ERT461 BIOSYSTEMS ENGINEERING DESIGN 1 ERT424 BIOPROCESS PLANT DESIGN 1 1

 The Interest Rate  Simple Interest  Compound Interest  Amortizing a Loan  Compounding More Than Once per Year  The Interest Rate  Simple Interest  Compound Interest  Amortizing a Loan  Compounding More Than Once per Year

$10,000 today $10,000 in 5 years Which would you prefer -- $10,000 today or $10,000 in 5 years?

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

 Compound Interest Interest paid (earned) on any previous interest earned, as well as on the principal borrowed (lent). u Simple Interest Interest paid (earned) on only the original amount, or principal, borrowed (lent).

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

$140  SI = P 0 (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?

FV $1,140 FV = P 0 + SI = $1,000 + $140 = $1,140  Future Value  Future Value is the value at some future time of a present amount of money, or a series of payments, evaluated at a given interest rate. Future Value FV  What is the Future Value (FV) of the deposit?

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

Future Value (U.S. Dollars)

$1,000 2 years Assume that you deposit $1,000 at a compound interest rate of 7% for 2 years $1,000 FV 2 7%

FV 1 P 0 $1,000 $1,070 FV 1 = P 0 (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.

FV 1 P 0 $1,000 $1,070 FV 1 = P 0 (1+i) 1 = $1,000 (1.07) = $1,070 FV 2 P 0 $1,000P 0 $1,000 $1, FV 2 = FV 1 (1+i) 1 = P 0 (1+i)(1+i) = $1,000(1.07)(1.07)= P 0 (1+i) 2 = $1,000(1.07) 2 = $1, $4.90 You earned an EXTRA $4.90 in Year 2 with compound over simple interest. Future Value Single Deposit (Formula) Future Value Single Deposit (Formula)

FV 1 FV 1 = P 0 (1+i) 1 FV 2 FV 2 = P 0 (1+i) 2 Future Value General Future Value Formula: FV n FV n = P 0 (1+i) n FV n FVIFSee Table I or FV n = P 0 (FVIF i,n ) -- See Table I

FVIF FVIF i,n is found on Table I at the end of the book.

FV 2 FVIF $1,145 FV 2 = $1,000 (FVIF 7%,2 ) = $1,000 (1.145) = $1,145 [Due to Rounding]

$10,000 5 years 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 $10,000 FV 5 10%

FV 5 FVIF $16,110  Calculation based on Table I: FV 5 = $10,000 (FVIF 10%, 5 ) = $10,000 (1.611) = $16,110 [Due to Rounding] FV n FV 5 $16, u Calculation based on general formula: FV n = P 0 (1+i) n FV 5 = $10,000 ( ) 5 = $16,105.10

“Rule-of-72”. 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.)?

72 Approx. Years to Double = 72 / i% 726 Years 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.)?

 Estimating Cost/Benefit for Engineering Projects  Incremental Cash Flows  Developing Cash Flow Statements  Generalized Cash Flow Approach 21

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. 22

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

Types of Cash Flow Elements in Project Analysis 24

Income Statement ApproachDirect Cash Flow Approach Operating revenues Cost of goods sold Depreciation Operating expenses Interest expenses Taxable income Income taxes Net income + Depreciation Operating revenues - Cost of goods sold - Operating expenses - Interest expenses - Income taxes Cash flow from operation Cash Flows from Operating Activities 25

Cash Flow Element Operating activities: Other Terms Used in Business Gross incomeGross revenue, Sales revenue, Gross Profit, Operating revenue Cost savingsCost reduction Manufacturing expensesCost of goods sold, Cost of revenue O&M costOperating expenses Operating incomeOperating profit, Gross margin Interest expensesInterest payments, Debt cost Income taxesIncome taxes owed Investing activities Capital investmentPurchase of new equipment, Capital expenditure Salvage valueNet selling price, Disposal value, Resale value Investment in working capitalWorking capital requirement Working capital releaseWorking capital recovery Gains taxesCapital gains taxes, Ordinary gains taxes Financing activities: Borrowed fundsBorrowed amounts, Loan amount Principal repaymentsLoan repayment 26

A Typical Format used for Presenting Cash Flow Statement Income statement Revenues Expenses Cost of goods sold Depreciation Debt interest Operating expenses Taxable income Income taxes Net income 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 Investing activities Financing activities

Depreciation

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

 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.

 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.

 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.

 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.

