Question

You’ve been asked to use the following historical sales information to forecast next year’s sales for Worldwide Widget Manufacturing, Inc. The actual sales for 2016 were $1,950,000.

Year	Sales
2011	$1,750,000
2012	$2,000,000
2013	$1,350,000
2014	$2,250,000
2015	$1,800,000

What would be the next year's forecast according to the naïve approach and the average sales approach? What would be the MAPE according to the naïve approach and the average sales approach?

Kindly show all detailed calculations.

Answer 1

Naive forecast is one of the Time Series Model to forecast sale.

It is simplest method-A naïve forecast simply uses the actual demand for the past period as the forecasted demand for the next period.

Here Forecast for 2016 would be sale of Actual sale of previous year i.e. $ 1,800,000 and forecast for 2017 would be actual sales of 2016 i.e. $1,950,000

For Average Sales approach - one simply takes the average of some number of periods of past data by summing each period and dividing the result by the number of periods.

Here =

Year	Amount of sale
2011	$1,750,000
2012	$2,000,000
2013	$1,350,000
2014	$2,250,000
2015	$1,800,000
Total	$91,50,000
No of years	5
Average Sales	$18,30,000
Forecast for 2016	$ 18,30,000

For MAPE- Mean Absolute Percentage error, measures the size of the error in percentage terms. It is calculated as the average of the unsigned percentage error, we need 3 variables

1. Actual sales for 2016

2. Forecast sales for 2016

3. Number of observations (n) - 1 year (Since we are calculating MAPE for single year i.e. 2016)

MAPE= 1/n * ∑|A-F|/ A *100

For Naive approach -

Here, n=1, A= $19,50,000 and F= $1,800,000

Hence = 1* (19,50,000-18,00,000)/19,50,000

=7.692%

For Average Sales approach-

Here, n=1, A= $19,50,000 and F= $1,830,000

Hence = 1* (19,50,000-18,30,000)/19,50,000

=6.15%

Note- In this case, MAPE was calculated as it was required in question, however MAPE should not be used in case of low volume. It is scale sensitive.

"Pro Tip - Since it is percentage error- Low no means good and high numbers means bad.

This can be seen are situation also, In sales average approach forecast was near to Actual sales figure and hence it had low error."