# cba2 - Engineering Risk Benefit Analysis 1.155 2.943 3.577...

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CBA 2. The Time Value of Money 1 Engineering Risk Benefit Analysis 1.155, 2.943, 3.577, 6.938, 10.816, 13.621, 16.862, 22.82, ESD.72 CBA 2. The Time Value of Money George E. Apostolakis Massachusetts Institute of Technology Spring 2007

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CBA 2. The Time Value of Money 2 The Importance of Time A dollar in hand now is worth more than a dollar received in the future, because of its earning power , i.e., it can be invested to generate income. The purchasing power of money, i.e., the amount of goods that a certain amount can buy, changes with time also. Objective: To develop methods for establishing the equivalence of sums of money . It depends on the amounts, the time of occurrence of the sums of money, and the interest rate.
CBA 2. The Time Value of Money 3 Overview of Lecture The Basics of Interest Rates – Simple and Compound Interest The Basic Discount Factors – Present Value, Future Value, Annual Value Economic Equivalence and Net Present Value Return to Interest Rates: Nominal and Effective Rates Inflation

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CBA 2. The Time Value of Money 4 Simple Interest P: Principal amount n: Number of interest periods i: Interest rate I: Interest earned Interest and principal become due at the end of n. I = Pni The interest is proportional to the length of time the principal amount was borrowed.
CBA 2. The Time Value of Money 5 Compound Interest Interest is payable at the end of each interest period. If the interest is not paid, the borrower is charged interest on the total amount owed (principal plus interest). Example: \$1,000 is borrowed for two years at 6% (compounded). A single payment will be made at the end of the second year. Amount owed at the beginning of year 2: \$1,060 Amount owed at the end of year 2: \$1,060x1.06 = \$1,000x(1.06) 2 = \$1,123.60 For simple interest, the amount owed at the end of year 2 would be: \$1,000 + 1,000x2x0.06 = \$1,120.00

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CBA 2. The Time Value of Money 6 Cash Flows over Time Up arrow = we receive \$; down arrow = we pay \$ Amount borrowed: \$1,000 Interest is paid at the end of each year at the rate of 10%. The principal is due at the end of the fourth year. \$1,000 \$100 \$100 \$100 \$1,100
CBA 2. The Time Value of Money 7 The Basic Discount Factors (future value) P (present value) A F (annual value or “annuity”)

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CBA 2. The Time Value of Money 8 Single-Payment Compound-Amount Factor A single payment is made after n periods. The interest earned at the end of each period is charged on the total amount owed (principal plus interest). \$1 now is worth (F/P,i,n) at time n if invested at i% P F= P(1+i) n 12 P(1+i) P(1+i) 2 n (F/P, i, n) = (1+i) n
CBA 2. The Time Value of Money 9 Single-Payment Present-Worth Factor The reciprocal of the single-payment compound amount factor.

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## This note was uploaded on 11/08/2011 for the course AERO 16.851 taught by Professor Ldavidmiller during the Fall '03 term at MIT.

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cba2 - Engineering Risk Benefit Analysis 1.155 2.943 3.577...

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