Introduction to Risk Analysis Using Excel. Learning Objective.

Introduction to Risk Analysis

Using Excel

Learning Objective

Time management

Methods

(1) the analytical, mathematical approach and

(2) the Monte Carlo simulation technique.

Warm-up

The president of the

small Pharmaceutical

company must make the

final decision about

whether to market a new

kind of cough drop. The

yearly forecast for this

venture is as follows:

Value ForecastTotal industry sales $15 millionMarket share 35%Quantity sold 5.25 millionPrice per ounce 15 centsRevenue $787,000Fixed cost $200,000Variable cost rate 7.5 centsVariable cost $393,750Total cost $593,750Profit $193,750

Warm-up Considering a five

year product live and 20% discount of the profit stream, analyze this venture using present value method and present some considerations about the decision based in your calcules.(10 minutes)

Value ForecastTotal industry sales $15 millionMarket share 35%Quantity sold 5.25 millionPrice per ounce 15 centsRevenue $787,000Fixed cost $200,000Variable cost rate 7.5 centsVariable cost $393,750Total cost $593,750Profit $193,750

Uncertainties

Additional Information Calculate the base-case, best-case and worst-

case scenarios, through excel using these additional information (10 minutes):• Total industry sales of cough drops will be between

$10 million and $20 million.•• The company's market share will be between 20% and

50%.•• The price will be between 10 and 20 cents per ounce.• The fixed cost of manufacturing will be between

$100,000 and $300,000.•• The variable cost rate of production will be between 5

and 10 cents.

Scenarios

Uncertainties There is a great deal of uncertainty in this venture.

The board of directors is quite risk‑averse, so they want to know:

• How good is the base‑case estimate?

• What is the variability in the profit function?

• What are the chances of making a profit?

• What are the chances of making a profit of $500,000 or more?

• What is the probability of a loss?

What is Risk Analysis?

Consider now that:• Marketing believes, based on past records,

competitive products, and intuition, that total industry sales will be around $15 million.

• They believe it is very unlikely that sales will be less than $10 million or more than $20 million, but they are unable to decide the likelihood of any particular sales figure within that range.

• Any value is equally likely. In other words, marketing feels that the probability distribution of total industry sales is a flat‑line segment between $10 million and $20 million, as shown in the next slide.

Probability Distribution

000,000,1

1P

10 20 30Total industry sales in millions of dollars

Probability Distribution of total industry sales

The cumulative probability Distribution

The probability that random variable is “up

to” a certain value is represented by the

area under the probability distribution.

10 20 30Total industry sales in millions of dollars

1.0

0.5

Cumulative Probability

Cumulative Probability Distribution

Risk simulation process

Risk analysis

Risk analysis calculates measures of uncertainty of

the output variables, such as sales, profit, labor

required, and so on. These measures include

expected value, variance, standard deviation,

median, mode, the complete output probability

distribution, and the cumulative probability

distribution.

Risk analysis scenarios The scenarios include not just single estimates of the

variables but also the calculated probability values associated with critical factors, and answers to such questions as:• What is the probability that there will be no profit?•

• What is the probability that the profit will be over $1,000,000?•

• What is the probability that the project will be late by 20%?

• What is the probability that the break‑even point will be under 1,000 units?

• What is the probability that lost sales will be under 1,500 units?

Using Excel: step 1

The first thing you need to learn is how to generate random numbers using the Excel function RAND().

When you enter this function, a random number between 0 and 1 appears.

This is an unusual function, for two reasons. First, it has no argument; that is, nothing goes inside the parentheses. However, the parentheses are required. Second, each time the worksheet is recalculated, a new random num ber appears automatically. You should play with the RAND( ) function to under stand how it works.

Uniform random number

Uniform random distribution between the lower limit L and upper limit U:

"=L+((U‑L) *RAND())".

For whole numbers:

"=RANDBETWEEN(100,150)"

The model

Open the model

123456789101112

A B

The modelTotal industry sales =RANDBETWEEN(10000000,20000000)/1000000Market share =0.3*RAND()+0.2Quantity sold =B2*B3Price per ounce =0.1*RAND()+0.1Revenue =B4*B5Fixed cost =RANDBETWEEN(100000,300000)/1000000Variable cost rate =0.05*RAND()+0.05Variable cost =B4*B8Total cost =B7+B9Profit =B6-B10Loss (1) or profit (0) =IF(B11<0,1,0)

The model

123456789101112

A B

The modelTotal industry sales =RANDBETWEEN(10000000,20000000)/1000000Market share =0.3*RAND()+0.2Quantity sold =B2*B3Price per ounce =0.1*RAND()+0.1Revenue =B4*B5Fixed cost =RANDBETWEEN(100000,300000)/1000000Variable cost rate =0.05*RAND()+0.05Variable cost =B4*B8Total cost =B7+B9Profit =B6-B10Loss (1) or profit (0) =IF(B11<0,1,0)

Runs

232425262728293031323334

A B C

Profit Loss - Yes?1 -0.2237708 12 0.195107 03 0.0324161 04 0.4500064 05 0.0759415 06 0.3426906 07 0.2254467 08 -0.0563199 19 -0.0890889 1

10 0.0803718 0

Table of 100 RunsIn order to repeat the simulation, a table was built in cells B25 to C124 based on the results in cells B11 and B12.

Results

14

15161718192021

A B

ResultsNumber of losses (out of 100) 22Probablity of loss 22%Average profit 0.189SumSquares 0.087Variance 0.051Standard deviation 0.226CF 1.195

14

15161718192021

A B

ResultsNumber of losses (out of 100) =SUM(C25:C124)Probablity of loss =B15/100Average profit =AVERAGE(B25:B124)SumSquares =SUMSQ(B25:B124)/100Variance =B18-B17^2Standard deviation =B19^0.5CF =B20/B17

Results

14

15161718192021

A B

ResultsNumber of losses (out of 100) 22Probablity of loss 22%Average profit 0.189SumSquares 0.087Variance 0.051Standard deviation 0.226CF 1.195

Cells B15 to B21

summarize the results of the

table. These of runs.

The average will hover

around $190,000.

The values of sigma and

CF are warnings of the

uncertainty involved. Indeed,

the probability of loss hovers

around 22%.

Probability Distribution function

Taunton Pharmaceuticals

0%

5%

10%

15%

20%

-0.3 -0.1 0.1 0.3 0.5 0.7 0.9 1.1 1.3

Profits in millions of dollars

Pro

bab

ilit

y

Making Decision

• The expected yearly profit is $193,402.• The standard deviation is $224,911.• There is approximately a 20% chance of

a loss.• There is approximately an 18% chance

that the yearly profit will be greater than $400,000.

Reference

Operations Analysis Using Excel. Weida; Richardson and Vazsony, Duxbury, 2001, Chapter 12.