A piece of equipment costs Cv to purchase new. It must be replaced every N years
ID: 2384543 • Letter: A
Question
A piece of equipment costs Cv to purchase new. It must be replaced every N years, at a cost gfCR. The capitalized equipment cost, CC, is defined as Cv + P, where P is the money that must be invested now, at an annual effective compound interest rate i, so that, N years from now, the investment is worth CR + P. Derive an equation for the capitalized cost when the interest rate is compounded annually. Your company needs to purchase a new heat exchanger. There are two options: an inexpensive heat exchanger with a short lifetime and no scrap value, and a more expensive heat exchanger with a longer lifetime that can be sold for scrap. Your company expects to earn al5% effective interest rate on all of its investments.Explanation / Answer
Answer to 12
Current cost of the new Equipment = C(v)
Period after which the equipment needs to be replaced = N
Cost of replacement after N years = C(g)
Effective compound interest rate = i
Replacement cost C(g) can be calculated using the formula
C(g) = C(v)*(1+r)^N - Scrap Value (if any) --- A
Capitalized cost of Equipment CC = C(v) + P
where p is the present value of investment which grows to C(g)
Present value of the investment can be calculated using the formula
P = C(g)/(1+r)^n
Therefore Capitalized cost of equiment is
CC = C(v)+P = C(v) + C(g)/(1+r)^n
Substituting the value of C(g) from A above
CC = C(v) + {((C(v)*(1+r)^N - scrap value)/(1+r)^N}
Answer to (13)
Heat Exchange A
Purchase price = 20000
Life Time N = 6 years
Scrap Value = 0
Effective rate of interst i = 15% or 0.15
Replacement cost C(r) = Purchase Price * (1+r)^n
C(r) = 20000*(1+0.15)^6 = 20000*2.31306 = 46261.22
Contribution to Sinking Fund
P = 46261.22 / (1+0.15)^6 = 46261.22/2.31306 = 20,000
Capitalized Cost = C(v) + P = 20000 + 20000 = $ 40,000
Heat Exchanger B
Purchase Price = 35000
Life Time = 10 years
Scrap Value = 4000
Replacement Cost C(g)= C(v) * (1+r)^N - Scrap Value = 35000 * (1.15)^10 - 4000
Replcement cost C(g) = 35000 * 4.0455577 - 4000 = 137,594.52
Present Value of annual investment P = C(g) / (1+r)^n = 137594.52 /(1.15)^10
= 137594.52/4.0455577 = 34,011.26
Capitalized Cost = C(v) + P = 35000 + 34011.26 = $ 69011.26
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