an automaker is buying some special tools for $100,000. The tools are being depr

Question

an automaker is buying some special tools for $100,000. The tools are being depreciated by doube declining balance depreciation using a 4-year depreciable life and a $6250 salvage value. It is expected the tools will actually be kept in service for 6 years and then sold for $6250. The before-tax benifit of owning the tools is as follows:

Year               Befote-tax cash flow

1                         $30,000

2                          30,000

3                          35,000

4                          40,000

5                         10,000

6                         10,000

                           6,250 selling price

compute the after-tax rate of return for this investment situation, assuming a 46% incremental tax rate.

Note: the correct answer should come out After Tax (AT) IRR =11.6%. Show me how to get that step-by-step please!

Explanation / Answer

Hi,

Please find the detailed answer as follows:

Step 1: Calculate Depreciation for Each Year (Upto Year 4):

Depreciation Per Straight Line Method = (Cost - Salvage Value)/Estimated Life*100 = (100000 - 6250)/4 = 23437.50

Depreciation Rate as Per Straight Line Method = Depreciation Per Straight Line Method/(Cost - Salvage Value)*100 = 25%

Depreciation Rate as per Double Declining Method = Depreciation Rate as Per Straight Line Method*2 = 50%

Depreciation (Year 1) = 100000*50% = 50000

Depreciation (Year 2) = (100000 - 50000)*50% = 25000

Depreciation (Year 3) = (100000 - 50000 - 25000)*50% = 12500

Depreciation (Year 4) = (1000000 - 50000 - 25000 - 12500)*50% = 6250

Step 2: Calculate Annual Net Cash Flows:

Step 3: Calculate IRR:

To calculate IRR, you need to put the value of NPV as 0 and solve for r as follows:

NPV = 0 = -100000 + 39200/(1+r)^1 + 27700/(1+r)^2 + 24650/(1+r)^3 + 24475/(1+r)^4 + 5400/(1+r)^5 + 6250/(1+r)^5

Solving for r (with the use of EXCEL/FINANCIAL CALCULATOR), we get IRR as 11.61% or 11.6%

Answer is 11.61% or 11.6%.

Thanks.

Year Before Tax Cash Flow Depreciation Earnings Before Tax Tax Earnings After Tax Depreciation Annual Cash Inflows
(EAT + Depreciation) Year 1 30000 50000 -20000 -9200 -10800 50000 39200 Year 2 30000 25000 5000 2300 2700 25000 27700 Year 3 35000 12500 22500 10350 12150 12500 24650 Year 4 40000 6250 33750 15525 18225 6250 24475 Year 5 10000 0 10000 4600 5400 0 5400 Year 6 10000 0 10000 4600 5400 0 5400

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