Class_Nov12_2013_Lec22_ISE460(1)(1)

f example 117 adjusteddiscounted method given

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Unformatted text preview:  ­ Step 1: Bring all cash ﬂows to have common purchasing power.  ­ Step 2: Consider the earning power. •  Method 2: Adjusted ­discount Method  ­ Combine Steps 1 and 2 into one step. Example 11.6 – Deﬂa%on Method Step 1: Conver%ng Actual Dollars into Step 2: Calcula%ng Equivalent Constant Dollars Present Worth Graphical Overview on Deﬂa%on Method (Example 11.6): Conver%ng actual dollars to constant dollars and then to equivalent present worth n=0 n=1 n=2 n=3 n=4 n=5 Actual Dollars Constant Dollars Present Worth -\$75,000 -\$75,000 \$32,000 \$35,700 \$32,800 \$29,000 \$58,000 \$30,476 \$32,381 \$28,334 \$23,858 \$45,455 \$28,218 -\$75,000 \$27,706 \$26,761 \$21,288 \$16,295 \$45,268 Adjusted ­Discount Method – Perform Deﬂa%on and Discoun%ng in One Step An (1 + f ) n Pn = (1 + i ' ) n Step 2 = = o  Discrete Compounding Step 1 Pn = An An = n (1 + i)n Ⱥ(1 + f )(1 + i ')Ⱥ Ⱥ Ⱥ An (1 + f )n (1 + i ')n An Ⱥ(1 + f )(1 + i ')Ⱥ Ⱥ Ⱥ An (1 + i)n (1 + i) = (1 + f )(1 + i ') = 1 + i '+ f + i ' f n i = i '+ f + i ' f o  Con%nuous Compounding i = i '+ f Example 11.7 Adjusted ­Discounted Method Given: inﬂa%on ­free interest rate = 0.10, general inﬂa%on rate = 5%, and cash ﬂows in actual dollars Find: i and NPW i = i '+ f + i ' f = 0.10 + 0.05 + (0.10)(0.05) = 15.5% n Cash Flows in Actual Dollars Multiplied by Equivalent Present Worth 0 -\$75,000 1 -\$75,000 1 32,000 (1+0.155)-1 27,706 2 35,700 (1+0.155)-2 26,761 3 32,800 (1+0.155)-3 21,288 4 29,000 (1+0.155)-4 16,296 5 58,000 (1+0.155)-5 28,217 \$45,268 Graphical Overview on Adjusted Discount Method: Conver%ng actual dollars to present worth dollars by applying the market interest rate n=0 Actual Dollars n=1 -\$75,000 \$32,000 n=2 n=3 n=4 \$35,700 \$32,800 \$29,000 \$58,000 i = i+ + f + i+ f = 15.5% Present Worth \$28,218 -\$75,000 \$27,706 n=5 \$26,761 \$21,288 \$16,295 \$45,268 Mixed ­Dollar Analysis – College Savings Plan  ­ Equivalence Calcula%on wit...
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