1

Applying Simulation

to

Decision Problems

2

Monte Carlo simulation: A simple example

Cash Cashinflows Probability outflows Probability ($) (%) ($) (%)50 000   30 50 000   4560 000   40 70 000   5570 000   30 100

100

3

Assigning random numbers to cash inflows

Cash inflow Probability Random

($) (%) numbers

50 000 30 00–29

60 000 40 30–69

70 000 30 70–99

4

Assigning random numbers to cash outflows

Cash outflowProbability Random ($) (%) numbers

50 000 45 00–44

70 000 55 45–99

5

Ten simulations of monthly cash flows

6

Estimating probabilities from the simulation results

7

The effect of the number of simulations on the reliability of the probability estimates

8

Factors affecting profit earned by the plate

9

Estimates of values for Elite pottery

10

Tornado diagram for Elite pottery

11

Probability distributions

12

Simulation results

13

Probability distribution of profit earned by commemorative plate

14

Probability distribution for profit on the figurine

15

A comparison of the two probability distributions

16

Cumulative probability distributions

17

First-degree stochastic dominance

18

Two more cumulative distributions

19

Second-degree stochastic dominance

20

The mean-standard deviation screening method

21

A normal distribution for profit

22

Examples of quadratic utility functions

23

Annual cash flows for two machines

24

Calculating the NPV for the Alpha machine

25

Calculating the NPV for the Beta machine

26

Probability distributions for Alpha machine

27

NPV probability distributions for the two machines