Economics Review1Economics Review -1or how you can use your money.ver.1ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20091ver. 1Outline• MoneyTime al e of mone•Time value of money• Manufacturing costs– Direct – Indirect• Decision metrics–Rate of Return on Investment– Payback PeriodME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20092What is money?What is money?•Asocial contractA social contract•A medium for the exchange of goods property and servicesgoods, property, and services•A representation of wealth$$$$$$$$$$ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20093Principal and InterestPrincipal and Interest• Principalp– Money you loan someone–Money you borrow from someoneyy• InterestMoney you are paid to loan your–Money you are paid to loan your money–Money you pay to borrowMoney you pay to borrow someone else’s moneyME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20094Future and Present ValuesFuture and Present Values•Future Value (FV) or (F):Future Value (FV) or (F):– Value of principal and interest at end of loan periodend of loan period.• Present Value (PV) or (P):Value of principal and interest at–Value of principal and interest at beginning of loan period.ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20095Types of Interest PaymentsTypes of Interest Payments•Single RepaymentSingle Repayment• Uniform Periodic RepaymentNote: by convention, everything happens at year end.ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20096Single Repayment• Borrow (P) at interest rate per period(i)for(n)periods and repayperiod (i)for (n)periods and repay it and the interest (F) at the end of the loan (balloon payment)the loan (balloon payment).()n• Future value: ()niPF +⋅=1⎤⎡1• Present value:()⎥⎥⎦⎤⎢⎢⎣⎡+⋅=niFP11ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20097Single Repayment Example -Future ValueAtb d(P)$20 000•Amount borrowed (P)= $20,000• Interest rate (i) = 9.5% per year• Number of periods (n) = 4 yearsHow much will you pay?How much will you pay?)095.01(000,20$4+⋅=F22.753,28$)095.01(000,20$=+FME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20098Single Repayment Example -Present ValueY d $250k(F)i16•You need $250k (F)in 16 years (n) to send your child to college. •Assume you can make 8% per year (i).How much should you invest today?⎤⎡()62.972,72$08.011000,250$16=⎥⎥⎦⎤⎢⎢⎣⎡+⋅=PME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 20099Uniform Periodic Repayment (1)Uniform Periodic Repayment (1)•Borrow(P)at interest rate perBorrow (P)at interest rate per period (i) and repay it with (n)equal payments(A)equal payments (A). • E.g., a car loantimePCashflowAAAAAAAME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200910Uniform Periodic Repayment (2)py ()()⎥⎤⎢⎡−+in11• Future value:()⎥⎥⎦⎢⎢⎣+⋅=iiAF11• Present value:()()⎥⎥⎦⎤⎢⎢⎣⎡+−+⋅=nniiiAP111• Equal payment series (Annuity):⎦⎣()()⎥⎥⎦⎤⎢⎢⎣⎡−++⋅=111nniiiPAME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200911()⎥⎦⎢⎣Uniform Periodic Repayment-Ex. 1-1You borrow $25,000(P)for a carUniform Periodic Repayment Ex. 11You borrow $25,000 (P)for a car at 8% per year (i) for 4 years (n).(n).How much will you pay back?How much will you pay back?How much will you pay per h?month?ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200912Uniform Periodic RepaymentEx 12Uniform Periodic Repayment -Ex. 1-2• Note: 4 years = 48 months•Note: 8% per year=0 67% perNote: 8% per year 0.67% per monthME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200913Uif P idi R tE13Uniform Periodic Repayment -Ex. 1-3Monthly Payment (A):()0067.010067.000025$48⎥⎤⎢⎡+⋅A()()79.610$10067.01000,25$48=⎥⎥⎦⎢⎢⎣−+⋅=A79.610$ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200914Uniform Periodic Repayment-Ex 1-4•Total Payments(Σ):Uniform Periodic Repayment Ex. 14Total Payments (Σ):∑9231729$4879.610$=⋅=∑•Interest payments=$4 317 9292.317,29$=Interest payments $4,317.92 (= 29,317.92 - 25,000)ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200915Uniform Periodic Repayment-Ex 2-1Uniform Periodic Repayment Ex. 21Using the previous example’s gp presults, should you borrow the money and use your savings to yygpay for the loan or buy the car from your savings?yg•You earn 6%(i)on savings in the•You earn 6% (i)on savings in the bank.ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200916Uif P idi R tE22Uniform Periodic Repayment -Ex. 2-2•Start with the amount of principalStart with the amount of principal.• Subtract the monthly payment.Cl lt d ddi th it t•Calculate and add in the interest on the amount of principal left.• Continue until you get to a negative number, which means you ran out of money. ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200917Uniform Periodic RepaymentEx 23Uniform Periodic Repayment -Ex. 2-3Month Principal + interest Payment0 25,000.001 24,511.16 610.79224,019.87 610.79,3 23,526.12 610.794 23,029.91 610.795 22,531.22 610.79622 030 03610 79622,030.03610.7943 1,613.91 610.7944 1,008.14 610.7945399 34610 7945399.34610.7946 -211.45 610.7947 -822.24 610.7948 -1,433.03 610.79ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200918Uniform Periodic Repayment - Ex. 2-4py• You would not have enough fimoney from your savings over the term of the loan to pay for th lthe loan:So, buy the car with your savings.• N.B., this ignores any tax issues, inflation, residual value of car your other monetaryresidual value of car, your other monetary needs, etc.ME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200919How do you makemoney?How do you make money?Profit=Selling priceCost to makeProfit=Selling price-Cost to makeorSelling price = Profit + Cost to makeME 6222: Manufacturing Processes and Systems Prof. J.S. Colton © GIT 200920Costs to Make a Product• Manufacturing–Direct– Indirect (AKA: overhead, burden)• Support–Engineering, Research and gg,Development– General and Administrative– Marketing and SalesME 6222: Manufacturing Processes and