Question

Koza Automotive purchased a CNC machine for $20,000 in year 0. The useful life of the machine is 10 years, at the end of which the machine is estimated to have a salvage value of zero. The machine generates net annual revenues of $6,000. The annual operating and maintenance expenses are estimated to be $1,000. If their MARR is 15%, how many years will it take before this machine becomes profitable?

Answer 1

let it takes n yrs to becomem profitable, then as per given condition

(6000 - 1000)*(P/A,15%,n) = 20000

5000*(P/A,15%,n) = 20000

(P/A,15%,n) = 20000 / 5000 = 4

((1 + 0.15)^n-1)/(0.15*(1 + 0.15)^n) = 4

((1.15)^n-1)/(0.15*(1.15)^n) = 4

(1.15)^n - 1 = 4*(0.15*(1.15)^n)

(1.15)^n - 1 = 0.6*(1.15)^n

(1.15)^n = 1 / (1-0.6) = 2.5

taking log both sides

n = log 2.5 / log 1.15 = 6.5560 yrs ~ 6.56 yrs