ABC company is considering the introduction of a new product line. The initial i

Question

ABC company is considering the introduction of a new product line. The initial investment required for this project is $400,000 , and annual maintenance costs are anticipated to be $55,000 . Annual operating costs will be directly proportional to the level of production at $11.5 per unit, and each unit of product can be sold for $42 . If the MARR is 20 % and the project has a life of five years, what is the minimum annual production level for which this project is economically viable?   (Enter your answer as a number rounded to the nearest whole number.)

Explanation / Answer

for economic viability of this project, we need to check the prooductiion level at which PV of future cash flow = inital cost i.e NPV of this project will be zero, that will be the minimum viable level of production

Let minimum viable level of production = x unit

annual profit = 42x-11.5x-55000 = 30.5x-55,000

let annual profit = 30.5x-55,000 = $y

MARR = 20%

time = 5 years

PVIFA is present valuee interest factor of annuity

PVIFA(r%,n) = ([1-(1+r)^-n]/r

PVIFA(20,5) = 2.9906

NPV = -400,000+y*PVIFA(20,5)

NPV = -400,000+y*2.9906 = 0 ( for minimum viable level)

solving for y

y = 400,000/2.9906 = $133752.424263

y = 30.5x-55,000 = 133752.424263

x =  (133752.424263+55,000 )/30.5 = 6188.60 unit

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