Math/Physic/Economic/Statistic Problems

Nando’s began in 1987 when Robert Brozin and Fernando Duarte bought a
restaurant called Chickenland in Rosettenville, southern Johannesburg, South
Africa. They renamed the restaurant Nando’s after Fernando. The restaurant
incorporated influences from former Portuguese colonists from Mozambique,
many of whom had a settled on the south-eastern side of Johannesburg, after
their homeland’s independence in 1975. Since day one, expansion was a vital
part of their vision. Growing from a single restaurant in 1987, Nando’s had
already expanded to four by 1990. To finance the rapid expansion plans,
Nando’s brought in the South African group Hollard as partners. New outlets
were kept as a separate company which eventually made decision making
inefficient and the implementation of a common strategy all but impossible.
This led to Nando’s buying out the joint venture partners in 1995. By this time
there were 45 outlets in South Africa and another 17 in other African countries
(Namibia, Botswana, Zimbabwe, and Swaziland).

By early 1997, another 46 outlets had been established in eight countries
outside the African continent, including Portugal, Australia, the United
Kingdom, Israel and Canada. The majority of these outlets were established by
bringing in local partners, mostly by the use of franchising. When exchange
controls began to relax in the mid-1990s, Nando’s began to take a direct equity
holding in those countries. This was seen as essential to facilitating Nando’s
international ambitions and providing ideal support to maintaining the
‘Nando’s Way’ of doing business.

By 1995, Managing this increasingly complex international structure had
become very difficult and a new international holding was formed – Nando’s
International Holdings (NIH). On 27 April 1997, Nando’s Group Holdings
(NGH) – the South African operation – was successfully listed on the
Johannesburg Stock Exchange. NIH held 54% of NGH – the remainder being
made available to former joint venture partners and members of the public. The
main purposes of the share offer and listing were to facilitate restructuring of
the group and to increase its capital base. Brozin, however, was certain that he
wanted to keep full control of all operations and keep his company
independent. By the end of 2006, Nando’s operated more than 400 restaurants
located in 30 countries worldwide and the company was set to continue its
growth into the future.

After the foundation of Nando’s International Holdings in the mid-1990s,
Nando’s continued its upward climb of record sales around the world. Suppose
the figures shown in Table 1 are Nando’s monthly sales figures from January
2012 through December 2020 (in €000s).

Assume you are the Sales Director at Nando’s International Holdings. You are
required to prepare a report for the Board of Directors on the following:

1. Describe the historical data on Nando’s sales, including a discussion of
the general direction of sales and any seasonal tendencies that might be
occurring.

2. Discuss, giving your justifications, which time series forecasting
techniques are appropriate for producing forecasts with this data set.

3. Apply the appropriate forecasting techniques and compare the models
based on ex post forecasts. Choose the best model.

4. Use your chosen forecasting model to generate forecasts for each of the
months in year 2021.

5. Discuss how these forecasts might be integrated into the planning
operations and policy makings in NIH.

Table 1. Nando’s sales (in €000s)
Month 2012 2013 2014 2015 2016 2017 2018 2019 2020
January 139.7 165.1 177.8 228.6 266.7 431.8 381 431.8 495.3
February 114.3 177.8 203.2 254 317.5 457.2 406.4 444.5 533.4
March 101.6 177.8 228.6 266.7 368.3 457.2 431.8 495.3 635
April 152.4 203.2 279.4 342.9 431.8 482.6 457.2 533.4 673.1
May 215.9 241.3 317.5 355.6 457.2 533.4 495.3 558.8 749.3
June 228.6 279.4 330.2 406.4 571.5 622.3 584.2 647.7 812.8
July 215.9 292.1 368.3 444.5 546.1 660.4 609.6 673.1 800.1
August 190.5 317.5 355.6 431.8 482.6 520.7 558.8 660.4 736.6
September 177.8 203.2 241.3 330.2 431.8 508 508 609.6 685.8
October 139.7 177.8 215.9 330.2 406.4 482.6 495.3 584.2 635
November 139.7 165.1 215.9 304.8 393.7 457.2 444.5 520.7 622.3
December 152.4 177.8 203.2 292.1 406.4 431.8 419.1 482.6 622.3