Answered: Passengers (thousands) 150000 145000…

Corporate Fin Focused Approach

5th Edition

ISBN:9781285660516

Author:EHRHARDT

Publisher:EHRHARDT

Chapter10: The Basics Of Capital Budgeting: Evaluating Cash Flows

Section10.4: Internal Rate Of Return (irr)

Problem 6ST

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Question

Figure 1 below displays the quarterly number of U.S. passengers (in thousands) using light rail as a mode of transportation. The series begins in the first quarter of 2015 and ends with the third quarter of 2024.

We can see a regularity to the series: the first quarter’s ridership tends to be lowest; then there is a progressive rise in ridership going into the second and third quarters, followed by a decline in the fourth quarter. Superimposed on the series are the moving-average forecasts based on a span of k = 4.

Notice that the seasonal pattern in the time series is not present in the moving averages. The moving averages are a smoothed-out version of the original time series, reflecting only the general trend in the series, which is upward.

Data Analysis Questions:

1. Calculate seasonal ratio for the passenger series y(t). The basic idea behind seasonal ratios can be seen by rearranging the trend-times-seasonal model:

For each of the estimated levels given by the centered moving averages, we calculate the ratio of actual sales divided by the centered moving average.

Because we have more than one seasonal ratio observation for a given quarter, we average these ratios by quarter. That is, we compute the average for all quarter 1 ratios, then the average for all the quarter 2 ratios, and so on. These averages become our seasonal ratio estimates.

Show the resulting ratios based on the periods of 1, 2, 3 and 4 in the table below: