3. The following costs and benefits are associated with two machines under consi

Question

3. The following costs and benefits are associated with two machines under consideration for investment. Using Rate of Return Analysis with Present Worth equations, determine which (f any) of the two alternatives is prefemed. MARR = 20%. Please find the exact ROR calculation in making your decision (round to the nearest 0.01% example. 10.47%). Show any Inaunterpolation equation thatsneeded Alsowme outeach stop,ofany Let 20% be yourfirstguess. AROR-18.37%) First Cost Annual Costs Annual Benefits Salvage Value Useful Life ROR Machine A $52,000 $15,000 S38,000 $13,000 Machine B $85,000 $10,000 $35,000 $20,000 24.46% 22.11%

Explanation / Answer

Machine A-

PW= first cost+(Annual benefit-Annual cost)(P/A,i,n)+salvage value(P/F,i,n)

PW= -52000+(38000-15000)(P/A,i,3)+13000(P/F,i,3)

PW= -52000+23000(P/A,i,3)+13000(P/F,i,3)

To determine i we equate PW to zero

0=  -52000+23000(P/A,i,3)+13000(P/F,i,3)

Now we use hit and trial method to find i, let i=20%

PW= -52000+ (23000*2,106)+(13000*0.5787)

= 3961.1

Let i=25%

PW= -52000+ (23000*1.952)+(13000*0.5120)

=-448

so the value of i will be between 20 and 25, usin interpolation

3961.1-( -448)/ 25%-20% = 3961.1-0/(i-20%)

4409.1/5%= 3961.1/(i-20%)

i-20%=  0.898392*5%

i = 0.04492+.20

i= 0.24492

i.e 24.49%

Machine B-

PW= -85000+(35000-10000)(P/A,i,6)+20000(P/F,i,6)

PW= -85000+25000(P/A,i,6)+20000(P/F,i,6)

To determine i we equate PW to zero

0=  -85000+25000(P/A,i,6)+20000(P/F,i,6)

Now we use hit and trial method to find i, let i=20%

PW= -85000+25000(3.326)+20000(0.3349)

= 4848

Let i=25%

PW= -85000+25000(2.951)+20000(0.2621)

=-5983

so the value of i will be between 20 and 25, usin interpolation

4848-( -5983/ 25%-20% = 4848-0/(i-20%)

10831/5%= 4848/(i-20%)

i-20%=  0.447604*5%

i = 0.02238+.20

i= 0.22238

i.e 22.23%

Since ROR > MARR for both machines are economically justified

Since PW at MARR=20% is higher for machine B we select machine B

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