show all work step by step Given the data in the table below, choose the better

Question

show all work step by step

Given the data in the table below, choose the better alternative using Present Worth Analysis. MARR is 7%. Alternative A Alternative B Initial Cost Annual Benefits Annual Expenses Salvage Value Useful Life (Years) $12,000 S5,500 $2,500 S1,000 S8,000 S5,200 S2,200 S1,100 4 a) Solve the problem using compounding factors. Show all required compounding factors (XX, i%, n) Round the answer to zero decimal place b) Solve the problem using Excel. Take a screenshot of your excel worksheet and submit it with your solution. Do not upload the excel file.

Explanation / Answer

ANSWER:

1) n = 6 years and i = 7% for alternative a

PW of alternative a = initial cost + annual benefits - annual expenses(p/a,i,n) + salvage value(p/f,i,n)

pw = -12,000 + 5,500 - 2,500(p/a,7%,6) + 1,000(p/f,7%,6)

pw = -12,000 + 3,000(p/a,7%,6) + 1,000(p/f,7%,6)

pw = -12,000 + 3,000 * 4.767 + 1,000 * 0.6663

pw = -12,000 + 14,301 + 666.3

pw = 2,967.3

n = 4 years and i = 75 for alternative b.

PW of alternative b = initial cost + annual benefits - annual expenses(p/a,i,n) + salvage value(p/f,i,n)

pw = -8,000 + 5,200 - 2,200(p/a,7%,4) + 1,100(p/f,7%,4)

pw = -8,000 + 3,000(p/a,7%,4) + 1,100(p/f,7%,4)

pw = -8,000 + 3,000 * 3.387 + 1,100 * 0.7629

pw = -8,000 + 10,161 + 839.19

pw = 3,000.19

we will choose alternative b because it has higher present worth.

2) excel sheet pasted here.

cash flow are found out by adding everything in the respective years as for year 0 it will be initial cost + annual benefits + annual expenses + salvage value and so on till the ending year.

present value in excel is found out by using the npv function:

=npv(rate,cash flows from year 1 to ending year) + cash flow in year 0

npv of alternative b =npv(7%,3000,3000,3000,4100)+(-8,000)

alternative a year 0 1 2 3 4 5 6 initial cost -12,000 annual benefits 5,500 5,500 5,500 5,500 5,500 5,500 annual expenses -2,500 -2,500 -2,500 -2,500 -2,500 -2,500 salvage value 1,000 cash flows -12,000 3,000 3,000 3,000 3,000 3,000 4,000 present value 2,966 alternative b year 0 1 2 3 4 initial cost -8,000 annual benefits 5,200 5,200 5,200 5,200 annual expenses -2,200 -2,200 -2,200 -2,200 salvage value 1,100 cash flows -8,000 3,000 3,000 3,000 4,100 present value 3,001

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