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Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. ENGINEERING ECONOMY Fifth Edition Blank and Tarquin Mc Graw Hill CHAPTER V PRESENT WORTH ANALYSIS Adopted and modified by Dr. W-. W. Li of UTEP, Fall, 2003 Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 1

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 1 FORMULATING MUTUALLY EXCLUSIVE ALTERNATIVES Mutually Exclusive set is where a candidate set of alternatives exist (more than one) Objective: Pick one and only one from the set. Once selected, the remaining alternatives are excluded. Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 2

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 1 INDEPENDENT PROJECT SET Given a set of alternatives (more than one) The objective is to: n n n Select the best possible combination of projects from the set that will optimize a given criteria. Subjects to constraints More difficult problem than the mutually exclusive approach Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 3

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 1 FORMULATING MUTUALLY EXCLUSIVE ALTERNATIVES Mutually exclusive alternatives compete with each other. Independent alternatives may or may not compete with each other The independent project selection problem deals with constraints and may require a mathematical programming or bundling technique to evaluate. Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 4

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 1 Type of Alternatives Revenue/Cost – the alternatives consist of cash inflow and cash outflows n Select the alternative with the maximum economic value Service – the alternatives consist mainly of cost elements n Select the alternative with the minimum economic value (min. cost alternative) Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 5

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 1 Evaluating Alternatives In part, the role of the engineer to properly evaluate alternatives from a technical and economic view Must generate a set of feasible alternatives to solve a specific problem/concern Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 6

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 1 Alternatives Do Nothing Analysis Alt. 1 Problem Alt. 2 Alt. m Selection Execution Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 7

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 2 Present Worth Approach A process of obtaining the equivalent worth of future cash flows to some point in time – called the Present Worth At an interest rate usually equal to or greater than the Organization’s established MARR. Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 8

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 2 THE PRESENT WORTH METHOD P(i%) = P( + cash flows) + P( - cash flows) If P(i%) > 0 then the project is deemed acceptable. If P(i%) < 0 – the project is usually rejected If P(i%) = 0 Present worth of costs = Present worth of revenues: Indifferent! Note: If the present worth of a project turns out to = “ 0, ” that means the project earned exactly the discount rate that was used to discount the cash flows! The interest rate that causes a cash flow’s NPV to equal “ 0” is called the Rate of Return of the cash flow! Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 9

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 2 PRESENT WORTH: Special Applications Present Worth of Equal Lived Alternatives with unequal lives: Beware Capitalized Cost Analysis Require knowledge of the discount rate before we conduct the analysis Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 10

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 2 PRESENT WORTH: Equal Lives Present Worth of Equal Lived Alternatives – straightforward Compute the Present Worth of each alternative and select the best, i. e. , smallest if cost and largest if profit. Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 11

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 2 PRESENT WORTH: Example Consider: Machine A Machine B First Cost $2, 500 $3, 500 Annual Operating Cost 900 700 Salvage Value 200 350 Life 5 years i = 10% per year Which alternative should we select? Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 12

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 2 PRESENT WORTH: Cash Flow Diagram F 5=$200 MA 0 1 2 3 4 A = $900 $2, 500 F 5=$350 MB 0 $3, 500 5 1 2 3 4 5 A = $700 Which alternative should we select? Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 13

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 2 PRESENT WORTH: Solving PA =-2, 500 - 900 (P|A, . 10, 5) + 200 (P|F, . 01, 5) =-2, 500 - 900 (3. 7908) + 200 (. 6209) = -2, 500 - 3, 411. 72 + 124. 18 = -$5, 788 PB = -3, 500 - 700 (P|A, . 10, 5) + 350 (P|F, . 10, 5) = -3, 500 - 2, 653. 56 + 217. 31 = -$5, 936 SELECT MACHINE A: Lower PW cost! Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 14

