The Ajax Manufacturing Company wishes to choose one of the following machines. M

Question

The Ajax Manufacturing Company wishes to choose one of the following machines.
Machine 1 Machine 2 Machine 3
Initial cost $12,000 $15,000 $21,000
Planning horizon 5 years 5 years 5 years
Salvage value $1200 $2,000 $3,000
Revenue years 1,..,k $3,000 +500(k -1) $3,500 + 750(k-1) $4,500 + 1000(k -1)
Operating and
maintenance
costs years 1, …, k $800 (1.1)k-1 $800 (1.08)k-1 $800 + 100(k -1)

MARR is 12% and the planning horizon is 5 years. Based on the internal rate of return determine the preferred alternative.

Please Solve ASAP!!!

Explanation / Answer

I cant understand the revenue years and maintenance cost thing.

I ll do the the remaining with an example.hope you may follow :

We have :

principle value cost : PV : I + (other costs)/(1+r)n - S/(1+r)n ; i is the interest , S is salvage value.

annuity or equivalent annual cost : PV[(1+r)nr]/[(1+r)n -1]

Machine 1 :

I = 12000$

n = 5

S = 1200$

say,maintenance increases by 200$ every year., initially being 800$

we have :

PV = 12000 + [800/(1+0.12) + 1000/(1.12)2 +..+ 1600/(1.12)5] - 1200/(1.12)5

and now calculate the equivalent annual cost from the formula :

equivalent annual cost : PV[(1+r)nr]/[(1+r)n -1]

=> A = PV[(1.12)5(0.12)]/[(1.12)5 -1] ;

now compare the Annuity of each of the machine and the lower one is preferred as per the profits and low maitenance costs.

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