Verify Unit of Measure in a Multivariate Equation © 2011 You can’t… + = ?? © 2011 Terminal Learning Objective • Task: Determine Unit of Measure in a Multivariate Equation • Condition: You are training to become an ACE with access to ICAM course handouts, readings, and spreadsheet tools and awareness of Operational Environment (OE)/Contemporary Operational Environment (COE) variables and actors • Standard: with at least 80% accuracy: • Describe mathematical operations using units of measure • Solve unit of measure equations Describe key cost equations â 2011 Importance of Units of Measure • You can’t add apples and oranges but you can add fruit • Define the Unit of Measure for a cost expression • Use algebraic rules to apply mathematical operations to various Units of Measure â 2011 Adding If two components of the cost expression have the same unit of measure, they may be added together • Example: Smoky Mountain Inn Depreciation on building Maintenance person’s salary Cleaning person’s salary Real estate taxes $60,000 per year $30,000 per year $24,000 per year $10,000 per year • Depreciation, maintenance, cleaning, and taxes are all stated in $ per year, so they may be added to equal $124,000 per year © 2011 Adding • If two components of the cost expression have the same unit of measure, they may be added together • Example: Smoky Mountain Inn Laundry service Food $4.00 per person-night $6.00 per person-night • Laundry and food are both stated in $ per personnight, so they may be added to equal $10 per person-night â 2011 Subtracting If two components of the cost expression have the same unit of measure, they may be subtracted • Example: • Selling price is $10 per widget • Unit cost is $3.75 per widget • Since both Selling price and Unit cost are stated in $ per widget, they may be subtracted to yield Gross Profit of $6.25 per widget © 2011 Dividing • “Per” represents a division relationship and should be expressed as such • Example: • Cost per unit = Total $ Cost / # Units • Total Cost = $10,000 • # Units = 500 • $10,000/500 units = $20/unit © 2011 Cancelling © 2011 Multiplication • When multiplying different units of measure, they become a new unit of measure that is the product of the two factors • Example: • 10 employees * 40 hrs = 400 employee-hrs • 2x * 3y = 6xy © 2011 10 The Value of Equations • Equations represent cost relationships that are common to many organizations • Examples: • Revenue – Cost = Profit • Total Cost = Fixed Cost + Variable Cost • Beginning + Input – Output = Ending © 2011 27 Input-Output Equation Beginning + Input – Output = End If you take more water out of the bucket than you put in, what happens to the level in the bucket? © 2011 28 Applications of Input-Output • Account Balances • What are the inputs to the account in question? • • • • Raw materials? Work In process? Finished goods? Your checking account? • What are the outputs from the account? © 2011 29 Applications of Input-Output © 2011 30 Using the Input-Output Equation • If any three of the four variables is known, it is possible to solve for the unknown • The beginning balance on your credit card is $950 During the month you charge $300 and make a payment of $325 At the end of the month your balance is $940 What was the finance charge? • What are the inputs? Charges and finance charge • What are the outputs? Payments © 2011 31 Using the Input-Output Equation • If any three of the four variables is known, it is possible to solve for the unknown • The beginning balance on your credit card is $950 During the month you charge $300 and make a payment of $325 At the end of the month your balance is $940 What was the finance charge? • What are the inputs? Charges and finance charge What are the outputs? Payments â 2011 32 Using the Input-Output Equation • Set up the equation: Beginning + Inputs – Outputs = Ending Beg + Charges + Finance Charges – Payments = End $950 + $300 + Finance Charge – $325 = $940 $1250 + Finance Charge – $325 = $940 $925 + Finance Charge = $940 Finance Charge = $940 – $925 Finance Charge = $15 © 2011 33 Using the Input-Output Equation • Set up the equation: Beginning + Inputs – Outputs = Ending Beg + Charges + Finance Charges – Payments = End $950 + $300 + Finance Charge – $325 = $940 $1250 + Finance Charge – $325 = $940 $925 + Finance Charge = $940 Finance Charge = $940 – $925 Finance Charge = $15 © 2011 34 Using the Input-Output Equation • Set up the equation: Beginning + Inputs – Outputs = Ending Beg + Charges + Finance Charges – Payments = End $950 + $300 + Finance Charge – $325 = $940 $1250 + Finance Charge – $325 = $940 $925 + Finance Charge = $940 Finance Charge = $940 – $925 Finance Charge = $15 © 2011 35 Using the Input-Output Equation • Set up the equation: Beginning + Inputs – Outputs = Ending Beg + Charges + Finance Charges – Payments = End $950 + $300 + Finance Charge – $325 = $940 $1250 + Finance Charge – $325 = $940 $925 + Finance Charge = $940 Finance Charge = $940 – $925 Finance Charge = $15 © 2011 36 Using the Input-Output Equation • Set up the equation: Beginning + Inputs – Outputs = Ending Beg + Charges + Finance Charges – Payments = End $950 + $300 + Finance Charge – $325 = $940 $1250 + Finance Charge – $325 = $940 $925 + Finance Charge = $940 Finance Charge = $940 – $925 Finance Charge = $15 â 2011 37 Using the Input-Output Equation Set up the equation: Beginning + Inputs – Outputs = Ending Beg + Charges + Finance Charges – Payments = End $950 + $300 + Finance Charge – $325 = $940 $1250 + Finance Charge – $325 = $940 $925 + Finance Charge = $940 Finance Charge = $940 – $925 Finance Charge = $15 © 2011 38 Using the Input-Output Equation • Set up the equation: Beginning + Inputs – Outputs = Ending Beg + Charges + Finance Charges – Payments = End $950 + $300 + Finance Charge – $325 = $940 $1250 + Finance Charge – $325 = $940 $925 + Finance Charge = $940 Finance Charge = $940 – $925 Finance Charge = $15 © 2011 39 Learning Check • What are three useful equations that represent common cost relationships? © 2011 40 Practical Exercises © 2011 41 ...You can’t… + = ?? © 2011 Terminal Learning Objective • Task: Determine Unit of Measure in a Multivariate Equation • Condition: You are training to become an ACE with access to ICAM course handouts,... Describe mathematical operations using units of measure • Solve unit of measure equations Describe key cost equations â 2011 Importance of Units of Measure • You can’t add apples and oranges but... expression have the same unit of measure, they may be added together • Example: Smoky Mountain Inn Depreciation on building Maintenance person’s salary Cleaning person’s salary Real estate taxes $60,000