Decomposing T wo Factor Models Cups per Hour

1. Decomposing Two Factor ModelsCups per Hour Ted Mitchell

2. Two Factor Model of Hours as an input in Biz Cafe • If you keep Biz-Café open longer hours you sell more cups of coffee • Output = Conversion Rate x Input • Cups Sold, Q = Cups per Hour x Hours open, H • Q = Qph x H • You have other related models • Revenue, R = Revenue per hour x Hours open, H • R = Rph x H • Gross Profit = Gross return per hour x Hours open, H • G = Gph x H

3. The hours are an important determinant of the gross profit • Gross Profit = Gross return per hour x Hours open, H • G = Gph x H • Sample Problem • The gross profit, G was higher this week than the week before. • Can we identify and explain how much of the change in gross profit was due to a change in the hours open, H, or a change in the Gph

4. Comparing the change in gross profitfrom week to week

5. The hours are an important determinant of the gross profit • Gross Profit = Gross return per hour x Hours open, H • G = Gph x H • G = (G/H) x H • But we would like to have other important variables to be included in the explanation of changes in gross profit, ∆G • A variable such as Sales Revenue, R • A variable such as number of cups sold, Q

6. To include Revenue, Rand Quantity sold • We use a process called expand, aggregate and decompose. • Sometimes just called the Decomposition Process • To Decompose the Two-Factor Model into a richer Four-Factor Model that includes Revenue, R, and Quantity Sold, Q.

7. To include Revenue, R and Quantity sold, Q • G = (G/H) x H • The expansion ofG = (G/H) x 1 x 1 x H • Changes nothing • the fact that 1 = R/R and 1 = Q/Q • G = (G/H) x (R/R) x (Q/Q) x H • Changes nothing • Combine The conversion ratios into an Aggregated Conversion Factor • G = (G x R x Q)/(R x Q x H) x H • Decompose the Aggregated Conversion Factor • G = (G/R) x (R/Q) x (Q/H) x H • Interpret the three new conversion factors • G = Gross Return on Sales x Selling Price x Cups per hour x Hours • Gross Profit = GROS x P x cph x Hours

8. Now explain the change in Gross profit • Gross Profit = GROS x P x cph x Hours • Any change in the Gross Profit = • any change in the gross return on sales x • any change in selling price x • any change the selling rate of cph • any change in the number of hours

9. Decomposition process allows • The decomposition of simple 2-factor marketing models into richer explanations with more factors being made explicit • Revenue and Price are always at work in the conversion of Hours into Gross Profits • But the Expansion, Aggregation and Decomposition made them explicit!

10. Decomposition process allows • A move From • Gross Profit = Gross profit per Hour x Hours • To a 4-Factor Explanation • Gross profit = GROS x Price x cph x Hours

11. In Future Lectures • Show how to measure how much of the change in Gross Profit, ∆G, was due to • 1) the changes in gross return on sales, I∆GROS • 2) the changes in the selling price, I∆P • 3) the changes in the sales rate per hour, I∆cph • 4) the change in the hours of operation I∆H • ∆G = I∆GROS + I∆P + I∆cph + I∆H

12. Any Questions