The quarterly seasonal indexes for a firm’s electricity consumption are 115, 92, 81, and 112 for quarters I-IV. It has been forecast that electricity consumption will be 850,000 kilowatt-hours during 2008. Forecast electricity consumption for each quarter of 2008
The quarterly seasonal index represents the ratio in percent of the expected value of the quarter over the quarterly average over the year.
For the yearly forecast consumption of 850,000 kWH, the quarterly average is 850,000/4 = 212,500 kWH.
The quarterly forecasts are therefore:
1. 212,500*115/100 = 244,375 kWH
2. 212,500*92/100 = 195,500 kWH
3. 212,500*81/100 = 172,125 kWH
4. 212,500*112/100 = 238,000 kWH
Check:
Total
= 244,375+195,500+172,125+238,000
= 850,000 (yearly consumption)
To forecast electricity consumption for each quarter of 2008, we will use the quarterly seasonal indexes provided (115, 92, 81, and 112) as well as the total forecasted consumption for the year (850,000 kilowatt-hours).
The formula to calculate quarterly forecasted consumption is:
Quarterly Forecast = Seasonal Index * Total Forecasted Consumption
Let's calculate the forecasted consumption for each quarter:
Quarter I:
Quarterly Forecast (Q1) = 115/100 * 850,000 = 977,500 kilowatt-hours
Quarter II:
Quarterly Forecast (Q2) = 92/100 * 850,000 = 782,000 kilowatt-hours
Quarter III:
Quarterly Forecast (Q3) = 81/100 * 850,000 = 688,500 kilowatt-hours
Quarter IV:
Quarterly Forecast (Q4) = 112/100 * 850,000 = 952,000 kilowatt-hours
Therefore, the forecasted electricity consumption for each quarter of 2008 would be as follows:
Quarter I: 977,500 kilowatt-hours
Quarter II: 782,000 kilowatt-hours
Quarter III: 688,500 kilowatt-hours
Quarter IV: 952,000 kilowatt-hours