Document Sample

Warm-Up Review Time Value of Money Calculation of Future Value Calculation of Current Value Simple interests and compound interests Continuous compounding 1 Basics of Time Value of Money Interest rate reward for use of capital$ usually expressed in % per year Simple Interest (self-study) Only the principal earns interest Interest amount =P • i • n Future value = P + P • i • n = P (1 + i • n) 2 Basics of Time Value of Money Compound Interest Interest on interest • dependant on compounding period (yearly, semi-annually, monthly) For 2 years: • Future value = P ( 1+i) + i • P (1+i) = P (1+ i)2 For n years: • Future value = P (1+ i)n • see column 2 of interest tables 3 What is Time Value? We say that money has a time value because that money can be invested with the expectation of earning a positive rate of return In other words, “a dollar received today is worth more than a dollar to be received tomorrow” That is because today’s dollar can be invested so that we have more than one dollar tomorrow 4 Compound Interest Note from the example that the future value is increasing at an increasing rate In other words, the amount of interest earned each year is increasing Year 1: $10 Year 2: $11 Year 3: $12.10 The reason for the increase is that each year you are earning interest on the interest that was earned in previous years in addition to the interest on the original principle amountchange 5 Interest Formulation Simple Interest F Pe rt I (iP)N F P I P(1 iN) Compound Interest P(1 i) i[P(1 i)] P(1 i)(1 i) P(1 i) 2 After N periods, the total accumulated value F will grow to F P(1 i) N F P (1 i ) N 6 Continuous Compounding There is no reason why we need to stop increasing the compounding frequency at daily We could compound every hour, minute, or second We can also compound every instant (i.e., continuously): F Pe rt Here, F is the future value, P is the present value, r is the annual rate of interest, t is the total number of years, and e is a constant 7 Topics Today Cash Flow Diagrams Equivalent Issues Engineer Decision 8 Cash Flow- expenses and receipts Engineering projects generally have economic consequences that occur over an extended period of time For example, if an expensive piece of machinery is installed in a plant were brought on credit, the simple process of paying for it may take several years Each project is described as cash receipts or expenses at different points in time 9 Categories of Cash Flows The expenses and receipts due to engineering projects usually fall into one of the following categories: First cost: expense to build or to buy and install Operations and maintenance (O&M): annual expense, such as electricity, labor, and minor repairs Salvage value: receipt at project termination for sale or transfer of the equipment (can be a salvage cost) Revenues: annual receipts due to sale of products or services Overhaul: major capital expenditure that occurs during the asset’s life 10 Examples of Cash Inflows & Outflows Receipts from customers--operating activity Loans made to other firms--investing activity Dividend payments--financing activity Payments to investing activity Payments of taxes--operating activity Slide 14.8 11 Types of Cash Flows Single cash flow Uniform series Linear gradient series Geometric gradient series Irregular series 12 Cash Flow Diagrams The costs and benefits of engineering projects over time are summarized on a cash flow diagram. Cash flow diagram illustrates the size, sign, and timing of individual cash flows, and forms the basis for engineering economic analysis Tool! To show expenses and receipts 13 Cash Flow Diagrams Pictorial representation of engineering economic problem incomes and expenditures time period interest rate 14 Cash Flow diagrams--How A cash flow diagram is created by first drawing a segmented time-based horizontal line, divided into appropriate time unit. Each time when there is a cash flow, a vertical arrow is added pointing down for costs and up for revenues or benefits. The cost flows are drawn to relative scale 15 Cash Flow Diagrams P-Pattern “present” 1 2 3 n F-Pattern “future” 1 2 3 n A-Pattern “annual” 1 2 3 n G-Pattern “gradient” 1 2 3 n 16 Cash Flow Diagrams $15,000 Positive net Cash flow $2000 (receipts) $13,000 is net positive cash flow 1 2 3 4 5 Time (# of interest periods) 0 Negative net Cash Flow (payments) 17 Single Cash Flow F Compounding Process P Discounting Process F F P(1 i) N P (1 i) N P=Present equivalent value A=Annual equivalent value F= Future equivalent value 18 Example: Value and Interest The“value” of money depends on the amount and when it is