cba3 - Engineering Risk Benefit Analysis 1.155, 2.943,...

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CBA 3. Bases for Comparison of Alternatives 1 Engineering Risk Benefit Analysis 1.155, 2.943, 3.577, 6.938, 10.816, 13.621, 16.862, 22.82, ESD.72 CBA 3. Bases for Comparison of Alternatives George E. Apostolakis Massachusetts Institute of Technology Spring 2007

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CBA 3. Bases for Comparison of Alternatives 2 Overview (Net) Present Worth or Value [(N)PW or (N)PV] and Annual Equivalent (AE) The Effect of Discount and Inflation Rates Using PW and AE as Decision Criteria The Internal Rate of Return as a Decision Criterion The Benefit-Cost Ratio as a Decision Criterion Comparing Projects with Unequal Lives
CBA 3. Bases for Comparison of Alternatives 3 Present Worth (1) Present Worth : The net equivalent amount at the present that represents the difference between the equivalent receipts and the equivalent disbursements of an investment cash flow for a selected interest rate i. If F t is the net cash flow at time t, then = + = n 0 t t t ) i 1 ( F ) i ( PW

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CBA 3. Bases for Comparison of Alternatives 4 Present Worth (2) Present worth may also refer to the present value of receipts (benefits) or disbursements (costs). In this case, the criterion for decision making is the Net Present Worth. We will follow the definition on slide 3 (Thuesen & Fabrycky). Present Worth, Net Present Worth, and Net Present Value are equivalent terms. = = = = + + = = = n t 0 t t t n t 0 t t t ) i 1 ( C ) i 1 ( B ) i ( NPV ) i ( NPW ) i ( PW
CBA 3. Bases for Comparison of Alternatives 5 Present Worth: Example You buy a car and you put down \$5,000. Your payments will be \$500 per month for 3 years at a nominal interest rate of 10%. Assuming monthly compounding, what is the present price you are paying? From CBA 2, Slide 14, we get 505 , 20 \$ 505 , 15 000 , 5 ] ) 0083 . 0 1 ( 0083 . 0 1 ) 0083 . 0 1 ( [ 500 000 , 5 P 36 36 = + = = + + + = n n ) i 1 ( i 1 i) (1 ) n , i , A / P ( + + = Here: A = \$500/mo, i = 10/12 = 0.83%, n = 36 months

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CBA 3. Bases for Comparison of Alternatives 6 Annual Equivalent The annual equivalent of receipts minus the annual equivalent of disbursements (the annualized profit). Any present worth can be converted to a series of equal annual amounts by multiplying by (A/P, i, n). = + + + = = n 0 t n n t t ] 1 ) i 1 ( ) i 1 ( i ][ ) i 1 ( F [ ) n , i , P / A )( i ( PW ) i ( AE Another name is Net Annual Value (NAV). For fixed i and n, AE and PW yield the same results, i.e., the same ranking of alternatives.
CBA 3. Bases for Comparison of Alternatives 7 PW and AE Criteria for Decision Making An investment alternative A j , j = 1,…,n, is a decision option representing a course of action. Decision Criteria : A j A k if PW(i) Aj > PW(i) Ak or A j A k if AE(i) Aj > AE(i) Ak These criteria are using the total investment. f f

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CBA 3. Bases for Comparison of Alternatives 8 Example of Total Investment Comparisons End of Year B 3 B 4 0 -\$12,000 -\$15,000 1 -1,200 -400 2 -1,200 -400 3 1,500 3,000 The benefits from these alternatives are identical. We must select one.
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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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cba3 - Engineering Risk Benefit Analysis 1.155, 2.943,...

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