### Analysing Decision Making under Risk for Projects

Decision making under risk refers to the assignment of probabilities to each state of nature occurring for a project. The best choice of strategy is the strategy with the largest expected value where the expected value is the sum of payoff multiplied by the probability of occurrence for each state of nature.

Strong fact: When assigning probabilities, it is important that they are based on valid information and are not assigned erroneously.

### Typical example…

A Ski resort sought to weigh the probabilities of different weather patterns against the cost of two different snow-hawking machines.

The Project Managers knew from past history that without any new machine, the Resort could make up to $100,000 but has the potential to make more with the addition of a snowmaking machine. The snowmaker lite cost $10,000 and the Deluxe model cost $25,000.

The following table indicates how much profit could be made in three different conditions after paying for power and materials to make snow.

STRATEGY |
LOTS OF SNOW |
LITTLE SNOW |
DRY AND COLD |

STRATEGY 1: SNOW MAKER | $90,000 | $55,000 | $35,000 |

STRATEGY 2: SNOW MAKER DELUXE | $75,000 | $70,000 | $65,000 |

To analyse each strategy under risk, probabilities must be assigned to the probability of each state of nature occurring. Based on weather history in their area, the probability of lots of snow is considered to be 45 %, of little snow 35 %, and of dry but cold season 20%.

NOTE: We should consider the cost of machines in this calculation. $10,000 should be subtracted from the profit value of Snowmaker Deluxe

STRATEGY | CALCULATION |

SNOWMAKER LITE | (80)(.35)+(25)(20)=56.75. |

SNOWMAKER DELUXE | (50)(.45)+(45)(.20)=46.25 |

The best choice of strategy is the strategy with the largest expected value (Snowmaker Lite Strategy) where the expected value is the sum of the payoffs multiplied by the probability of occurrence for each state of nature.

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