Homework SourseA granary has two options for a conveyor used in the manufac
A granary has two options for a conveyor used in the manufacture of grain for transporting, filling, or emptying. One conveyor can be purchased and installed for $100,000 with $3,500 salvage value after 16 years. The other can be purchased and installed for $105,000 with $5,000 salvage value after 16 years. Operation and maintenance for each is expected to be $17,000 and $15,500 per year, respectively. The granary uses MACRS-GDS depreciation, has a marginal tax rate of 40%, and has a MARR of 9% after taxes.
Determine which alternative is less costly, based upon comparison of after-tax annual worth.
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Solution
The following assumption are taken to calculate NPV of conveyor
the cost of investment is $100,000
the depreciation taken is MACRS 15 year convention
the annual cost or cash outflow is $ 17,000
the tax rate is 40%
the cost of capital is 9%
the salvage value is $3,500
the net present value is difference between present value of cash inflow and cash outflow .
the calculation of NPV of conveyor cost $100,000
The following assumption are taken to calculate NPV of conveyor
the cost of investment is $105,000
the depreciation taken is MACRS 15 year convention
the annual cost or cash outflow is $ 15,500
the tax rate is 40%
the cost of capital is 9%
the salvage value is $5000
the net present value is difference between present value of cash inflow and cash outflow .
the calculation of NPV of conveyor cost $105,000
The total cost when equipment is purchases at $100,000 at 9% cost of capital for 16 years and salvage value of $3,500 is $240,432
The total cost when equipment is purchases at $105,000 at 9% cost of capital for 16 years and salvage value of $5,000 is $227,585 hence it is less costly
| NPV calculation | |||||||||||
| year | equipment cost | dep rate % | Depreciation of new asset MACRS 15 year schedule | operation and maintenance cost | savings before tax | tax @.40 | savings after tax | add -: deprecition | annual cash inflow | pV factor @12% | cash inflow at present value |
| (100,000) | 1 | - | |||||||||
| 1 | 5 | (5,000) | (17,000) | (22,000) | - | (22,000) | 5,000 | (17,000) | 0.91743 | (15,596.33) | |
| 2 | 9.5 | (9,500) | (17,000) | (26,500) | - | (26,500) | 9,500 | (17,000) | 0.84168 | (14,308.56) | |
| 3 | 8.55 | (8,550) | (17,000) | (25,550) | - | (25,550) | 8,550 | (17,000) | 0.77218 | (13,127.12) | |
| 4 | 7.7 | (7,700) | (17,000) | (24,700) | - | (24,700) | 7,700 | (17,000) | 0.70843 | (12,043.23) | |
| 5 | 6.93 | (6,930) | (17,000) | (23,930) | - | (23,930) | 6,930 | (17,000) | 0.64993 | (11,048.83) | |
| 6 | 6.23 | (6,230) | (17,000) | (23,230) | - | (23,230) | 6,230 | (17,000) | 0.59627 | (10,136.54) | |
| 7 | 5.9 | (5,900) | (17,000) | (22,900) | - | (22,900) | 5,900 | (17,000) | 0.54703 | (9,299.58) | |
| 8 | 5.9 | (5,900) | (17,000) | (22,900) | - | (22,900) | 5,900 | (17,000) | 0.50187 | (8,531.73) | |
| 9 | 5.91 | (5,910) | (17,000) | (22,910) | - | (22,910) | 5,910 | (17,000) | 0.46043 | (7,827.27) | |
| 10 | 5.9 | (5,900) | (17,000) | (22,900) | - | (22,900) | 5,900 | (17,000) | 0.42241 | (7,180.98) | |
| 11 | 5.91 | (5,910) | (17,000) | (22,910) | - | (22,910) | 5,910 | (17,000) | 0.38753 | (6,588.06) | |
| 12 | 5.9 | (5,900) | (17,000) | (22,900) | - | (22,900) | 5,900 | (17,000) | 0.35553 | (6,044.09) | |
| 13 | 5.91 | (5,910) | (17,000) | (22,910) | - | (22,910) | 5,910 | (17,000) | 0.32618 | (5,545.04) | |
| 14 | 5.9 | (5,900) | (17,000) | (22,900) | - | (22,900) | 5,900 | (17,000) | 0.29925 | (5,087.19) | |
| 15 | 5.91 | (5,910) | (17,000) | (22,910) | - | (22,910) | 5,910 | (17,000) | 0.27454 | (4,667.15) | |
| 16 | 2.95 | (2,950) | (17,000) | (19,950) | - | (19,950) | 2,950 | (17,000) | 0.25187 | (4,281.79) | |
| 100 | -100000 | 100000 | |||||||||
| Total value of cash inflow at PV | (141,313) | ||||||||||
| Present value of cash inflows for 16 years | (141,313) | ||||||||||
| present value of scrap value at end of 16 years (3500 x 0.25187) | 882 | ||||||||||
| present value of total cash inflow | (140,432) | ||||||||||
| less | |||||||||||
| present value of cash outflow | |||||||||||
| equipment | 100000 | ||||||||||
| Total cash outflow | 100000 | ||||||||||
| Net NPV | (240,432) |
