Monte Carlo Simulation

Monte Carlo simulation methods use repeated random sampling to model a phenomenon involving significant uncertainty in inputs. These simulations aid decision makers by providing them with a range of outcomes and associated probabilities.

1. A greeting card company wants to determine the ideal level of production for Valentine cards. A card sells for $4 and the variable cost is $1.50 per card. However, leftover cards must be picked up and disposed off at a cost of $0.20 per card. Based on prior experience, the company has determined the following probability distribution for demand.

Probability	Demand
.10	10,000 cards
.35	20,000 cards
.3	40,000 cards
.25	60,000 cards

2. A small convenience store is trying to determine the optimal weekly order size for People magazine. The store pays one dollar for each copy and sells it for $1.95. The unsold copies can be returned for $0.50 each. The probability distribution for the demand is given below:

Probability	Demand
.10	15 copies
.20	20
.30	25
.25	30
.15	35

3. A GMC dealer wants to order an optimal number of Envoys. He believes the demand for Envoys is normally distributed with a mean of 200 and standard deviation of 30. It costs him $25,000 to order a vehicle, which he sells for $40,000. Unsold vehicles are discounted and sold at a loss of $2,000 per vehicle. How many Envoys should he order, assuming he must order a minimum of 200 vehicles?

4. A young entrepreneur is considering investing in a motel (see details in the table below). The motel business is cyclical, with the occupancy rate varying with the state of the economy. The annual occupancy rates for the previous ten years are available for this market. You may assume normal distribution. Estimates for the fixed and variable costs are also provided. Run a simulation analysis and compute the mean profit after taxes and the lower and upper limits at the 95% confidence level. The entrepreneur will invest in the motel provided the expected rate of return on his capital is at least 25%.

Year	Occupancy rate
1995	45%
1996	56%
1997	45%
1998	65%
1999	70%
2000	55%
2001	40%
2002	38%
2003	45%
2004	50%

Mid-Tier Motel in a City (population: 70,000)	Industry Average
Variable costs (33%) as % of revenue
Advertising, Promotion, Franchise or Group Fees	3.3%
In-room Supplies	2.7%
Other variable costs	27%
Fixed costs
Lease payments on equipment	$15,000
Interest on bank loan of $400,000	$60,000
Telephone & Fax	$5,000
Depreciation expense	$23,000
Employees' Wages & Salaries	$125,000
Expected average tax rate	25%
Number of Guest Rooms	50
Average room rent	$55
Total investment in the motel is $800,000, with 50% of this as owner investment

Note: The entrepreneur is not confident about the total variable cost percentage. He thinks this percentage can be 33% or 37% or even 40% of revenues.

Depreciation expense will be reinvested to maintain the quality level of the property.