The capitalized cost of an assset is the sum of the original cost of the asset a

Question

The capitalized cost of an assset is the sum of the original cost of the asset and the present value of maintaining the asset. Suppose a company is considering the purchase of two different machines. Machine 1 costs $10000 and t years from now will cost M1(t)=1000(1+0.05t) dollars to maintain. Machine 2 costs only $7000, but its maintenance cost at time t is M2(t)=1500 dollars. If the cost of money is 5% per year compounded continuously, what is the capitalized cost of each machine?

Machine 1 cost:

Machine 2 cost:

Explanation / Answer

Interest Rate is 5% compounded continuously So for t years the   discount factor =1/(1+e^rt)^t Machine 1 Capitalized cost: Original Cost = $      10,000.00 Maintenance cost in Yr t=   1000(1+0.5t) PV of all Maintenance cost = [1000(1+0.5)t]/(1+e^rt)^t] , (t= 1…..t) So Capitalized cost of Machine 1= 10000 +[1000(1+0.5)t]/(1+e^rt)^t] , (t= 1…..t) Machine 2Capitalized cost: Original Cost =                  7,000 Maintenance cost in Yr t=                  15,000 PV of all Maintenance cost = =15000/(1+e^rt)^t , (t=1….t) So Capitalized cost of Machine 2= 7000+15000/(1+e^rt)^t   , (t=1….t)

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