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 3 PRESENT WORTH: Different Lives Comparison must be made over equal time periods n Compare over the least common multiple, LCM, for their lives Note: if the lives of the alternatives are not equal, one must create or force a study period where the life is the same for all of the alternatives. One cannot effectively compare the PW of one alternative with a study period different from another alternative that does not have the same study period. Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 15

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 3 PRESENT WORTH: Lowest Common Multiple of Lives If the alternatives have different study periods, you find the lowest common life for all of the alternatives in question. Example: {3, 4, and 6} years. The lowest common life is 12 years. Evaluate all over 12 years for a PW analysis. Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 16

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 3 PRESENT WORTH: Example Unequal Lives EXAMPLE Machine A Machine B First Cost $11, 000 $18, 000 Annual Operating Cost 3, 500 3, 100 Salvage Value 1, 000 2, 000 Life 6 years 9 years i = 15% per year Note: Where costs dominate a problem it is customary to assign a positive value to cost and negative to inflows Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 17

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 3 PRESENT WORTH: Unequal Lives Machine A 0 1 2 F 6=$1, 000 3 4 5 6 A 1 -6 =$3, 500 F 6=$2, 000 $11, 000 0 1 2 Machine B 3 4 5 6 7 8 9 A 1 -9 =$3, 100 i = 15% per year $18, 000 LCM(6, 9) = 18 year study period will apply for present worth Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 18

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 3 Unequal Lives: 2 Alternatives Machine A 6 years Cycle 1 for A Cycle 2 for A 6 years Cycle 3 for A Machine B 9 years Cycle 1 for B Cycle 2 for B 18 years i = 15% per year LCM(6, 9) = 18 year study period will apply for present worth Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 19

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 3 Example: Unequal Lives Solving LCM = 18 years Calculate the present worth of a 6 -year cycle for A PA = -11, 000 - 3, 500 (P|A, . 15, 6) + 1, 000 (P|F, . 15, 6) = -1, 000 - 3, 500 (3. 7845) + 1, 000 (. 4323) = -$23, 813, which occurs at time 0, 6 and 12 Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 20

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 3 Example: Unequal Lives Machine A 0 6 $23, 813 12 $23, 813 18 $23, 813 PA= -23, 813 (P|F, . 15, 6)23, 813 (P|F, . 15, 12) = -23, 813 - 10, 294 - 4, 451 = -$38, 558 Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 21

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 3 Unequal Lives Example: Machine B Calculate the Present Worth of a 9 -year cycle for B F 6=$2, 000 0 1 2 3 4 5 6 7 8 9 A 1 -9 =$3, 100 $18, 000 Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 22

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 3 9 -Year Cycle for B Calculate the Present Worth of a 9 -year cycle for B PB = -18, 000 -3, 100(P|A, . 15, 9) + 2, 000(P|F, . 15, 9) = -18, 000 - 3, 100(4. 7716) + 2, 000(. 2843) = -$33, 359 which occurs at time 0 and 9 Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 23

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 3 Alternative B – 2 Cycles Machine A: PW =$38, 558 0 9 $32, 508 18 $32, 508 PB = -32, 508 - 32, 508 (P|F, . 15, 9) = -32, 508 - 32, 508(. 2843) PB = -$41, 750 Choose Machine A Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 24

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 3 Unequal Lives – Assumed Study Period Approach n n Assume alternative: 1 with a 5 -year life Alternative: 2 with a 7 -year life Alt-1: N = 5 yrs LCM = 35 yrs Alt-2: N= 7 yrs Could assume a study period of, say, 5 years. Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 25

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 3 Unequal Lives – Assumed Study Period Assume a 5 -yr. Study period Estimate a salvage value for the 7 -year project at the end of t = 5 Truncate the 7 -yr project to 5 years Alt-1: N = 5 yrs Alt-2: N= 7 yrs Now, evaluate both over 5 years using the PW method! Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 26

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 4 FUTURE WORTH APPROACH FW(i%) is an extension of the present worth method Compound all cash flows forward in time to some specified time period using (F/P), (F/A), … factors or, Given P, the F = P(1+i)N Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 27

