 # 6.2 cash flow - time diagrams

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Information about 6.2 cash flow - time diagrams
Engineering

Published on April 22, 2014

Author: arcaliza

Source: slideshare.net

Building Economy ARE 431 Dr. Mohammad A. Hassanain 1 Time Value of Money Cash Flow/Time Diagrams 2 The Concept of Cash Flow. Cash Flow Tabulation. Examples Illustrating Cash Flow Tabulations. Cash Flow Diagrams. Example Illustrating the Use of Cash Flow Diagrams. Today’s Lecture

Building Economy ARE 431 Dr. Mohammad A. Hassanain 2 3 Symbols and Cash Flow Diagrams The mathematical relations used in engineering economy employ the following symbols: P = Value of sum of money at a time denoted as the present. F = Value or sum of money at some future time, or a single sum of money at the end of n interest period. A = A series of periodic, equal amount of money. n = Number of interest periods. i = Interest rate per interest period. Note: The dollar amount of F and A are considered at the end of the interest period. 4 Cash Flow Every person or company has cash receipts (income) and cash disbursement (costs). The results of income and costs is called cash flow. Cash Flow = Receipts – Disbursements A positive cash flow indicates a net receipts in a particular interest period or year. A negative cash flow indicates a net disbursement in that period.

Building Economy ARE 431 Dr. Mohammad A. Hassanain 3 5 Cash Flow Example: If you buy a printer in 1999 for \$300, maintain it for three years at a cost of \$20 per year, and then sell it for \$50, what are your cash flows for each year? + \$30\$20\$502002 - \$20\$2002001 - \$20\$2002000 - \$300\$30001999 Cash FlowDisbursementReceiptsYear Its important to remember that all receipts and disbursements and thus cash flows are assumed to be end-of period amounts. Therefore, 1999 is the present (now) and 2002 is the end of year 3. 6 Cash Flow Example: Suppose you borrowed \$1,000 on May 1, 1984, and agree to repay the loan in one lump sum of \$1,402.60 at the end of four years at 7%. Tabulate the cash flows? 000May 1, 1987 - \$1,402.60\$1,402.600May 1, 1988 000May 1, 1986 000May 1, 1985 + \$1,0000\$1,000May 1, 1984 Cash FlowDisbursementReceiptsDate

Building Economy ARE 431 Dr. Mohammad A. Hassanain 4 7 Cash Flow Diagrams A cash flow diagram is simply a graphical representation of cash flows (in vertical direction) on a time scale (in horizontal direction). Time zero is considered to be present, and time 1 is the end of time period 1. This cash flow diagram is set up for five years. 0 4321 5 Year 1 Year 5 8 Cash Flow Diagrams The direction of the cash flows (income or outgo) is indicated by the direction of the arrows. From the investor’s point of view, the borrowed funds are cash flows entering the system, while the debt repayments are cash flows leaving the system. Time 321 (+ve) Cash Flow (\$) (-ve) 4

Building Economy ARE 431 Dr. Mohammad A. Hassanain 5 9 Cash Flow Diagrams Example 1: If you borrow \$2,000 now and must repay the loan plus interest (at rate of 6% per year) after five years. Draw the cash flow diagram. What is the total amount you must pay? P = \$2,000 5 31 (+ve) Cash Flow (\$) (-ve) 420 F = is to be found after 5 years F = \$2,000 (1+0.06)5 F = \$2,676.45 10 Cash Flow Diagrams Example 2: If you start now and make five deposits of \$1,000 per year (A) in a 7% per year account, how much money will be accumulated immediately after you have made the last deposit. Draw the cash flow diagram. What is the total amount you will accumulate? A = \$1,000 3 4210 F = is to be found after 4 years Since you have decided to start now, the first deposit is at year zero and the fifth deposit and withdrawal occur at end of year 4

Building Economy ARE 431 Dr. Mohammad A. Hassanain 6 11 Cash Flow Diagrams Example 3: Assume that you want to deposit an amount (P) into an account two years from now in order to be able to withdraw \$400 per year for five years starting three years from now. Assume that the interest rate is 5.5% per year. Construct the cash flow diagram. A = \$400 64 20 1 3 P = ? 5 7 12 Cash Flow Diagrams Example 4: Suppose that you want to make a deposit into your account now such that you can withdraw an equal amount (A1) of \$200 per year for the first five years starting one year after your deposit and a different annual amount (A2) of \$300 per year for the following three years. With an interest rate (i) of 4.5% per year, construct the cash flow diagram. P = ? A = \$200 642 0 1 3 5 7 A = \$300 8 i = 4.5% The first withdrawal (positive cash flow) occurs at the end of year 1, exactly one year after P is deposited.

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