Solutions To Lecture 4
Q
Suppose we are thinking about replacing an old computer with a new one. The old one cost us 650,000; the new one will cost 780,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about 140,000 after five years. The old computer is being depreciated at a rate of 130,000 per year. It will be completely written off in three years. If we do not replace it now, we will have to replace it in two years. We can sell it now for 230,000; in two years it will probably be worth 90,000. The new machine will save us 125,000 per year in operating costs. The tax rate is 38% and the discount rate is 14%. Suppose we recognize that if we do not replace the computer now, we will be replacing it in two years. Should we replace now or should we wait?
A
Since the two computers have unequal lives, the correct method to analyze the decision is the EAC. We will begin with the EAC of the new computer. Using the depreciation tax shield approach, the OCF for the new computer system is:
OCF = ($125,000)(1 – .38) + ($780,000 / 5)(.38) = $136,780
Aftertax salvage value = $140,000(1 – .38) = $86,800
Now we can calculate the NPV of the new computer as:
NPV = –$780,000 + $136,780(PVIFA14%,5) + $86,800 / 1.145= –$265,341.99
And the EAC of the new computer is:
EAC = – $265,341.99 / (PVIFA14%,5) = –$77,289.75
PVIFA14%,5 is the present value of a 5-year annuity of 1$ each year when discount rate is 14%.
Analyzing the old computer, the only OCF is the depreciation tax shield, so: OCF = $130,000(.38) = $49,400 The initial cost of the old computer is a little trickier. You might assume that since we already own the old computer there is no initial cost, but we can sell the old computer, so there is an opportunity cost. We need to account for this opportunity cost. To do so, we will calculate the aftertax salvage value of the old computer today. We need the book value of the old computer to do so. We can assume the book value is
Suppose we are thinking about replacing an old computer with a new one. The old one cost us 650,000; the new one will cost 780,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about 140,000 after five years. The old computer is being depreciated at a rate of 130,000 per year. It will be completely written off in three years. If we do not replace it now, we will have to replace it in two years. We can sell it now for 230,000; in two years it will probably be worth 90,000. The new machine will save us 125,000 per year in operating costs. The tax rate is 38% and the discount rate is 14%. Suppose we recognize that if we do not replace the computer now, we will be replacing it in two years. Should we replace now or should we wait?
A
Since the two computers have unequal lives, the correct method to analyze the decision is the EAC. We will begin with the EAC of the new computer. Using the depreciation tax shield approach, the OCF for the new computer system is:
OCF = ($125,000)(1 – .38) + ($780,000 / 5)(.38) = $136,780
Aftertax salvage value = $140,000(1 – .38) = $86,800
Now we can calculate the NPV of the new computer as:
NPV = –$780,000 + $136,780(PVIFA14%,5) + $86,800 / 1.145= –$265,341.99
And the EAC of the new computer is:
EAC = – $265,341.99 / (PVIFA14%,5) = –$77,289.75
PVIFA14%,5 is the present value of a 5-year annuity of 1$ each year when discount rate is 14%.
Analyzing the old computer, the only OCF is the depreciation tax shield, so: OCF = $130,000(.38) = $49,400 The initial cost of the old computer is a little trickier. You might assume that since we already own the old computer there is no initial cost, but we can sell the old computer, so there is an opportunity cost. We need to account for this opportunity cost. To do so, we will calculate the aftertax salvage value of the old computer today. We need the book value of the old computer to do so. We can assume the book value is