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ENGINEERING ECONOMICS

ENGINEERING ECONOMICS. ERT461 BIOSYSTEMS ENGINEERING DESIGN 1 ERT424 BIOPROCESS PLANT DESIGN 1. PART I Time Value of Money. The Interest Rate Simple Interest Compound Interest Amortizing a Loan Compounding More Than Once per Year. The Interest Rate.

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ENGINEERING ECONOMICS

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  1. ENGINEERING ECONOMICS ERT461 BIOSYSTEMS ENGINEERING DESIGN 1 ERT424 BIOPROCESS PLANT DESIGN 1

  2. PART ITime Value of Money • The Interest Rate • Simple Interest • Compound Interest • Amortizing a Loan • Compounding More Than Once per Year

  3. The Interest Rate Which would you prefer -- $10,000 today or $10,000 in 5 years?

  4. TIME allows you the opportunity to postpone consumption and earn INTEREST. Why is TIME such an important element in your decision? Why TIME?

  5. Compound Interest Interest paid (earned) on any previous interest earned, as well as on the principal borrowed (lent). Types of Interest • Simple Interest • Interest paid (earned) on only the original amount, or principal, borrowed (lent).

  6. Simple Interest Formula FormulaSI = P0(i)(n) SI: Simple Interest P0: Deposit today (t=0) i: Interest Rate per Period n: Number of Time Periods

  7. SI = P0(i)(n)= $1,000(.07)(2) = $140 Assume that you deposit $1,000 in an account earning 7% simple interest for 2 years. What is the accumulated interest at the end of the 2nd year? Simple Interest Example

  8. FV = P0 + SI = $1,000+ $140 =$1,140 Future Valueis the value at some future time of a present amount of money, or a series of payments, evaluated at a given interest rate. What is the Future Value (FV) of the deposit? Simple Interest (FV)

  9. The Present Value is simply the $1,000 you originally deposited. That is the value today! Present Valueis the current value of a future amount of money, or a series of payments, evaluated at a given interest rate. What is the Present Value (PV) of the previous problem? Simple Interest (PV)

  10. Why Compound Interest? Future Value (U.S. Dollars)

  11. Future Value Single Deposit (Graphic) Assume that you deposit $1,000 at a compound interest rate of 7% for 2 years. 0 12 7% $1,000 FV2

  12. Future Value Single Deposit (Formula) FV1 = P0 (1+i)1 = $1,000(1.07) = $1,070 Compound Interest You earned $70 interest on your $1,000 deposit over the first year. This is the same amount of interest you would earn under simple interest.

  13. Future Value Single Deposit (Formula) FV1 = P0(1+i)1 = $1,000 (1.07) = $1,070 FV2 = FV1 (1+i)1 = P0 (1+i)(1+i) = $1,000(1.07)(1.07) = P0(1+i)2 = $1,000(1.07)2 = $1,144.90 You earned an EXTRA$4.90 in Year 2 with compound over simple interest.

  14. General Future Value Formula FV1 = P0(1+i)1 FV2 = P0(1+i)2 General Future Value Formula: FVn = P0 (1+i)n or FVn = P0 (FVIFi,n) -- See Table I

  15. Valuation Using Table I FVIFi,nis found on Table I at the end of the book.

  16. Using Future Value Tables FV2 = $1,000 (FVIF7%,2) = $1,000 (1.145) = $1,145[Due to Rounding]

  17. Story Problem Example Julie Miller wants to know how large her deposit of $10,000 today will become at a compound annual interest rate of 10% for 5 years. 0 1 2 3 4 5 10% $10,000 FV5

  18. Story Problem Solution • Calculation based on Table I: FV5= $10,000(FVIF10%, 5)= $10,000(1.611) = $16,110 [Due to Rounding] • Calculation based on general formula:FVn = P0 (1+i)nFV5= $10,000 (1+ 0.10)5 = $16,105.10

  19. We will use the “Rule-of-72”. Quick! How long does it take to double $5,000 at a compound rate of 12% per year (approx.)? Double Your Money!!!

  20. Approx. Years to Double = 72/ i% 72 / 12% = 6 Years [Actual Time is 6.12 Years] Quick! How long does it take to double $5,000 at a compound rate of 12% per year (approx.)? The “Rule-of-72”

  21. PART IIDeveloping Project Cash Flows • Estimating Cost/Benefit for Engineering Projects • Incremental Cash Flows • Developing Cash Flow Statements • Generalized Cash Flow Approach

  22. Elements of Investment Decision • Identification of Investment Opportunities • Generation of Cash Flows • Measures of Investment Worth • Project Selection • Project Implementation • Project-Control/Post-Audit Our focus in this chapter is to develop the format of after-tax cash flow statements.