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 4 Applications of Future Worth Projects that do not come on line until the end of the investment period n n Commercial Buildings Marine Vessels Power Generation Facilities Public Works Projects Key – long time periods involving construction activities Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 28

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 4 Future Worth Example (Figure 5. 3) See Example 5. 3 Calculate the Future Worth of determining the selling price in order to earn exactly 25% on the investment Draw the cash-flow diagram!! Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 29

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 5 CAPITALIZED COST- the present worth of a project that lasts forever. Government Projects Roads, Dams, Bridges (projects that possess perpetual life) Infinite analysis period Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 30

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 5 Derivation for Capitalized Cost Start with the closed form for the P/A factor Next, let N approach infinity Or, CC(i%) = A/i Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 31

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 5 CAPITALIZED COST Assume you are called on to maintain a cemetery site forever if the interest rate = 4% and $50/year is required to maintain the site. 1 2 3 4 5. . …………………. . N=inf. A=$50/yr P=? Find the PW of an infinite annuity flow Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 32

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 5 CAPITALIZED COST P 0 = A[P/A, i%, N] 1 2 3 4 5. . …………………. . N=inf. A=$50/yr P=? Find the PW of an infinite annuity flow P 0=A(1/i) Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 33

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 5 CAPITALIZED COST P 0 = $50[1/0. 04] P 0 = $50[25] = $1, 250. 00 Invest $1, 250 into an account that earns 4% per year will yield $50 of interest forever if the fund is not touched and the i-rate stays constant. Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 34

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 5 CAPITALIZED COST: Endowments Assume a wealthy donor wants to endow a chair in an engineering department. The fund should supply the department with $200, 000 per year for a deserving faculty member. How much will the donor have to come up with to fund this chair if the interest rate = 8%/yr. Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 35

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 5 CAPITALIZED COST: Endowed Chair The department needs $200, 000 per year. P = $200, 000/0. 08 = $2, 500, 000 If $2, 500, 000 is invested at 8% then the interest per year = $200, 000 The $200, 000 is transferred to the department, but the principal sum stays in the investment to continue to generate the required $200, 000 Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 36

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 5 Capitalized Cost Example EXAMPLE Calculate the Capitalized Cost of a project that has an initial cost of $150, 000. The annual operating cost is $8, 000 for the first 4 years and $5000 thereafter. There is an recurring $15, 000 maintenance cost each 15 years. Interest is 15% per year. Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 37

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 5 Cash Flow Diagram “i”=15%/YR 0 1 2 3 4 5 6 7 15 30 ……… $4, 000 $8, 000 $150, 000 $15, 000 N= How much $$ at t = 0 is required to fund this project? The capitalized cost is the total amount of $ at t = 0, when invested at the interest rate, will provide annual interest that covers the future needs of the project. Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 38

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 5 CAPITALIZED COST - Example Continued 1. Consider $4, 000 of the $8, 000 cost for the first four years to be a one-time cost, leaving a $4, 000 annual operating cost forever. 2. 855 P 0= 150, 000 + 4, 000 (P|A, . 15, 4) = $161, 420 Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 39

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 5 CAPITALIZED COST - Continued Recurring annual cost is $4, 000 plus the equivalent annual of the 15, 000 end-ofcycle cost. 0 15 30 45 ……. 60 ……. . Take any 15 -year period and find the equivalent annuity for that period using the F/A factor. Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 40

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 5 CAPITALIZED COST: One Cycle Take any 15 -year period and find the equivalent annuity for that period using the F/A factor 0 15 30 45 ……. 60 ……. . $15, 000 A for a 15 -year period Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 41

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 5 CAPITALIZED COST 2. Recurring annual cost is $4, 000 plus the equivalent annual of the 15, 000 end -of-cycle cost. A= -4, 000 - 15, 000 (A|F, . 15, 15) = -4, 000 - 15000 (. 0210) = -$4, 315 Recurring costs = -$4, 315/i = 4, 315/0. 15 =-$28, 767/yr Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 42

