3) Maintenance costs on a bridge are $5,000 every other year starting at the end of year 2. For analysis purposes, the

Question

3) Maintenance costs on a bridge are $5,000 every other year starting at the end of year 2. For analysis purposes, the bridge is assumed to have an infinite life. What is the Capitalized Equivalent (CE) cost of these infinite payments, assuming an annual interest rate of 10% compounded annually? Answer 4) Machine A costs $35,000, lasts 3 years and has a salvage value of $7,500. Machine B costs $25,000, lasts 2 years and has a salvage value of $3,500. The machines can be purchased at the same price with the same salvage value in the future, and are needed for a 6 year project. Which machine would you purchase and why? Provide justification using an Annualized Equivalent Cost analysis. Interest is 10% annual rate, compounded annually. Answer

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3) Computation of Capitalized Equivalent Cost: Future value of annuity at 10% for 2 Years (1+r)^n-1/r 2.1 Present worth = Maintenance Cost/FVAF at 10% for 2 years = 5000/2.1 $2,380.95 Capitalized Equivalent Cost Present Worth/r = $2,380.95/.10 $23,809.52 4) Annualized Equivalent Cost of a machine = [Machine cost - (Salvage value*discount factor @10% at the end of life the machine)]/Annuity factor @10% for the life of the machine Annuity factor @10% for the life of the machine A = [1 - {1/(1+0.10)^3}]/0.10 = 2.48685 Discount factor @10% at the end of life the machine A = 1/(1+0.10)^3 = 0.75131 Annualized Equivalent Cost of a machine A= [$35000 - ($7500*0.75131)]/2.48685 = $11,808.16 Annuity factor @ 10% for the life of the machine B = [1 - {1/(1+0.10)^2}]/0.10 = 1.73554 Discount factor @ 10% at the end of life the machine B = 1/(1+0.10)^2 = 0.82645 Annualized Equivalent Cost of a machine B= [$25000 - ($3500*0.82645)]/1.73554 = $12,738.07 I will purchase machine A as it has lower Annualized Equivalent cost compared to Machine B.

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3) Maintenance costs on a bridge are $5,000 every other year starting at the end of year 2

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Archived Solution

Future value of annuity at 10% for 2 Years	(1+r)^n-1/r	2.1
Present worth = Maintenance Cost/FVAF at 10% for 2 years	= 5000/2.1	$2,380.95
Capitalized Equivalent Cost	Present Worth/r = $2,380.95/.10	$23,809.52