Question

Q2. (5 pts) The estimates for two machines, X and Y, are given in different ways in a company as shown below: Machine X in constant-value (today's) dollars while Machine Y in future (then-current) dollars. The company's MARR is equal to the real rate of return of 10% per year, and inflation is 3% per year. Use PW analysis to determine which machine is better. You can use the below factor formula in case the factors table is not available. Factor X Machine Y Machine Notation Formula in CV dollars) (in Future dollars) (P/A..n) (1 + )" - 1 First cost (5) - 220,000 - 150,000 Annual Operation Cost (S/year) - 20,000 - 45,000 (A/P.1.0) (1+ 1 Life, 8 years (1 + 1"-1

Answer 1

Ans:

Calculating PW for each machine:

MARR : 10%

Inflation : 3%

Required rate of return : 10+3 = 13%

Machine X:

First Cost : $220,000

Annual Operating Cost : $20,000

Annuity Factor @13% for 8 Years : 1/(1.13)^1 + 1/(1.13)^2 + 1/(1.13)^3 + .........1/(1.13)^8 = 4.79877

Present value of Annual Operating costs : $20,000 * 4.79877 = $95,975

Present value Cost of Machine X : $220,000 + $95,975 = $315,975

Machine Y:

First Cost : $150,000

Annual Operating Cost : $45,000

Annuity Factor @13% for 8 Years : 1/(1.13)^1 + 1/(1.13)^2 + 1/(1.13)^3 + .........1/(1.13)^8 = 4.79877

Present value of Annual Operating costs : $45,000 * 4.79877 = $215,945

Present value Cost of Machine Y : $150,000 + $215,945 = $365,945

So cost of Machine X is low. Machine X is better.

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