Answer to Question #194271 in Microeconomics for Narendra

Question

A mining corporation purchased $120,000 of

production machinery and depreciated it using 40%

bonus depreciation with the balance using 5-year

MACRS depreciation, a 5-year depreciable life, and

zero salvage value. The corporation is a profitable

one that has a 22% combined incremental tax rate.

At the end of 5 years the mining company

changed its method of operation and sold the

production machinery for $40,000. During the 5

years the machinery was used, it reduced mine

operating costs by $32,000 a year, before taxes. If

the company MARR is 12% after taxes, was the

investment in the machinery a satisfactory one?

Answer 1

Initial cost = $120000

Depreciation: Since there is 40% bonus depreciation, we need to add that to the first year MACRS to get the increased depreciation for year 1. So the first year depreciation is 40% plus the MACRS rate of 20% calculated on the differential. 

Year 2 onwards the depreciation is calculated on the differential amount based on MACRS rates. 

For the final year, the balance remaining is taken as depreciation since the asset's book value is reduced to 0. 

Based on the depreciation, we can calculate the depreciation tax shield which is just the tax component of the depreciation values. This is the amount saved due to depreciation amount reduction in the income.

Working:

Annual savings: 

We can estimate the after tax annual savings by taking the reduced operating costs and reducing the tax on these savings.

Salvage: 

We can reduce the tax on the profit from selling at salvage value to determine the after tax value of the salvage.

Calculation of NPV: 

The calculation of the NPV is self explanatory. 

The after-tax gain from the reduced costs along with the depreciation tax shield provides the total cash flow. The initial investment is reduced from these cash flows which are discounted at MARR. 

 Working;

As we can see above, the NPV is positive, indicating that the project is profitable since the value of the cash flows ( discounted at MARR) is greater than the initial investment. 

We can also test this by calculating the IRR. The IRR is determined using the RATE function in Excel and shows the internal rate of return of the cash flows. This is 14.8% which is considerably higher than the MARR, which shows that the project was profitable.  

Therefore the investment in the machinery was satisfactory.