 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

 Useful economic life is not equal to physical life  It is the period over which the present owner intends to use the asset

 It is the amount received after disposal of the asset Cost of asset - Residual value = Total amount to be depreciated

Cost of asset $1200 Residual/scrap/salvage value $200 Estimated useful life4 years Annual charge for depreciation = $1200-$200 4 = $ =$250

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

Income Statement Revenues$100,000 Expenses: Labor20,000 Material12,000 Overhead8,000 Depreciation17,86330,61321,86315,6135,581 Taxable Income$42,137$29,387$38,137$44,387$54,419 Income Taxes (40%)16,85511,75515,25517,75521,768 Net Income$25,282$17,632$22,882$26,632$32,651 40

Cash Flow Statement Operating Activities: Net Income$25,282$17,632$22,882$26,632$32,651 Depreciation17,86330,61321,86315,6135,581 Investment Activities: Investment(125,000) Salvage50,000 Gains Tax(6,613) Net Cash Flow($125,000)$43,145$48,245$44,745$42,245$81,619 41

Net Cash Flow Table Generated by Traditional Method ABCDEFGHIJ Year End Investment & Salvage Value RevenueLaborExpenses Materials OverheadDepreciationTaxable Income Income Taxes Net Cash Flow 0-$125,000 1$100,00020,00012,0008,000$17,86342,13716,855$43, ,00020,00012,0008,00030,61329,38711,755$48, ,00020,00012,0008,00021,86338,13715,255$44, ,00020,00012,0008,00015,61344,38717,755$42, ,00020,00012,0008,0005,58154,41921,678$38,232 50,000*16,5256,613$43,387 Information required to calculate the income taxes *Salvage value Note that H = C-D-E-F-G I = 0.4 * H J= B+C-D-E-F-I 42

 Is this investment justifiable at a MARR of 15%?  PW(15%) = -$125, $43,145(P/F, 15%, 1) $81,620 (P/F, 15%, 5) = $43,151 > 0 ◦ Yes, Accept the Project ! Question (b): $125,000 $43,145 $48,245 $44,745 $42,245 $81,619 Years 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%) n = 0n =1n = 2n = 3n = 4n = 5 Beginning Balance -$125,000-$116,376-$100,271-$83,218-$63,955 Return on Investment (interest) -$34,521-$32,140-$27,692-$22,982-$17,665 Payment-$125,000+$43,145+$48,245+$44,745+$42,245+$81,620 Project Balance -$125,000-$116,376-$100,271-$83,218-$63,

 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 Price (revenue) per unit$10 Unit variable manufacturing costs Labor Material Overhead $2 $1.20 $0.80 Monthly volume833 units Finished goods inventory to maintain2 – month supply Raw materials inventory to maintain1 – month supply Accounts payable30 days Accounts receivable60 days (Example 12.2) 47

Income /Expense Reported Actual cash Received/paidDifference Sales$100,000 (10,000 units) $83,333-$16,666 Expenses$40,000 (10,000 units) $46,665 (11,667 units) +$6665 Income taxes Net amount $16,855 $43,145 $16,855 $19, $23,333 During year 1 Required Working Capital Investments 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 Years $23,331 Working capital recovery cycles $43,145 $48,245 $44,745 $42,245 $81,619 Working capital recovery $23,331 $125,000 Investment in physical assets $23,331 Investment in working capital 50

 Key issue: Interest payment is a tax- deductible expense.  What Needs to Be Done: Once loan repayment schedule is known, separate interest payment from the annual installment.  What about Principal Payment? As the amount of borrowing is NOT viewed as income to the borrower, the repayment of principal is NOT viewed as expenses either– NO tax effect. 51

Loan Repayment Schedule (Example 12.4) End of Year Beginning Balance Interest Payment Principal Payment Ending Balance 1$62,500$6,250$10,237$52, ,2635,22611,26141, ,10012,38728, ,86113,62614, ,49914,9880 Amount financed: $62,500, or 50% of total capital expenditure Financing rate: 10% per year Annual installment: $16,487 or, A = $62,500(A/P, 10%, 5) $16,487 52

Items related to financing activities Table

 Negative taxable income (project loss) means you can reduce your taxable income from regular business operation by the amount of loss, which results in a tax savings.  Handling Project Loss Regular Business ProjectCombined Operation Taxable income Income taxes (35%) $100M $35M (10M) ? $90M $31.5M Tax Savings = $35M - $31.5M = $3.5M Or (10M)(0.35) = -$3.5M Tax savings 54

 When to Use: When undertaking a project does not change a company’s marginal tax rate.  Pros: The cash flows can be generated more quickly.  Cons: The process is less intuitive and not commonly understood by business people. 55

Table 12.8 Investing activities Operating activities Financing activities 56

Summary Identifying and estimating relevant project cash flows is perhaps the most challenging aspect of engineering economic analysis. All cash flows can be organized into one of the following three categories: 1. Operating activities. 2. Investing activities 3. Financing activities. 57

Cash Items 1. New investment and disposal of existing assets 2. Salvage value (or net selling price) 3. Working capital 4. Working capital release 5. Cash revenues/savings 6. Manufacturing, operating, and maintenance costs. 7. Interest and loan payments 8. Taxes and tax credits 58

Non-cash items 1. Depreciation expenses 2. Amortization expenses The income statement approach is typically used in organizing project cash flows. This approach groups cash flows according to whether they are operating, investing, or financing functions. The generalized cash flow approach to organizing cash flows can be used when a project does not change a company’s marginal tax rate. The cash flows can be generated more quickly and the formatting of the results is less elaborate than with the income statement approach. However, the generalized approach is less intuitive and not commonly understood by business people. 59