Your firm is contemplating the purchase of a new $1,461,500 computer-based order
ID: 2740732 • Letter: Y
Question
Your firm is contemplating the purchase of a new $1,461,500 computer-based order entry system. The system will be depreciated straight-line to zero over its 5-year life. It will be worth $142,200 at the end of that time. You will be able to reduce working capital by $197,500 (this is a one-time reduction). The tax rate is 30 percent and your required return on the project is 21 percent and your pretax cost savings are $637,850 per year.
1. What is the NPV of this project?
2. What is the NPV if the pretax cost savings are $459,250 per year?
3. 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 $1,461,500 computer-based order entry system. The system will be depreciated straight-line to zero over its 5-year life. It will be worth $142,200 at the end of that time. You will be able to reduce working capital by $197,500 (this is a one-time reduction). The tax rate is 30 percent and your required return on the project is 21 percent and your pretax cost savings are $637,850 per year.
1. What is the NPV of this project?
2. What is the NPV if the pretax cost savings are $459,250 per year?
3. At what level of pretax cost savings would you be indifferent between accepting the project and not accepting it?
Explanation / Answer
1. NPV of the project:
Annual depreciation expense = $ 1,461,500 / 5 = $ 292,300
Present value of cash outflows = $ ( 1,461,500 - 197,500) = $ 1,264,000
Annual cash inflows = $ 637,850 x 0.70 + $ 292,300 = $ 738,795
Present value of cash inflows = $ 738,795 x PVIFA21%, 5years + ( 142,200 x 0.70) x PVIF21%, 5th year
= $ 738,795 x 2.926 + $ 99,540 x 0.386 = $ ( 2,161,714.17 + 38,422.44) = $ 2,200,136.61
NPV = $ ( 2,200,136.61 - 1,264,000) = $ 936,136.61
2. If the pretax cost savings are $ 459,250 , annual cash inflows = $ 459,250 x 0.70 + $ 292,300 = $ 613,775
Present value of cash inflows = $ 613,775 x 2.926 + $ 99,540 x 0.386 = $ ( 1,795,905.65 + 38,422.44) = $ 1,834,328.09
NPV = $ ( 1,834,328.09 - 1,264,000) = $ 570,328.09
3. At NPV =0
Present value of cash outflows = $ 1,264,000
Let the pretax cost savings be S
(0.70S + 292,300) x 2.926 + 38422.44 = 1,264,000
or S = 180,797
At a pretax cost savings level,of $ 180,797, one would be indifferent between accepting and not accepting the project.
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