Homework 8 Ektek [PDF]

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Homework #8 Questions : A ready-mix concrete producer is considering to install a new mixer system:



at rate of return 10% determine which system should be installed using B/C analysis? Solutions : Benefit/ cost ratio analysis :



From equation



Modified B/C



Conventional B/C :



- includes operation & maintenance cost - initial investment replaces cost as denominator



B/C 



B  D O&M I



Calculation can be made in present worth, future worth or annuity With : B = Benefit ; D = Disbenefit ; C = Cost ; I = Initial Cost ; O&M = Operation &maintenance / AOC (Annual Operating Cost) In this case , Assume using annual worth analysis







For system A : Cash flow diagram. SV = $221500



First cost



(+)



Total unit price :



unit price $1286250



Unit price x annual production : 122.50$/cm x 10500cm =



0



1



2



3



$1286250



AOC = $320000 OC = $220000 $2.25M



(-)



Read from table (A/F, 10%, 3) = 0.30211 B1 = SV =$221500(A/F, 10%, 3) = $221500 x 0.30211 = $66917.37 Total unit price : Unit price x annual production : 122.50$/cm x 10500cm = $1286250 B2 = $1286250



Read from table (P/F, 10%, 2) = 0.8264 ; (A/P, 10%, 3) = 0.40211 C1 = OC (Overhaul Cost) = $220000(P/F, 10%, 2)(A/P, 10%, 3) = $220000.(0.8264).(0.40211)=$73106.81 Read from table (A/P, 10%, 3) =0.40211 C2 = Initial Investment = $2250000(A/P, 10%, 3) = $2250000.(0.40211) = $904747.5 C3 = AOC (Annual Operating Cost) = $320000 Conventional B/C analysis : B/C =



=



= 1.042



Modified B/C analysis : B/C =



=



= 1.061







For system B : Cash flow diagram SV = $308000



First cost



unit price $2597000 (+)



Total unit price : Unit price x annual production : 122.50$/cm x 21200cm =



0



1



2



3



4



$2597000



AOC = $495000 OC = $245000 $2.95M



OC = $245000 (-)



Read from table (A/F, 10%, 4) = 0.21547 B1 = SV =$308000(A/F, 10%, 4) = $308000 x 0.21547 = $66364.76 Total unit price : Unit price x annual production : 122.50$/cm x 21200cm = $2597000 B2 = $2597000 Read from table (P/F, 10%, 2) = 0.8264 ; (A/P, 10%, 4) = 0.31547 ; (A/F, 10%, 4) = 0.21547 C1 = OC (Overhaul Cost) = $245000(P/F, 10%, 2)(A/P, 10%, 4)+ $245000(A/F, 10%, 4) = $245000.(0.8264).(0.31547) + $245000.(0.21547) = $116662.7 Read from table (A/P, 10%, 4) = 0.31547 C2 = Initial Investment = $2950000(A/P, 10%, 4) = $2950000.(0.31547) = $930636.5 C3 = AOC (Annual Operating Cost) = $495000 Conventional B/C analysis : B/C =



=



= 1.726



Modified B/C analysis : B/C =



=



= 2.070







For system C : Cash flow diagram SV = $367500



First cost



unit price $2437750 (+)



Total unit price : Unit price x annual production : 122.50$/cm x 19900cm =



0



1



2



3



4



$2437750



AOC = $401500 OC = $295000 $2.75M



OC = $295000 (-)



Read from table (A/F, 10%, 4) = 0.21547 B1 = SV =$367500(A/F, 10%, 4) = $367500 x 0.21547 = $79185.225 Total unit price : Unit price x annual production : 122.50$/cm x 19900cm = $2437750 B2 = $2437750 Read from table (P/F, 10%, 2) = 0.8264 ; (A/P, 10%, 4) = 0.31547 ; (A/F, 10%, 4) = 0.21547 C1 = OC (Overhaul Cost) = $295000(P/F, 10%, 2)(A/P, 10%, 4) )+ $245000(A/F, 10%, 4) = $295000.(0.8264).(0.31547) + $295000.(0.21547) = $140471.4 Read from table (A/P, 10%, 4) = 0.31547 C2 = Initial Investment = $2750000(A/P, 10%, 4) =$2750000.(0.31547) = $867542.5 C3 = AOC (Annual Operating Cost) = $401500 Conventional B/C analysis : B/C =



=



= 1.785



Modified B/C analysis : B/C =



=



= 2.098



For conclusion after we compare system A, B & C, we chose system C because it has more benefit - cost ratio.