received or spent. Example: What amount must be paid to settle a current debt of $1000 in two years at an interest rate of 8% ? Solution: $1000 (1 + 0.08) (1 + 0.08) = $1166 $1000 1 2 $1166 19 An Example of Cash Flow Diagram Boney (right) borrowed $1,000 from a bank at 8% interest. Two end-of-year payments: at the end of the first year, he will repay half of the $1000 principal plus the interest that is due. At the end of the second year, he will repay the remaining half plus the interest for the second year. 20 An Example of Cash Flow Diagram Cashflow for this problem is: End of year Cash flow 0 +$1000 1 -$580 (-$500 - $80) 2 -$540 (-$500 - $40) 21 Cash Flow Diagram $1,000 Time (# of interest periods) 1 2 0 $540 $580 22 Uneven Payment Series Find the present worth of any uneven stream of payments by calculating the present value of each individual payment and summing the results Future worth can then be calculated by using the interest formula P5 P1 P2 P6 P3 F P0 P4 P (1 i) N 0 Years 23 Equal Payment Series F 0 1 2 3 N-1 N A A A A A A N 1 N2 F A(1 i) A(1 i) ......A(1 i) A F A A(1 i) A(1 i) 2 ..... A(1 i) N 1 2 N (1 i)F A(1 i) A(1 i) .... A(1 i) N 1 Subtracting two above equations from each other yields: (1 i) FA N F(1 i) F - A A(1 i) i 24 Linear Gradient Series (N-1)G A1 2G G Uniform Series 0 0 1 2 N-1 N (1 i) N iN 1 P G i (1 i) 2 N Composite Series: uniform series + linear gradient Find P, given A1, G, I, N 25 Geometric Gradient Series •Particularly relevant to construction costs •Cash flows increase by a constant %(g); compound growth •Example: price changes due to inflation A1(1+g)N-1 Present Worth, Pn, of any Cash Flow An Pn A n (1 i) n A 1 (1 g) n 1 (1 i) n A1(1+g) N (1 g) n 1 A1 P A1 If i=g, then P=? 0 n 1 (1 i) n 1 2 3 N-1 N g>0 1(1g)N (1i) N P PA ....i g 1 i g Find P, given A1, g, i, N 26 Principal Uses of A Statement of Cash Flows Evaluate a business’s ability to produce positive cash flows in the future. Determine whether a company can satisfy its financial obligations. Identify sources of differences between a business’s net income and its related (net) cash flow from revenue and expense transactions. Analyze the impact on a business’s financial condition of its major investing and financing transactions. 27 Cash-Flow Data Can Be Used to Address Will a company generate sufficient cash to retire a long- term debt that matures soon? Why doesn’t a company’s record profits translate into positive cash flows? Is a company likely to suspend (or increase) its dividend payments? How does the composition of a company’s cash flows compare to that of its competitors? 28 Three Major Types of Business Activities Operating activities: those transactions and events related to the production and delivery of goods and services. Investing activities: include the making and collecting of loans, the acquisition and disposal of PP&E assets, and the purchase and sale of securities other than trading securities and cash equivalents. Financing activities: involve obtaining cash from lenders and repaying those amounts and obtaining cash from investors and providing them with a return of and a return on their investments. Slide 14.7 29 Economic Equivalence Which one would you prefer? •$20,000 today •$50,000 ten years from now •$ 8,000 each year for the next ten years We need to compare their economic worth! Economic equivalence exists between cash flows if they have the same economic effect. Convert cash flows into an equivalent cash flow at any point in time 30 Equivalence Principles 1 Use a common time basis Equivalent cash flows are equivalent at any common point in time Use the present time = present worth Use some future point in time = future worth 2 Equivalence depends on interest rate Changing the interest rate destroys equivalence 31 Equivalence Principles 3 Requires conversion of multiple payment cash flows to a single cash flow 4 Equivalence is maintained regardless of the point of view 32 The Decision Making Process Define problem Choose objectives Identify alternatives Evaluate consequences Select the best Implement Audit results 33 Making Decisions Preferences Politics People Facts research opinion Market Expert Costs … 34 Example: buying a car 57 Chevy 97 Neon 93 Mercedes Purchase $12,000 $7,000 $20,000 Operation 200/mth 50/mth 150/mth Resale $13,000 $5,000 $20,000 35 Modeling Real World Analysis The Model Information for decision making 36

DOCUMENT INFO

Shared By:

Categories:

Tags:

Stats:

views: | 3 |

posted: | 9/15/2011 |

language: | English |

pages: | 36 |

OTHER DOCS BY yaoyufang

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.