Answered: Year Quarter t y(t) 2015 1 1 110569 2 2…

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.

Question:

1. When you divide the original series by the seasonal component, you are then left with the trend component with no seasonality. This adjusted series does not show the regular ups and downs of the original unadjusted data. At this stage, you can come up with a trend line equation.

a) Regress adjusted seasonality (deseasonality component) to time component. Show the trend line equation using regression for trend-and-season predictive model here and substitute the intercept and slope using the coefficient from the simple linear regression output:

= [a + b (t)] × SR

Show the regression output here: