Problem 2 Assume that Company XYZ wants to forecast sales for next year. Below a

Question

Problem 2 Assume that Company XYZ wants to forecast sales for next year. Below are the data for the past 4 years: Period 4 Year 1 Year 2 Year 3 Year 4 Period 1 210 215 220 225 Period 2 178 180 176 178 Period 3 250 250 260 260 215 213 220 225 a. Calculate the forecast for year 4 using moving averages (Weights: 3, 2, 1 with the heaviest weights applied to the most recent years) (4 points) b. Calculate a seasonal index for each period. (8 points) c. If the yearly trend equation for this problem is y- 840 11.5x, what is the forecast for each period in year 5? (8 points) d. What is the MAD for the trend projection method? (5 points)

Explanation / Answer

a)

Year 1 total sales = 210 + 178 + 250 + 215 = 853

Year 2 total sales = 215 + 180 + 250 + 213 = 858

Year 3 total sales = 220 + 176 + 260 + 220 = 876

weightage for year 3 = 3

year 2 = 2

year 1 = 1

forecast for year 4 = (3*876 + 2*858 + 853)/6 = (2628+1716+853)/6 = 866.17

forecast for year 4 = 866.17

b)

average for each period for year 1 = 853/4 = 213.25

average for each period for year 2 = 858/4 = 214.5

average for each period for year 3 = 876/4 = 219

average for each period for year 4 = (225+178+260+225)/4 = 888/4=222

seasonal index for year 1 period 1 = 210/213.25 = 0.985

similarly seasonal index for year 1 period 2 = 178/213.25 = 0.835

similarly we calculate all the season al index, the final values are given in table below

average of the season index calculated above is the final season index for that period

average for period 1/ seasonal index for period 1 = 1.001

seasonal index for period 2 = 0.820

seasonal index for period 3 = 1.174

seasonal index for period 4 = 1.005

c)

yearly trend equation: y = 840 + 11.5x

for year 5, x = 5

hence y = 840 + 11.5*5 = 897.5 = 898

average for each period = 898/4 = 224.5

forecast for period 1 = 224.5*seasonal index = 224.5*1.001 = 224.72 = 225

forecast for period 2 = 224.5*0.820 = 184.09 = 184

forecast for period 3 = 224.5*1.174 = 263.56 = 264

forecast for period 4 = 224.5*1.005 = 225.62 = 226

d)

using the trend line above:

year 1 projection = 840+11.5*1 = 851.5

year 2 projection = 840+11.5*2 = 863

year 3 projection = 840+11.5*3 = 874.5

year 4 projection = 840+11.5*4 = 886

difference of projection and actual sames for each year:

year 1 = 853-851.5 = 1.5

year 2 = 858-863 = |-5| = 5

year 3 = 876 - 874.5 = 1.5

year 4 = 888 - 886 = 2

total difference for 4 years = 1.5 + 5 + 1.5 +2 = 10

MAD = 10/4 = 2.5

Period 1 Period 2 Period 3 Period 4 Year 1 0.985 0.835 1.172 1.008 Year 2 1.002 0.839 1.166 0.993 Year 3 1.005 0.804 1.187 1.005 Year 4 1.014 0.802 1.171 1.014

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