QUESTION TWO: 20 MARKS

The quarterly sales of a product are monitored by a multiplicative time series model. The trend in sales is described by

Y=100 + 5X

Where y denotes sales volume and X denotes the quarterly time period.

The trend in sales for the most recent quarter (first quarter 20x1, when x=20) was 200 units. The average seasonal variations for the product are as follows:-

Quarter Q1 Q2 Q3 Q4

Seasonal effect o -20% +40% -20%

The price of a unit was sh.1,000 during the first quarter of 20x1. This price is revised every quarter to allow for inflation, which is running at 2% a quarter.

Required:-

a. Forecast the trend in the number of units sold for the remaining three quarters of 20x1. [7marks]

b. Forecast the actual number of units sold (to the nearest whole number) for the remaining 3 quarters of 20x1. [7 marks]

c. Forecast the price per unit for the remaining quarters of 20x1, giving your answers to 2 decimal places. [6 marks]