Question

In: Accounting

Your company has the sales for year 1 below. You want to select from one of...

Your company has the sales for year 1 below. You want to select from one of three models for forecasting: a three-month moving average, a weighted moving average (you believe that the weights should be 0.2, 0.3, and 0.5), and an exponential smoothing average in which you use an alpha of 0.2 and an assumed forecast for January of year one of $35,000. Determine sales forecast for January year 2 and calculate MAD.


Jan Yr 1 34284
Feb 34000
Mar 31017
Apr 33406
May 34518
Jun 35469
Jul 35360
Aug 34894
Sep 34547
Oct 31015
Nov 31167
Dec 32925

A) Three-month moving average:
Sales forecast: $  
MAD:  

B) Weighted moving average:
Sales forecast: $  
MAD:  

C) Exponential moving average:
Sales forecast: $  
MAD:  

Which forecasting method should you use for your company? (enter A, B, C):

Solutions

Expert Solution

Year1 (Months)

Sales

3-month Moving Average

3-month Weighted Moving Average (weights: 0.2, 0.3, 0.5)

Exponential Smoothing (alpha = 0.2)

Jan

34284

Feb

34000

(0.2*34280)+(0.8*34280)= 34280

Mar

31017

(0.2*34000)+(0.8*34280)= 34224

Apr

33406

(34284+34000+31017)/3= 33100

(0.2*34284)+(0.3*34000)+(0.5*31017)= 32562

(0.2*31017)+(0.8*34224)= 33582

May

34518

(34000+31017+33406)/3= 32808

(0.2*34000)+(0.3*31017)+(0.5*33406)= 32808

(0.2*33406)+(0.8*33582)= 33547

Jun

35469

(31017+33406+34518)/3= 32980

(0.2*31017)+(0.3*33406)+(0.5*34518)= 33484

(0.2*34518)+(0.8*33547)= 33742

Jul

35360

(33406+34518+35469)/3= 34464

(0.2*33406)+(0.3*34518)+(0.5*35469)= 34771

(0.2*35469)+(0.8*33742)= 34088

Aug

34894

(34518+35469+35360)/3= 35116

(0.2*34518)+(0.3*35469)+(0.5*35360)= 35225

(0.2*35360)+(0.8*34088)= 34342

Sept

34547

(35469+35360+34894)/3= 35241

(0.2*35469)+(0.3*35360)+(0.5*34894)= 35149

(0.2*34894)+(0.8*34342)= 34453

Oct

31015

(35360+34894+34547)/3= 34934

(0.2*35360)+(0.3*34894)+(0.5*34547)= 30263

(0.2*34547)+(0.8*34453)= 34471

Nov

31167

(34894+34547+31015)/3= 33485

(0.2*34894)+(0.3*34547)+(0.5*31015)= 32851

(0.2*31015)+(0.8*34471)= 33780

Dec

32925

(34547+31015+31167)/3= 32243

(0.2*34547)+(0.3*31015)+(0.5*31167)= 31796

(0.2*31167)+(0.8*33780)= 33257

Year 2 (Month)

Jan

(31015+31167+32925)/3= 31702

(0.2*31015)+(0.3*31167)+(0.5*32925)= 32015

(0.2*32925)+(0.8*33257)= 33191

Calculation of Mean Absolute Deviation (MAD)

Sales

3-month Moving Average

Deviation

Absolute deviation

33406

33100

33406 – 33100 = 306

306

34518

32808

34518 – 32808= 1710

1710

35469

32980

35469 – 32980 = 2489

2489

35360

34464

35360 – 34464 = 896

896

34894

35116

34894 – 35116 = -222

222

34547

35241

34547 – 35241 = -694

694

31015

34934

31015 – 34934 = -3919

3919

31167

33485

31167 – 33485 = -2318

2318

32925

32243

32925 – 32243 = 682

682

Sum of absolute deviation = 306 + 1710 + 2489 + 896 + 222 + 694 + 3919 + 2318 + 682 = 13236

MAD = 13236/9 = 1470.66

Sales

3-month Weighted Moving Average

Deviation

Absolute Deviation

33406

32562

33406 – 32562 = 844

844

34518

32808

34518 – 32808 = 1710

1710

35469

33484

35469 – 33484 = 1985

1985

35360

34771

35360 – 34771 = 589

589

34894

35225

34894 – 35225 = -331

331

34547

35149

34547 – 35149 = -602

602

31015

30263

31015 - 30263 = 752

752

31167

32851

31167 – 32851 = -1684

1684

32925

31796

32925 – 31796 = 1129

1129

Sum of absolute deviation = 844 + 1710 + 1985 + 589 + 331 + 602 + 752 + 1684 + 1129 = 9626

MAD = 9626/9 = 1069.55

Sales

Exponential Smoothing

Deviation

Absolute Deviation

33406

33582

33406 – 33582 = -176

176

34518

33547

34518 – 33547 = 971

971

35469

33742

35469 – 33742 = 1727

1727

35360

34088

35360 – 34088 = 1272

1272

34894

34342

34894 – 34342 = 552

552

34547

34453

34547 – 34453 = 94

94

31015

34471

31015 – 34471 = -3456

3456

31167

33780

31167 – 33780 = -2613

2613

32925

33257

32925 – 33257 = -332

332

Sum of Absolute Deviation = 176 + 971 + 1727 + 1272 + 552 + 94 + 3456 + 2613 + 332 = 11193

MAD = 11193/9 = 1243.66

Therefore,

Requirement A:

3- month Moving Average

Sales forecast = $31702

MAD = 1470.66

Requirement B:

Weighted Moving Average

Sales forecast = $32015

MAD = 1069.55

Requirement C:

Exponential Moving average

Sales forecast = $33191

MAD = 1243.66

Hence, B- weighted moving average has the lowest MAD and is considered to be the best forecast method among the three.

ekkarill92 answered 7 months ago
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