Verify Unit Of Measure In A Multivariate Equation Principles of Cost Analysis and Management © Dale R Geiger 2011 You can’t… + = ?? © Dale R Geiger 2011 Terminal Learning Objective • Task: Verify Unit Of Measure In A Multivariate Equation • Condition: You are a cost advisor technician with access to all regulations/course handouts, and awareness of Operational Environment (OE)/Contemporary Operational Environment (COE) variables and actors • Standard: with at least 80% accuracy: • Solve unit of measure equations Describe key cost equations â Dale R Geiger 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 © Dale R Geiger 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 $60,000 per year Maintenance person’s salary $30,000 per year Cleaning person’s salary $24,000 per year Real estate taxes $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 â Dale R Geiger 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 $4.00 per person-night Food $6.00 per person-night • Laundry and food are both stated in $ per person-night, so they may be added to equal $10 per person-night © Dale R Geiger 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 © Dale R Geiger 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 â Dale R Geiger 2011 Cancelling • If the same Unit of Measure appears in both the numerator and denominator of a division relationship, it will cancel • Example: $25 thousand 10 thousand units = $2.50/unit © Dale R Geiger 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 © Dale R Geiger 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 © Dale R Geiger 2011 28 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? © Dale R Geiger 2011 29 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? © Dale R Geiger 2011 30 Applications of Input-Output • Gas Mileage: Miles/Gallon = Miles Driven/Gallons Used • Calculate Miles Driven using the odometer • How you know Gallons Used? • If you always fill the tank completely, then: Beginning + Input – Output = Ending Or, chronologically: Beginning – Output + Input = Ending Full Tank – Gallons Used + Gallons Added = Full Tank Full Tank – Gallons Used + Gallons Added = Full Tank – Gallons Used + Gallons Added = Gallons Used = Gallons Added © Dale R Geiger 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 Dale R Geiger 2011 32 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 Dale R Geiger 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 © Dale R Geiger 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 © Dale R Geiger 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 © Dale R Geiger 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 © Dale R Geiger 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 © Dale R Geiger 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 © Dale R Geiger 2011 39 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 © Dale R Geiger 2011 40 Check on Learning • What are three useful equations that represent common cost relationships? © Dale R Geiger 2011 41 Practical Exercises © Dale R Geiger 2011 42 ... Solve unit of measure equations Describe key cost equations â Dale R Geiger 2011 Importance of Units of Measure • You can’t add apples and oranges but you can add fruit • Define the Unit of Measure. .. Units of Measure on the diagonal will cancel • Example: Variable Cost • Variable cost $4 /unit * 100 units = $4 * 100 units Unit = $400 â Dale R Geiger 2011 11 Factoring If the same unit of measure. .. components of a cost expression have the same unit of measure, they may be either or • Which mathematical operation using two different units of measure results in a new unit of measure? © Dale