  23. Classification of Investment Projects Expansion project Profit-adding project Product Improvement project Cost Improvement project Project Profit-maintaining project Replacement Project Necessity project

  24. Types of Cash Flow Elements in Project Analysis

  25. Cash Flows from Operating Activities

  26. A Typical Format used for Presenting Cash Flow Statement • Cash flow statement • + Net income • +Depreciation • Capital investment • + Proceeds from sales of • depreciable assets • Gains tax • Investments in working • capital • + Working capital recovery • + Borrowed funds • Repayment of principal • Net cash flow Operating activities Income statement Revenues Expenses Cost of goods sold Depreciation Debt interest Operating expenses Taxable income Income taxes Net income + Investing activities + Financing activities

  27. Depreciation

  28. Definition • defines depreciation as the ‘allocation of the depreciable amount of an asset over its estimated life’.

  29. The Objective of Depreciation • According to the matching concept, revenues should be matched with expenses in order to determine the accounting profit. • The cost of the asset purchased should be spread over the periods in which the asset will benefit a company.

  30. Depreciable Assets • The assets are acquired or constructed with the intention of being used and not with the intention for resale. • regards assets as depreciable when they • Are expected to be used in more than one accounting period. • Have a finite useful life, and • Are held for use in the production or supply of goods and services, for rental to others, or for administrative purposes.

  31. Non-Depreciable Asset • Freehold Land • It has an indefinite useful life, and it retains its value indefinitely. • Leasehold Land (Long Lease) • It has an unexpired lease period not less than 50 years • Investment Property • Which construction work and development have been completed • Which is held for its investment potential, any rental income being negotiated at arm’s length.

  32. Non-Depreciable Asset • Freehold Land • It has an indefinite useful life, and it retains its value indefinitely. • Leasehold Land (Long Lease) • It has an unexpired lease period not less than 50 years • Investment Property • Which construction work and development have been completed • Which is held for its investment potential, any rental income being negotiated at arm’s length.

  33. (A) Straight Line Method • Depreciation is computed by dividing the depreciable amount of the asset by the expected number of accounting periods of its useful life. Depreciation = Cost of Asset – Estimated Residual Value Estimated Useful Economic Life

  34. Useful Economic Life • Useful economic life is not equal to physical life • It is the period over which the present owner intends to use the asset

  35. Residual Value • It is the amount received after disposal of the asset Cost of asset - Residual value = Total amount to be depreciated

  36. Example Cost of asset $1200 Residual/scrap/salvage value $200 Estimated useful life 4 years Annual charge for depreciation = $1200-$200 4 = $1000 4 =$250

  37. When Projects Require only Operating and Investing Activities • Project Nature: Installation of a new computer control system • Financial Data: • Investment: $125,000 • Project life: 5 years • Salvage value: $50,000 • Annual labor savings: $100,000 • Annual additional expenses: • Labor: $20,000 • Material: $12,000 • Overhead: $8,000 • Depreciation Method: 5-yr Straight Line Method • Income tax rate: 40% • MARR: 15%

  38. Questions • (a) Develop the project’s cash flows over its project life. • (b) Is this project justifiable at a MARR of 15%? • (c) What is the internal rate of return of this project?

  39. Example 12.1 - Income Statement

  40. Cash Flow Statement

  41. Net Cash Flow Table Generated by Traditional Method Note that H = C-D-E-F-G I = 0.4 * H J= B+C-D-E-F-I Information required to calculate the income taxes *Salvage value

  42. Question (b): • Is this investment justifiable at a MARR of 15%? • PW(15%) = -$125,000 + +$43,145(P/F, 15%, 1) + . . . . + $81,620 (P/F, 15%, 5) = $43,151 > 0 • Yes, Accept the Project ! $81,619 $48,245 $44,745 $42,245 $43,145 0 1 2 3 4 5 Years $125,000

  43. Question (C): • Determine the IRR for this investment project. • At i = 25% • PW(25%) = $7,351 • At i = 30% • PW (30%) = -$6,124 • IRR = 27.61% > 15%, accept the project.

  44. Rate of Return Analysis (IRR = 27.61%)

  45. When Projects Require Working Capital Investments • Working capital means the amount carried in cash, accounts receivable, and inventory that is available to meet day-to-day operating needs. • How to treat working capital investments: just like a capital expenditure except that no depreciation is allowed.

  46. Working Capital Requirements (Example 12.2)

  47. Required Working Capital Investments During year 1 This differential amount must be invested at the beginning of the year

  48. Table 12.4 Item related to working capital investment

  49. Cash Flow Diagram including Working Capital $23,331 Working capital recovery $44,745 $81,619 $48,245 $43,145 $42,245 1 2 3 4 5 0 $125,000 Investment in physical assets $23,331 Investment in working capital $23,331 5 1 2 3 4 0 Years $23,331 Working capital recovery cycles

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