Suppose we are thinking about replacing an old computer with a new one. The old
ID: 341465 • Letter: S
Question
Suppose we are thinking about replacing an old computer with a new one. The old one cost us $1,210,000; the new one will cost $1,470,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $210,000 after five years.
The old computer is being depreciated at a rate of $242,000 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 $330,000; in two years, it will probably be worth $111,000. The new machine will save us $281,000 per year in operating costs. The tax rate is 40 percent, and the discount rate is 11 percent.
Calculate the EAC for the old computer and the new computer. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
What is the NPV of the decision to replace the computer now? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your 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 $1,210,000; the new one will cost $1,470,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $210,000 after five years.
Explanation / Answer
a. EAC for old and New computer New computer: Cash inflow Savings in operating cost after tax=281000*(1-0.40)=168600 Depreciation tax shield=(1470000/5)*0.40=117600 Salvage value after tax=210000*(1-0.38)=130200 Cashoutflow Initial cost=1470000 NPV=-1470000+(168600+117600)*PV factor @11% for 5 years+130200*PV factor @11% for 5th year NPV=-1470000+(286200*3.6959)+(130200*0.5935)=-334960 EAC=NPV/PV factor @11% for 5 years=-334960/3.6959=-90630 Old Computer: Cash inflow Depreciation tax shield=242000*0.40=96800 After tax salvage value in 2 years=Salvage value+(Book value-Salvage value)*Tax After tax salvage value in 2 years=111000+(242000-110000)*0.40=163800 Initial cost will be the opportunity cost of selling the old computer today Book value now will be the remaining depreciation=242000*3=726000 Initial cost=330000+(726000-330000)*0.40=488400 NPV=-488400+96800*PV factor @11% for 2 years+163800*PV factor @11% for 2nd year NPV=-488400+(96800*1.7125)+(163800*0.8116)=-189690 EAC=NPV/PV factor @11% for 2 years=-189690/1.7125=-110768 Decision: Replace the old computer with new one today. b. Year New computer Old Computer Diference PV @11% Present Value 0 -1470000 -488400 -981600 1 -981600 1 286200 49400 236800 0.900901 213333.3 2 286200 49400 73000 0.811622 59248.44 163800 3 286200 0 286200 0.731191 209267 4 286200 0 286200 0.658731 188528.8 5 286200 0 416400 0.593451 247113.1 130200 Net present value -64109.3 You should not replace the old computer since NPV is negative.