Question

A company had costs this year for air conditioning units of $10,000. The company expects these costs to decrease steadily over the next 5 years. The cost in year two and each year thereafter decreases by $650. (a) Draw a cash flow diagram of this scenario. (b) What is the equivalent annual cost for a five-year period, at an interest rate of 10% per year?

Answer #1

Equivalent Annual Cost = NPV × r / 1 − (1 + r)^{-n}
Where *r* is the periodic discount rate, which equals annual
percentage rate divided by number of periods per year, and
*n* is the number of years.

cf1= 10000$ cf2= 9350$ cf3= 8700$ cf4= 8050$ cf5= 7400$ total=43500$

NPV = | CF_{1} |
+ | CF_{2} |
+....+ | CF_{n} |
− I |

(1 + r)^{1} |
(1 + r)^{2} |
(1 + r)^{n} |

NPV= 10000/(1+10)^{1} + 9350/ (1+10)^{2} +
8700/(1+10)^{3} + 8050/(1+10)^{4} +
7400/(1+10)^{5} = 909.09+77.27+6.536+0.549+0.0459

NPV=993.4909$

total present value= 993.4909$

Now that we have the net present value, we must convert it to annual terms which we can do by treating the net present value obtained as the present value of an ordinary annuity of duration equal to the asset life.

EAC= 993.4909x10 / 1- (1+10)^{5} = -160001709.445$

Equivalent Annual Cost = -160001709.445$

(1)^{10000}-_{650}-------(2)^{9350}-_{650}-------(3)^{8700}-_{650}-------(4)^{8050}-_{650}---------(5)^{7400}

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