# Question

A truck manufacturer produces the Off Road truck. The company wants to gain information about the discounted profits earned during the next three years. During a given year, the total number of trucks sold in the United States is 500,000 + 50,000G – 40,000I, where G is the number of percentage points increase in gross domestic product during the year and I is the number of percentage points increase in the consumer price index during the year. During the next three years, Value Line has made the predictions listed in the file S16_56.xlsx. In the past, 95% of Value Line’s G predictions have been accurate within 6%, and 95% of Value Line’s I predictions have been accurate within 5%. You can assume that the actual G and I values are normally distributed each year.

At the beginning of each year, a number of competitors might enter the trucking business. The probability distribution of the number of competitors that will enter the trucking business is also given in the same file. Before competitors join the industry at the beginning of year 1, there are two competitors. During a year that begins with n competitors (after competitors have entered the business, but before any have left, and not counting Off Road), Off Road will have a market share given by 0.5(0.9)n. At the end of each year, there is a 20% chance that any competitor will leave the industry. The selling price of the truck and the production cost per truck are also given in the file.

Simulate 1000 replications of the company’s profit for the next three years. Estimate the mean and standard deviation of the discounted three-year profits, using a discount rate of 10% and Excel’s NPV function. Do the same if the probability that any competitor leaves the industry during any year increases to 50%.

At the beginning of each year, a number of competitors might enter the trucking business. The probability distribution of the number of competitors that will enter the trucking business is also given in the same file. Before competitors join the industry at the beginning of year 1, there are two competitors. During a year that begins with n competitors (after competitors have entered the business, but before any have left, and not counting Off Road), Off Road will have a market share given by 0.5(0.9)n. At the end of each year, there is a 20% chance that any competitor will leave the industry. The selling price of the truck and the production cost per truck are also given in the file.

Simulate 1000 replications of the company’s profit for the next three years. Estimate the mean and standard deviation of the discounted three-year profits, using a discount rate of 10% and Excel’s NPV function. Do the same if the probability that any competitor leaves the industry during any year increases to 50%.

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