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 5 CAPITALIZED COST Capitalized Cost = 161, 420 + 5315/. 15 = $196, 853 Thus, if one invests $196, 853 at time t = 0, then the interest at 15% will supply the end-of-year cash flow to fund the project so long as the principal sum is not reduced or the interest rate changes (drops). Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 43

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 6 Payback Period Analysis Two forms for this method n n Discounted Payback Period (uses an interest rate) Conventional Payback Period (does not use an interest rate) Payback is the period of time it takes for the cash flows to recover the initial investment. Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 44

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 6 Payback Period Analysis Discounted Payback Approach Find the value of np such that: Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 45

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 6 Payback for Example 5. 8 Discounted n n Machine A: 6. 57 years Machine B: 9. 52 years Undiscounted n n Machine A: 4. 0 years Machine B: 6. 0 years Go with Machine A – lower time period payback to recover the original investment Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 46

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 6 Payback Method Summarized Payback is only a rough estimator of desirability Use as an initial screening method Avoid using this method as a primary analysis technique for selection projects Totally avoid the no-return payback period Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 47

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 7 Life Cycle Costs (LCC) Extension of the Present Worth method Used for projects over their entire life span where cost estimates are employed Used for: n n n Military/Defense Projects New Product Lines Large construction projects Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 48

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 7 Life Cycle Defined – Detailed Phases Needs Assessment Phase Conceptual Design Phase Detailed Design Phase Production/Construction Phase Operation – (upgrading to extend) Phase Retirement/Disposal Phase The life can be for years into the future Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 49

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 7 Life Cycle: Two General Phases Cost-$ Cumulative Life Cycle Costs Acquisition Phase Operation Phase TIME Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 50

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 7 Life-Cycle Costs: Impact of Design Changes Cost of a design change tends to multiply by 10 with each phase Any design changes that might occur late in the life cycle drastically increase the total life cycle costs! Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 51

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 7 Life-Cycle Costs: Acquisition Phase Rule: About 80% of LCC are locked in by the end of the Acquisition Phase. Emphasis is on good design! Costs - $ Needs Assessment Conceptual Design Detailed Design Acquisition Phase Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 52

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 7 Life-Cycle Costs – Purpose Make explicit as possible the relationship of costs over the total life span of a product/system Design Process Objective n n n Minimize the life-cycle costs And meet other performance requirements By making correct trade-offs between costs in the acquisition phase and costs during the operations phase Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 53

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 7 Life-Cycle Costs – Warning Beware of introducing certain costcutting measures in the acquisition phase and early production phase Such cost-cutting measures could impact the future operations and degrade safety or require modifications later on These cost-cutting measures can be misleading and dangerous! Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 54

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 7 Life-Cycle Costs – Warning Engineers have a ethical and moral responsibility to ensure that designs are: n n Economically sound Functional Safe Perform as expected Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 55

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 8 Present Worth of Bonds represent a source of funds for the firm. Bonds are sold (floated) by investment banks for firms in order to raise additional debt capital A bond is similar to an IOU Bonds are evidence of Debt Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 56

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 8 Bond Types – Treasury Bonds Treasury bonds n n Issued by Federal Government Full backing of the Government 1 year or less; 2 -10 year issues; and 10 -30 year issues Conservative-type investment Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 57

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 8 Bond Types – Municipal Bonds State and Municipal Bonds n n Issued by states and local governments Generally tax-exempt by the Federal Government Used to finance state and local projects Backed by future tax and user fees to pay the interest and face value Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 58

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 8 Bond Types – Mortgage Bonds n n n Issued by Corporations Secured by the firm’s assets Money received by the firm is used to fund projects Referred to a Debt Capital Buyers of these bonds are not owners – they are lenders to the firm Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 59

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 8 Bond Types – Debentures Debenture Bond n n n n Issued by Corporations Not backed by specific assets Backing – good faith of the firm Pays higher interest rates Higher risks involved Bond interest rate may “float” Could be convertible to common stock Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 60

