Question
In: Finance
you are considering investing in a project that increases annual costs by $25,000 per year over...
you
are considering investing in a project that increases annual costs
by $25,000 per year over the project's 5 year life. The project has
an initial cost of $500,000 and will be deprciated straight-line
over 5 years. Assume a 32% tax bracket and a discount rate of 11%.
Suppose the equipment is sold at the end of year 5 for $300,000,
pretax. What is the NPV?
Solutions
Expert Solution
| Year | 0 | 1 | 2 | 3 | 4 | 5 | ||
| Cost of project | $ -5,00,000 | |||||||
| Annual cost | $ -25,000.00 | $ -25,000.00 | $ -25,000.00 | $ -25,000.00 | $ -25,000.00 | |||
| Depreciation expense | $ -1,00,000.00 | $ -1,00,000.00 | $ -1,00,000.00 | $ -1,00,000.00 | $ -1,00,000.00 | |||
| Pretax income | $ -1,25,000.00 | $ -1,25,000.00 | $ -1,25,000.00 | $ -1,25,000.00 | $ -1,25,000.00 | |||
| Tax expense | $ 40,000.00 | $ 40,000.00 | $ 40,000.00 | $ 40,000.00 | $ 40,000.00 | |||
| Operating income | $ -85,000.00 | $ -85,000.00 | $ -85,000.00 | $ -85,000.00 | $ -85,000.00 | |||
| Depreciation expense | $ 1,00,000.00 | $ 1,00,000.00 | $ 1,00,000.00 | $ 1,00,000.00 | $ 1,00,000.00 | |||
| Operating cash flow | $ 15,000.00 | $ 15,000.00 | $ 15,000.00 | $ 15,000.00 | $ 15,000.00 | |||
| After tax sale of asset | $ 2,04,000.00 | |||||||
| Cash flow | $ -5,00,000.00 | $ 15,000.00 | $ 15,000.00 | $ 15,000.00 | $ 15,000.00 | $ 2,19,000.00 | ||
| Discount factor | 1.00000 | 0.90090 | 0.81162 | 0.73119 | 0.65873 | 0.59345 | ||
| Present value | $ -5,00,000.00 | $ 13,513.51 | $ 12,174.34 | $ 10,967.87 | $ 9,880.96 | $ 1,29,965.84 | ||
| Net Present value (NPV) | $ -3,23,497.47 | |||||||
| Working: | ||||||||
| Straight line depreciation | = | (Cost - Salvage Value)/Useful Life | ||||||
| = | (500000-0)/5 | |||||||
| = | $ 1,00,000.00 | |||||||
| After tax sale of system | = | Sales -((Sales - Book Value)*Tax Rate) | * | (1- Tax Rate) | ||||
| = | 300000-((300000-0)*32%) | |||||||
| = | $ 2,04,000.00 | |||||||
| Discount factor of Year: | ||||||||
| 0 | = | 1.11^-0 | = | 1.0000 | ||||
| 1 | = | 1.11^-1 | = | 0.9009 | ||||
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