Gemini, LLC, invested $1 million in a state-of-the-art information system that p

Question

Gemini, LLC, invested $1 million in a state-of-the-art information system that promises to reduce processing costs for its purchasing activities by $120,000 per year for the next 10 years. The company will scrap its old information system and will receive no money as a consequence. The new system will be depreciated over 10 years at a rate of $100,000 per year. Gemini's tax rate is 30 percent, and the company has a 7 percent after-tax cost of capital.

Required:

What is the after-tax net present value of Gemini's new information system? Use the time value of money charts as needed for your calculations. If required, use a minus sign to indicate a negative net present value. Do not round intermediate amounts. Round your final answer to two decimal places.

Explanation / Answer

pre-tax cost of capital (rc):
0.07 = rc(1 -tax rate)
0.07 = rc (0.70)
rc = 0.10, or 10%

For NPV, value the "savings" produced by the investment...
With $120,000 in op costs saved per year, the company gets an additional $120k per year in NI before taxes, so they keep 120,000 * (1 - tax rate) = 84,000 after taxes
They also have a depreciation tax shield. Because depreciation is $100k per year, this reduces their tax bill by: 100,000 * 0.30 = 30,000
For a total of $114,000 net.

[You can also do that a different way. 120,000 - 100,000 =NI b/4 tax= 20,000... * 0.70 = 14,000 <NI after tax+ add backdepreciation expense(non-cash) of $100k = 114,000 ]

Now calc NPV using the 10% as the discount rate...
CF0 = ($1m)
CFs 1 - 10 = 114,000
NPV = (299,519.19) <parens indicate a negative #

Hope this helps...

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