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 8 Present Worth of Bonds – Overview Investment Bankers The Firm Sell the Bonds to The lending public Proceeds from The sale Commissions/Fees Bondholders Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 61

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 8 Bonds – Basics Bonds are negotiable instruments Can be traded by the current bondholder Source of funds to the firm Debt capital Bondholders are loaning $$ to the firm Earn periodic interest Sell the bonds at any time Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 62

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 8 Bonds – Firm’s View Firm authorizes a bond sale Bonds are sold by an outside agency Firm pays a commission to the selling agency The firm receives the proceeds from the sale This is now DEBT capital to the firm Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 63

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 8 Bond Basics – Continued The bondholders are not owners They are lendors The firm pays periodic interest payments to the current bond holders At the end of the bond’s life, the bonds are redeemed (bought back) from the current bond holder Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 64

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 8 Bond Basics - Continued The bond itself is just a piece of paper Evidence of the debt the firm has incurred The firm may be able to “call” the bonds back by paying the current bondholder a calculated sum Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 65

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 8 Bonds – Notation P 0 – The time t = 0 selling price of the bond – the cost to the buyer of the bond V – The face value of the bond n The value printed on the bond n Face values are usually: w $100, $1, 000, $5, 000, $10, 000 increments N – The life of the bond in years r – The nominal annual bond interest rate Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 66

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 8 Bonds – Notation and Example Given the nominal annual bond interest rate, the payment frequency of the interest (monthly, quarterly semiannually, etc. ) is also stated Example: n n n V = $5, 000 (face value) r = 4. 5% per year paid semiannually N = 10 years Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 67

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 8 Bonds – Example – Continued The interest the firm would pay to the current bondholder is calculated as: The bondholder, buys the bond and will receive $112. 50 every 6 months for the life of the bond Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 68

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 8 Bonds – Example 5. 11 Given n n V = $10, 000 (Face value of the bond) r = 4. 5% paid semiannually N = 10 years or 20 interest periods $I/6 months = $5, 000(0. 045/2) = $112. 50 paid to the current bondholder Bonds are bought at sold in a bond market. Thus the price of the bond is subject to the pressures of the bond market. Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 69

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 8 Example 5. 11 Key Point – The purchase price of the bond can be considered a value that is determined by a willing buyer and a willing seller. Assume the potential buyer of this bond requires a interest rate of no less than 8%/year compounded quarterly. Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 70

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 8 Example 5. 11 – Continued The purchaser will consider this bond if he/she can earn 8%/yr c. q. What is fixed? n n The future interest payments are fixed The future face value of the bond in fixed What can vary? n The purchase price such that the buyer can earn at least the 8%/yr c. q. Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 71

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 8 Example 5. 11 – Continued 8% c. q is the same as n n 0. 08/4 = 0. 02 = 2% per quarter. Bond interest flows every 6 months Need an effective 6 -month rate The effective 6 -month rate is then w (1. 02)2 – 1 – 0. 0404 = 4. 04%/6 months w This is the potential buyer’s required interest rate Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 72

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 8 Example 5. 11 – Solving The objective is to determine the purchase price of this bond discounted at the buyer’s required rate of 4. 04% per 6 months Draw the cash-flow diagram Work the problem with N = 20 (not 10) n We have 20 interest payments (every 6 months) = 10 years Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 73

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 8 Example 5. 11 – Cash-Flow Diagram $5, 000 i=4. 04%/6 months A = 112. 50/6 months 0 P=? ? 1 2 3 4 …. . 19 20 Find the PW(4. 04%) of the future cash flows to the potential bond buyer Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 74

Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display. 5. 8 Example 5. 11 – Solving P = $112. 50(P/A, 4. 04%, 20) + $5, 000(P/F, 2%, 40) P = $3, 788 IF the buyer can buy this bond for $3, 788 or less, he/she will earn at least the 8% c. q. rate. Blank & Tarquin: 5 th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University. 75