Question

cost for machine tool are expected to be 1000$ at the end of the first year of the machines life and increase 100$/year thereafter. The machine tools expected like is 15 years. The firms MARR is 10%/year. What is the annual worth of the maintenance cost? Draw the cash flow diagram to help solve. HINT End of year one tools are expected to be 1000$, and then increases 100$ thereafter up to 15 years. Show ALL WORK and EQUATIONS, and explain work. This is a intrest formulas for continuous compounding and discrete cash flow type of problem.

Answer 1

ANSWER:

Cash flow diagram couldn't be uploaded due to technical reasons and so i am drawing the cash flow table.

year	cash flow ($100 increase from year 2 onwards )
1	1,000
2	1,100
3	1,200
4	1,300
5	1,400
6	1,500
7	1,600
8	1,700
9	1,800
10	1,900
11	2,000
12	2,100
13	2,200
14	2,300
15	2,400

i = 10% and n = 15

we will find the present worth and then the annual worth.

pw = cost in 1st year(p/a,i,n) + increase in cost per year(p/g,i,n)

pw = 1,000(p/a,10%,15) + 100(p/g,10%,15)

pw = 1,000 * 7.606 + 100 * 40.152

pw = 7,606 + 4,015.2

pw = 11,621.2

aw = pw(a/p,i,n)

aw = 11,621.2(a/p,10%,15)

aw = 11,621.2 * 0.1315

aw = 1,528.1878

so the annual worth of the maintenance cost is $1,528.1878