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# Monthly Number of Airline Tickets Sold

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I need help with the following questions. I have the data on an excel spreadsheet.

1. Using the data for the monthly number of airline tickets sold, answer the following:
a. Fit a linear trend to this data. Estimate and interpret the coefficients of this model.
Does the linear model fit well? Interpret the coefficient of determination and standard error of estimate.
b. Provide three measures of forecast accuracy.
c. Is data seasonal? Please discuss.

2. Using the monthly data related to U.S. national debt (in \$) answer the following questions:
a. Fit an exponential growth model to this data. Hint: Use LN(Y).
b. If the national death continues at the same rate estimate its value in 2020.

3. The table provides data for the proportion of the Americans under the age of 18 that are living below the poverty level. Please answer the following:
a. Find the first six autocorrelations of this time series (TS)?
b. Fit an autoregressive model with four lags.
c. Propose the best autoregressive model.
d. Using the model of part c, calculate the MSE, MAE, and MAPE.
e. Find the forecast for the proportion of American children living below poverty level in the next year.

4. Consider the 30-year mortgages rates in the U.S. Answer the following:
a. Develop a good autoregressive model based on autocorrelations.
b. Using the model of part a, forecast the monthly mortgage rates for the next three years.

5. Using the daily closing prices of American Express stock for a one year period, answer the following:
a. Using moving average method with span of 3, forecast the price of stock for the next trading day.
b. Repeat part a with a span of 10.
c. Which of the above two models do you recommend? Justify your answer.

6. The closing prices for DJIA for each trading day of the year is given in the table.
a. Using moving average method with span of 3 forecast the price of this index on the next trading day.
b. Repeat the model of part a with 10 and 15 day spans.
c. Which of the three spans appear to be more appropriate? Why?

7. Re-considering the airline ticket data, answer the following:
a. Graph the time series data. Based on the graph of part a, which exponential smoothing model do you recommend? Why?
b. Use simple exponential smoothing to make a forecast for the next 12 months, with no holdout period.
Use the default smoothing constant of 0.10.
c. Repeat part b, using the optimizing smoothing constant feature of the software. Does it result in a significant improvement in the model? Explain.

8. Re-consider the poverty level data and answer the following:
a. Plot the time series data. Based on the graph, which exponential smoothing model do you propose and why?
b. Using simple exponential smoothing technique forecast for three future periods. Make sure that you use default smoothing constant (a=0.10) and no holdout periods.
c. Repeat part b using the optimize feature for the smoothing constant. Graph the models of part b and c superimposed. Is the model of part c preferable to the model of part b?
d. Write a short report to summarize the results.

9. Using the monthly retail sales (in millions) of beer, wine and liquor in the U.S., answer the following:
a. Is seasonality present in this data? If so, deseasonalize the time series data using the ratio-to-moving-
average method.
b. If you decided to deseasonalize the data, forecast the deseasonalized data for each month of the next year using the moving average method with an appropriate span.
c. Redo part b using Holt's model. Is the Holt's model preferable to the moving average method? Why or why not?

10. Continue the previous problem and answer the following:
a. Deseasonlize the data again and use Winters' method to handle seasonality. Forecast for the next 12 months.
b. Which of the moving average, Holt's exponential smoothing, or Winters' method do you prefer? Why?

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## Cost-volume-profit analysis for Provincial Airlines

Cost-volume-profit analysis

Provincial Airlines is a small local carrier that operates passenger flights between the Atlantic provinces. 100% Newfoundland and Labrador owned, the airline services 13 destinations throughout Newfoundland and Labrador. After experiencing healthy early profits, the company has recently been beset by instability and a string of quarterly losses. Management at the company has engaged you to provide some assistance with planning and decision-making. At an initial meeting, you were able to obtain the following data:

All seats are economy
Average full passenger fare = \$150
Number of seats per plane = 120
Average load factor (seats occupied) = 70%
Average variable cost per passenger = \$40
Fixed operating costs per month = \$1,800,000

Specifically, you have been asked for the following:

(a) What is the breakeven point in passengers and revenues?

(b) What is the breakeven point in number of flights?

(c) If Provincial Airlines raises its average full passenger fare to \$200, it is estimated that the load factor will decrease to 55%. What will be the breakeven point in number of flights in this event?

(d) The cost of fuel is a significant variable cost to any airline. If fuel charges increase by \$8 per barrel, it is estimated that the variable cost per passenger will rise to \$60. In this case, what will be the new breakeven point in passengers and in number of flights?

(e) Provincial Airlines management forecasts an imminent increase in variable cost per passenger to \$50 and an increase in total fixed costs to \$2,000,000. In response, the company is contemplating raising the average fare to \$180. What number of passengers would be needed to generate an after-tax profit of \$600,000 if the tax rate is 40%?

(f) Provincial Airlines is considering offering a discounted fare of \$120, which the company feels would increase the load factor to 80%. Only the additional seats would be sold at the discounted fare. Additional monthly advertising costs would be \$100,000. How much before-tax profit would the discounted fare provide Provincial if the company has 40 flights per day, 30 days per month?

(g) Provincial has an opportunity to obtain a new route to Port Hope Simpson. The company feels it can sell seats at \$175 on the route, but the load factor would be only 60%. The company would fly the route 20 times per month. The increase in fixed costs for additional crew, additional planes, landing fees, maintenance and so on, would total \$100,000 per month. Variable cost per passenger would remain at \$40 according to estimates.

I. Should the company obtain the route?
II. How many flights would Provincial need to earn before-tax profit of \$57,500 per month on this route?
III. If the load factor could be increased to 75%, how many flights would the company need in order to earn before-tax profit of \$57,500 per month on this route?
IV. What qualitative factors should Provincial consider in making its decision about acquiring this route?

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