Question

1. [7pts] A machine is to be purchased for $300,000, used for 8 years, and then sold for an estimated salvage value (in current or constant dollars) of $50,000. MARR=18% and inflation for this type of equipment is expected to average 2% during this time. Determine the annual capitalized recovery (CR) cost for the machine.

Answer 1

Investment Required at time 0, I = $300,000

Salvage Value after 8 years, S = $50,000

Time , n = 8 years

Minimum Acceptable Rate of Return, MARR = 18%

Inflation, f = 2%

Inflation adjusted MARR, i = MARR + f + (MARR)*(f) = 20.36%

Annual Capital Recovery Cost, ACRC = I(A/P, i, n) - S(A/F, i, n)

Discounting Factors:

$(A/P, i, n) = \frac{i(1+i)^{n}}{(1+i)^{n}-1}$

$(A/F, i, n) = \frac{i}{(1 + i)^{n} - 1}$

ACRC = $300,000 * (0.2634) - $50,000*(0.0598)

ACRC = $79,023.05 - $2990.509

ACRC = $76,032.55