Suppose we are thinking about replacing an old computer with a new one. The old
ID: 2756348 • Letter: S
Question
Suppose we are thinking about replacing an old computer with a new one. The old one cost us $1,240,000; the new one will cost, $1,500,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $240,000 after five years. The old computer is being depreciated at a rate of $248,000 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 $360,000; in two years, it will probably be worth $114,000. The new machine will save us $284,000 per year in operating costs. The tax rate is 40 percent, and the discount rate is 11 percent. a.1 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)) EAC New computer $ Old computer $ a.2 What is the NPV of the decision to replace the computer now? (Negative amounts 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)) NPV $
Explanation / Answer
a.1
Equivalent annual cost = (Asset price*Discount rate) / [1 - (1 + Discount rate)-Number of Periods ]
Old equipment = ($1,240,000*0.11) / [1 - (1 + 0.12)-5]
= $136,400/1-(1 + 0.59345)
= $136,400/0.40655
= $335,506
New equipment = ($1,500,000*0.11) / [1 - (1 + 0.12)-5]
= $165,000/1-(1 + 0.59345)
= $165,000/0.40655
= $405,854
Working note:
a. 2
NPV, if equipment is replaced:
First calculate the increase in cash savings:
Annual savings in operating costs by replacing the new computer = $284,000
Less: Increase in depreciation of new computer = $16,000 [($1,500,000/5 years) - $284,000]
Increase in annual savings be replacing the new computer = $268,000
Now calculate the increase in after tax savings = $268,000 * (1 - 0.40)
= $160,800
Increase in cash savings by replacing the new computer = $160,800 + $16,000
= $176,800
Present value of annual savings = $176,800*3.695897 (See working note)
= $653,435
Present value of cash inflows from sale of new computer after 5 years = $142,428 [$240,000 * 0.5934513 (See working note at 5th year)]
Cash inflows from sale of old computer = $360,000
Total present value of cash inflows = $653,435 + $142,428 + $360,000
= $1,155,863
Therefore, Net present value (NPV) = Total present value of cash inflows - Cost of new computer
= $1,155,863 - $1,500,000
= -$344,137 (Negative)
Working note:
Year PV Factor at 11% (1/1.11=) 0 1 1 0.900900901 2 0.811622433 3 0.731191381 4 0.658730974 5 0.593451328