) and prob. of loss.
Example 1
[This problem is easier than the next two.]
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Initial investment = $150,000
Annual revenues are uniformly distributed between $200,000 and $300,000.
Annual costs are uniformly distributed between $175,000 and $275,000.
Salvage value has a 75% chance of being $40,000 and 25% chance of being $80,000.
n=8
MARR = 10%
Example 2
[This problem is more advanced because the annual costs have a constraint that requires additional coding in excel.]
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Initial investment = $150,00
Annual revenues are uniformly distributed between $65,000 and $98,000.
Annual costs are normally distributed with a mean of $35,200 and standard deviation of $14,500 (annual costs
can only be negative, so make positive values =0).
Salvage value = $60,000.
n=8
MARR = 10%
Example 3
[This problem is more advanced because the salvage value has a discrete distribution that requires a vlookup table in
excel. The annual revenue also has a discrete distribution but it can be dealt with using =randbetween().]
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Initial investment = $80,000
Annual revenues have an equal chance of being $30,000, $40,000, or $50,000.
Annual costs are uniformly distributed between $27000 and $38,500.
Salvage value could be: $30,000 (60% chance), $50,000 (20% chance), or $75,000 (20% chance).
n=8
MARR = 10%
Example 4
[This problem is more advanced because (1) the useful life has a discrete distribution that requires additional
“dependency” coding in excel and (2) the salvage value depends on useful life so requires an if statement.]
Calculate IRR for the following business venture:
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Initial investment = $45,000
Annual sales are uniformly distributed between 100 and 900.
Annual revenues = $85*(annual sales)
Annual costs are uniformly distributed between $20,000 and $40,000.
Salvage value is $35,000 if n = 9 years and $20,000 if n = 10 years
Useful life, n, has a 80% chance of being 9 years and a 20% chance of being 10 years.
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