CTC 475 Review Course Requirements Applications Multiple Decision Criteria Selling The Project PSP-Problem Solving Process

CTC 475 Cost Concepts

Objectives Understand the concept of money having a time value Know the definition of several cost concepts Know how to use the discrete compound interest equation and the factor tables found in the back of your book

Economic Analysis Relies on economics to justify an alternative Estimating and quantifying costs requires research Company Production Records Accounting Records Manufacturer’s Catalog’s Government Publications Need to know cost concepts used in these type of reports

Basic Cost Concepts Time Value of Money Cost Terminology Basic single sum equation Factor form to solve equations

Money has a Time Value Would you prefer $100 today or $X one year from now if $X equaled: $100 $200 $1000

Time Value of Money Most people prefer current consumption over postponed consumption unless they’re compensated at a higher level for waiting

Cash Flow Diagrams Identify cash flows by time End of period Usually year (EOY) Identify viewpoint (person, company, bank) + Cash flows are placed above the time line mean $ coming in (income) - Cash flows are placed below the time line mean $ going out (expenses)

Cash Flow Tables EOY ($2000) 1 $200 2 3 4 5 $200+$50 Cash Flow

Simple vs Compound Interest On Board

Cost Terminology Life-Cycle Costs Past and Sunk Costs Future & Opportunity costs Direct and Indirect Costs Average and Marginal Costs Fixed and Variable Costs Intangibles Interest Rate/ROR/MARR

Life-Cycle Costs Sum of all expenditures associated with an ‘item’ during it’s entire service life Item: Equipment Product Line Project Building Bridge Process “Cradle to Grave” costs

Life-Cycle Costs First costs Operating & maintenance costs (O&M) Design & Development Purchasing costs Fabrication & testing Training Shipping & Installation Tooling costs Supporting Equipment Costs Operating & maintenance costs (O&M) Disposal costs

Life-Cycle Costs O&M costs are usually recurring costs Labor Materials Overhead items (fuel, energy source, insurance, etc. At disposal, item may have a market or trade-in value Salvage Value = Market Value – Disposal Costs

Past Costs Past costs are historical costs that have occurred

Sunk Costs Sunk costs are past costs that are not recoverable Sunk costs should not be included in an analysis

Sunk Cost Example Investor buys 100 shares of stock ($25/share) Brokerage Fees are $85 Total expenditures were $2585

Sunk Cost Example (Cont.) Two months later stock sells for only $20 per share but investor sell the 100 shares because money is needed Brokerage Fee for selling the stocks is $70 Net Loss = $2000-$70-$2585 = ($655) The $655 (capital loss) is a sunk cost because it can never be recovered Capital losses are sometimes advantageous: Offsets capital gains Future estimates

Future Costs Costs that occur in the future from some reference time (t=0). Future costs may be known (contract, loan, etc.) Future costs may be estimated (O&M, salvage, etc.)

Opportunity Costs Cost of foregoing the opportunity to earn interest, or a return, on investment funds MARR: minimum attractive rate of return “Cost of Capital”

Opportunity Cost Example You have $20,000 and you purchase a car You could have invested the money at 4% per year. The opportunity cost per year associated with owning the car is $800 (4% x $20,000=$800)

Direct & Indirect Costs Direct costs (material, labor) are easily measured and allocated to a specific operation, product, or project Indirect costs are impractical or uneconomical to allocate to a specific operation, product, or project (utilities, insurance, supplies, etc.) Indirect costs are sometimes called overhead or burden costs

Average Cost Ratio of total cost to quantity of output Average costs may change as a function of output: Avg. operating cost of vehicle may be $0.25 per mile if a driver travels 10,000 miles/year Avg. operating cost of vehicle may be $0.20 per mile if a driver travels 20,000 miles/year

Marginal (Incremental) Costs Cost required to increase the output quantity by one If the marginal cost is smaller than the average cost than an increase in output will result in a reduction of unit cost

Fixed and Variable Costs Fixed costs are those which do not vary in proportion of the quantity of output: Insurance Building depreciation Some utilities Variable costs vary in proportion to quantity of output Direct Labor Direct Material

Fixed & Variable Costs Fixed costs are expressed as one number $200 Variable costs are expressed as an amount per unit $10 per unit

Total Costs (TC) Total Costs (TC) over some time period = Fixed Costs (FC) + Variable Costs (VC) * # of Units Produced

Costs for Owning a Vehicle Unit of Production=Miles Driven per year Fixed: ? Variable: ?

Intangibles Factors that are difficult to quantify with respect to costs: Safety Customer Acceptance Reliability Convenience Goodwill Aesthetics

Interest Rate, Rate of Return, MARR Interest (simple/compound) “Rent” paid for use of money Interest paid or interest earned (Interest= end amount-original amount) Example: Deposited $100; after 1 year bank pays you back $106; interest=(106-100)/100=6% Rate of Return MARR-Minimum attractive rate of return ROR must be greater than MARR and MARR must be greater than cost of capital

Now let’s talk about cash flows

Terminology & Symbols P-Present value at time=0 F-Future value at some time t i-interest rate per time period t t-time It is important to list knowns and unknowns and state time increments (year, month, etc.)

Equation (Discrete) relating F,P, i,n

Example (Find F) A new college graduate plans to borrow $10,000 from her parents to help purchase a car. She has arranged to pay the entire principal plus 2% per year interest after 5 years. Identify knowns/unknowns P=$10K i=2% per year n=5 years F=?

Table Factors (back of book) Find F given P (at i,n) Find P given F (at i,n) Find A given F (at i,n) Find F given A (at i,n) Find A given P (at i,n) Find P given A (at i,n) Spreadsheets and some calculators also have functions for calculations

Example (Find F) P=$10K i=2% per year n=5 years F=? F=10,000(1+.02)5=$11,041 (using equation) or 10,000(1.1041)=$11,041 (using table)

Equation (Discrete) relating F,P, i,n Note: Although we used the equation to solve for F, we can also use the equation to solve for P, i, or n given the other three variables

Presentation next Week Half on Tuesday; Half on Thursday Homework is due next Tuesday at the beginning of class.