Question

Question 12 15 points For alternatives shown in the table below you are trying to decide which alternative you should choose based on their capitalized costs (CC). Use an interest rate of 10% per year. Machine A Machine B First cost (AED) 20,000 240,000 Annual maintenance cost per year, AED5,000 2,300 Periodi e cost every 10 years, AED 10,000 Salvage cost 2000 Life, years Match the closest correct answers for the below questions: A. [Alternative A] B. -44,483.50] C. I-269,275] D. [Alternative B] E. I-627.5] F. [-1,300] G. [-253,627.50] H. [-23,000] I. -108,784] Calculate the present value of the maintenance costs for Alternative B. Calculate the Anuual value of the periodic costs for Alternative B. - Calculate CC of Alternative B # Calculate the CC of Alternative A Which alternative should be selected?

Answer 1

Answer a)

Present Cost of Maintenance of Machine B:

Annual cost AED 2300 for infinite period is given by PV = P/r where P = AED 2300, r=10%

Hence Capital Cost = 2300/10% = 2300/0.1 = -AED 23000

Hence option H is correct

Answer b)

Annual Value of Periodic Cost of Machine B:

Periodic cost AED 10000 every 10 years for infinite period. AED 10000 can be seen as a Future Value of a 10 year annuity and FV = P *((1+r)^n - 1)/r , where P= Annuity, r= 10%, n=10 years

Hence, 10000 = P * ((1+10%)^10 - 1)/10%

or, 10000 = P*(1.1^10 - 1)/0.1

or, 10000 *0.1 = P * (2.594-1)

or, 1000 = P * 1.594

or P= 1000/1.594 = 627.35

Hence Annual Value of Periodic Cost = -AED 627.35

Hence option E is correct

Answer c)

Initial Cost = AED 240000

Capitalized Maintenance Cost = AED 23000

Capitalized Periodic Cost = P/r = 627.35/10% = 627.35/0.1 = 6273.5

Total Capitalized Cost = 240000 + 23000 + 6273.5

= -AED 269273.4

Hence option C is ccorrect

Answer d)

Initial Cost = AED 20000

Present Cost of Maintenance of Machine A:

Annual cost AED 5000 for 4 year period is given by PV= P * (1- (1+r)^-n) / r , P= AED 5000, r = 10%, n= 4 years

Hence PV = 5000 * (1-(1+10%)^-4 /10%

= 5000 * (1-(1.1)^-4 /0.1

= 5000 * (1-0.683) /0.1

= 5000 * 0.317/0.1

= AED 15849.33

Present Value of Salvage Value = P/(1+r)^n , P=AED 2000, r= 10%, n=4 years

PV = 2000/ (1+10%)^4 = 2000/1.4641 = AED 1366.07

Hence Total Capitalized cost = -20000 - 15849.33 + 1366.07 = - AED 34483.26

Hence option B is correct (it is wrongly printed as 44483)

Answer e)

Option with less capitalized cost shall be chosen. Hence machine A shall be chosen

Hence option A is correct