Question

Your firm is thinking about investing ​$250 comma 000 in the overhaul of a manufacturing cell in a lean environment. Revenues are expected to be ​$36 comma 000 in year one and then increasing by ​$12 comma 000 more each year thereafter. Relevant expenses will be ​$15 comma 000 in year one and will increase by ​$7 comma 500 per year until the end of the​ cell's nine​-year life. Salvage recovery at the end of year nine is estimated to be ​$8 comma 000. What is the annual equivalent worth of the manufacturing cell if the MARR is 15​% per​ year?

Answer 1

Answer:

Equivalent Annual Cost -$ 4,833.000

Explanation:

The equivalent annual cost is the equivalent cost per year to all the cost associate with the project. In this case, the manufacturing cell's overhaul

F0 250,000

cash flow per year:

36,000 revenue + 12,000 per year

cost outflow per year:

15,000 expenses + 7,500 per year

net:

21,000 inflow per year + 4,500 inflow per year

present value of an arithmetics annuity:

$(C+\frac{d}{r} + n.d) \frac{1-(1+r)^{-time} }{rate}-\frac{n.d}{r}$

C: 21,000

d:   4,500

r = Minimun accepter rate of return: 15%

time 9 years:

$(C+\frac{d}{r} + n.d) \frac{1-(1+r)^{-time} }{rate}-\frac{n.d}{r}$

$166,599.93

present value of the salvage value:

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity  8,000.00

time  9.00

rate  0.15000

$\frac{8000}{(1 + 0.15)^{9} } = PV$  

PV   2,274.10

present worth:

166,599.93 + 2,274.10 - 250,000 = -81,126

Now, to know the equivalent annual cost we calcualte the PMT of the present worth:

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV -81,126

time 9

rate 0.15

$-81125.98 \div \frac{1-(1+0.15)^{-9} }{0.15} = C$

C -$ 4,833.000