Weighted average question

[viciam]

Hi guys,

I am doing some research into McDonalds and it's international businesses. It's a small study for people who are interested in good company structures.

I came across a section in their annual report where they give some weighted average figures but I don't know how they arrived at those figures and I'm not very good at maths, so I was hoping someone might know the answer to my question.

$6,889.1 is the weighted average cash... how did they arrive at this figure using the numbers in the screen shot below? :S

In the notes it says: " The denominator is the weighted average cash used for investing activities during the applicable one or three year period. The weighted average cash used for investing activities is based on a weighting applied on a quarterly basis.

Here is a screenshot of what I am looking at: (if the screenshot isn't visible please see it as http://postimg.org/image/de0tttj71/ )

http://www.aussiestockforums.com/forums/attachment.php?attachmentid=55635&d=1385913667

Thank you in advance, sorry if its a dumb question,

 

[mfb]

There is no screenshot visible. If you see it: maybe you have to be registered there to see it.

 

[viciam]

Here is the link for the screenshot

http://postimg.org/image/de0tttj71/

 

[mfb]

The weighting could be related to the variable exchange rates. Instead of averaging the exchange rate over all quarters, the cash spent in that quarter is used as weight. That is a more complicated way to say "in each quarter, the money is converted according to the exchange rate at that point" (maybe even with smaller steps than quarters).

 

[viciam]

I know this is going to be asking too much but any chance of providing a calculation? Is it possible to do the calculation using the information that's shown on that screenshot?

 

[mfb]

If my guess is right, the data there is not sufficient to check the numbers.

 

[Office_Shredder]

Based on the footnote (3) and (4) it sounds like the weighted average is not related to currency changes, they just assumed a flat exchange rate by averaging the exchange rate over the whole period.

It sounds like the weights in the average are supposed to be the percents at the bottom of the page, but I don't understand how they are averaging the adjusted cash and coming up with a number larger than any of the individual adjusted cash numbers.

If I didn't know this gave the wrong number I would think the calcuation they are doing is
$$\frac{3167.3*(.875+.625+.375+.125) + 2570.9*4 + 2056*4 + 1655.3*(.875+.625+.375+.125) }{8+2*(.875+.625+.375+.125)}$$

 

[nasu]

The problem is that the 3167.3 and so on seem to be amounts per year whereas the weights are per quarter. But they don't show how the money is split between quarters.

 

[viciam]

Hi guys,

Thanks for actually giving this some thought. I just found this in the annual report and it has to do with the original question.

RECONCILIATION OF RETURNS ON INCREMENTAL INVESTED CAPITAL

ROIIC is a measure reviewed by management over one-year and three-year time periods to evaluate the overall profitability of the business units, the effectiveness of capital deployed and the future allocation of capital. This measure is calculated using operating income and constant foreign exchange rates to exclude the impact of foreign currency translation. The numerator is the Company’s incremental operating income plus depreciation and amortization from the base period. The denominator is the weighted-average cash used for investing activities during the applicable one-or three-year period. The weighted-average cash used for investing activities is based on a weighting applied on a quarterly basis. These weightings are used to reflect the estimated contribution of each quarter’s investing activities to incremental operating income. For example, fourth quarter 2012 investing activities are weighted less because the assets purchased have only recently been deployed and would have generated little incremental operating income (12.5% of fourth quarter 2012 investing activities are included in the one-year and three-year calculations). In contrast, fourth quarter 2011 is heavily weighted because the assets purchased were deployed more than 12 months ago, and therefore have a full-year impact on 2012 operating income, with little or no impact to the base period (87.5% and 100.0% of fourth quarter 2011
investing activities are included in the one-year and three-year calculations, respectively). Management believes that weighting cash used for investing activities provides a more accurate reflection of the relationship between its investments and returns than a simple average.
The reconciliations to the most comparable measurements, in accordance with accounting principles generally accepted in the U.S.,for the numerator and denominator of the one-year and three-year ROIIC are as follows: