Suppose we are thinking about replacing an old computer with a new one. The old
ID: 2383971 • Letter: S
Question
Suppose we are thinking about replacing an old computer with a new one. The old one cost us $1,250,000; the new one will cost, $1,510,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $250,000 after five years.
The old computer is being depreciated at a rate of $250,000 per year. It will be completely written off in three years. If we don’t replace it now, we will have to replace it in two years. We can sell it now for $370,000; in two years, it will probably be worth $115,000. The new machine will save us $285,000 per year in operating costs. The tax rate is 38 percent, and the discount rate is 12 percent.
Calculate the EAC for the old computer and the new computer. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))
What is the NPV of the decision to replace the computer now? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
Suppose we are thinking about replacing an old computer with a new one. The old one cost us $1,250,000; the new one will cost, $1,510,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $250,000 after five years.
Explanation / Answer
Answer:
a1. Calculation of Equivalent Annual Cost (EAC)
Equivalent Annual Cost refers to annual cost of running and maintaining an asset and it can be calculated by using the following formula;
EAC = (Asset Price x Discount Rate) / {1 - (1 + Discount Rate)-Number of Periods}
Therefore;
For Old Computer EAC = ($ 1,250,000 x 0.12) / {1 - (1+0.12)-5} = $ 150,000 / 0.43257 = $ 346,765
For New Computer EAC = ($ 1,510,000 x 0.12) / {1 - (1+0.12)-5} = $ 181,200 / 0.43257 = $ 418,892
a2. Calculation of Net Present Value (NPV) of Replacement Decision;
Annual Saving in Operating Cost by use of New Computer = $ 285,000
Less: Incremental Depreciation of New Plant = $ 1,510,000 / 5 - $ 250,000 = $ 52,000
Incremental Savings per year by use of New Computer = $ 233,000
Incremental After Tax Saving by use of New Computer = $ 233,000 (1-0.38) = $ 144,460
Incremental Cash Savings by use of New Computer = $ 144,460 + $ 52,000 = $ 196,460
Present Value of Annual Savings = $ 196,460 x Present Value Annuity Factor at 12% for 5 years = $ 196,460 x 3.604776 = $ 708,194
Add: Cash in flow from sale of old computer = $ 370,000
Add: Present Value of Cash Inflow from Sale of New Computer after 5 years = $ 250,000 x 0.567426 = $ 141,857
Therefore, Total Present Value of Cash Inflows = $ 708,194 + $ 370,000 + $ 141,857 = $ 1,220,051
NPV = $ 1,220,051 - $ 1,510,000 = - $ 289,950 (NPV = Present Value of CIF - Present Value of COF)
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