Question

You can continue to use your less efficient old machine with an initial cost zero and...

You can continue to use your less efficient old machine with an initial cost zero and a maintenance cost of $8,960 annually for the next five years. Alternatively, you can purchase a more efficient new machine for $12,000 initial cost today, plus $5,000 annual maintenance with the same 5 years life. At a cost of capital of 15%, you should:

  • A. Buy the new machine and save $380 in equivalent annual annuity.
  • B. Keep the old machine and save $380 in equivalent annual annuity.
  • C. Keep the old machine and save $600 in equivalent annual annuity.
  • D. Buy the new machine and save $480 in equivalent annual annuity.
  • E. Keep the old machine and save $480 in equivalent annual annuity.
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Answer #1

EAA of Old Machine:

Equivalent Annual Annuity for Old machine = $8,960

EAA of New Machine:

P = Initial Investment = $12,000

Annual Maintenance Cost = $5,000

n = 5 years

r = cost of capital = 15%

EAA of New Machine = [r * P] / [1 - (1+r)^-n] + Annual Maintenance Cost

= [15% * $12,000] / [1 - (1+15%)^-5] + $5,000

= [$1,800 / 0.502823265] + $5,000

= $3,579.78663 + $5,000

= $8,579.78663

Equivalent Annual Annuity for New machine is $8,580

Annual Saving = EAA of Old Machine - EAA of New Machine = $8,960 - $8,580 = $380

EAA of New Machine is lower than EAA of Old Machine

Buy the New machine and save $380 in Equivalent Annual Annuity

Option A is correct

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