Your firm is contemplating the purchase of a new $943,500 computer-based order e
ID: 2616439 • Letter: Y
Question
Your firm is contemplating the purchase of a new $943,500 computer-based order entry system. The system will be depreciated straight-line to zero over its 5-year life. It will be worth $91,800 at the end of that time. You will be able to reduce working capital by $127,500 (this is a one-time reduction). The tax rate is 31 percent and your required return on the project is 22 percent and your pretax cost savings are $425,250 per year.
At what level of pretax cost savings would you be indifferent between accepting the project and not accepting it?
Your firm is contemplating the purchase of a new $943,500 computer-based order entry system. The system will be depreciated straight-line to zero over its 5-year life. It will be worth $91,800 at the end of that time. You will be able to reduce working capital by $127,500 (this is a one-time reduction). The tax rate is 31 percent and your required return on the project is 22 percent and your pretax cost savings are $425,250 per year.
Explanation / Answer
a). First we will calculate the annual depreciation of the new equipment. It will be:
Annual depreciation charge = $943,500/5
Annual depreciation charge = $188,700
The aftertax salvage value of the equipment is:
Aftertax salvage value = $91,800(1 ? 0.31)
Aftertax salvage value = $63,342
To evaluate the project with a $425,250 cost savings, we need the OCF to compute the NPV. Using the tax shield approach, the OCF is:
OCF = $425,250(1 ? 0.31) + 0.31($188,700) = $351,919.50
NPV = ?$943,500 + 127,500 + $351,919.50(PVIFA22%,5) + [($63,342 ? 127,500) / (1.22)5]
NPV = ?$943,500 + 127,500 + ($351,919.50 * 2.8636) + [-64,158/1.225]
= $168,018.2682
b). The NPV with a $306,200 cost savings is:
OCF = $306,200(1 ? 0.31) + 0.31($188,700) = $269,775
NPV = ?$943,500 + 127,500 + $269,775(PVIFA22%,5) + [($63,342 ? 127,500) / (1.22)5]
NPV = ?$943,500 + 127,500 + ($269,775 * 2.8636) + [-64,158/1.225]
NPV = ?$67,210.72204
We would accept the project if cost savings were $425,250, and reject the project if the cost savings were $306,200.
c). The required pretax cost savings that would make us indifferent about the project is the cost savings that results in a zero NPV. The NPV of the project is:
NPV = 0 = ?$943,500 + 127,500 + OCF(PVIFA22%,5) + [($63,342 ? 127,500) / (1.22)5]
Solving for the OCF, we find the necessary OCF for zero NPV is:
0 = ?$943,500 + 127,500 + (OCF * 2.8636) + [-64,158/1.225]
OCF = $839,738.412 / 2.8636
OCF = $293,245.71
Using the tax shield approach to calculating OCF, we get:
OCF = $293,245.71 = (S ? C)(1 ? 0.31) + 0.31($188,700)
(S ? C) = $234,748.71/0.69
(S - C) = $340,215.52
The cost savings that will make us indifferent is $340,215.52
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