S. Sarah Miller is an engineer trying to determine the economic life of a new me

Question

S. Sarah Miller is an engineer trying to determine the economic life of a new metal year maintenance cost is $1,000. per year for each year after the first. press. The The interest rate is 15%. Fill in the table below and determine the economic life of the press initially. First Maintenance cost is forecast to increase $1,000 press costs $10,000 Consider only maintenance and capital recovery in your analysis. EUAC = Equivalent Uniform Annual Cost Economic life is point at which the total EUAC is at minimum Maintenance EUAC of EUAC of Total Year Cost Recovery Maintenance EUAC $ 1000 $ 2000 3000 4 4000 $ 5000 $6000 7000 $ 8000 Show formula Sarah used to calculate EUAC of Capital recovery and a sample calculation for one of the years. Show formula Sarah used to calculate EUAC of Maintenance and a sample calculation for one of the years.

Explanation / Answer

To compute the equated uniform annual cost (EUAC), you need a single cost first which is the total present value of the respective cash flows. When you get a single cost, you divide it by the Present Value Interest Factor Annuity (PVIFA) @ given rate for the given years to compute the EUAC.

EUAC Cost of Machine / EUAC of Capital Recovery

Since cost of machine, i.e., $10000 is incurred in initially or in the beginning of the first year, its total present value would be $10000 only.

EUAC = $10000 / PVIFA (15%, 8 years) = $10000 / 5.74663894353 = $1740.14760597 or $1740.15

EUAC of maintenance cost

First, we compute one total present value of uneven increasing (by $1000 every year) maintenance cost as follows -

Now, similar to capital recovery, we compute the EUAC by dividing it by the PVIFA -

EUAC = $23689.9115002 / PVIFA(8%, 8years) = $23689.9115002 / 5.74663894353 = $4122.39427828 or $4122.39

So, the Total EUAC for every year would be = $1740.15 + $4122.39 = $5862.54

Partculars Year PVF@8% Amount Present Value Maintenance Cost 1 0.92592592592 $1000 $925.92592592 2 0.85733882029 $2000 $1851.85185184 3 0.793832241 $3000 $2381.496723 4 0.73502985277 $4000 $2940.11941108 5 0.680583197 $5000 $3402.915985 6 0.63016962685 $6000 $3781.0177611 7 0.58349039523 $7000 $4084.43276661 8 0.54026888447 $8000 $4322.15107576 Total Present Value $23689.9115002

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.