Determining NPV including MACRS tax depreciation

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marie27

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A project requires an initial investment of $100,000 and is expected to produce a cash inflow before tax of $26,000 per year for five years. Company A has substantial accumulated tax losses and is unlikely to pay taxes in the foreseeable future. Company B pays corporate taxes at a rate of 35 percent and can depreciate the investment for tax
purposes using the five-year MACRS tax depreciation schedule. Suppose the opportunity cost of capital is 8 percent. Ignore inflation.

a. Calculate project NPV for each company.

PV = (26000 / 1.08) + (26000 / 1.08)^2 + (26000 / 1.08)^3 + (26000 / 1.08)^4 + (26000 / 1.08)^5 = 24074.07 + 22290.81 + 20639.64 + 19110.78 + 17695.16 = 103810.46
NPV = -100000 + 103810.46 = 3810.46
Company A: $3810.46


***This is where I need some help. I am quite confused as to what the next step is.
Am I totally missing something with this statement from the text: "Tax shield = depreciation x tax rate=  1,583 x .35 =554, or $554,000. The present value of the tax shields ($554,000 for six years) is $1,842,000 at a 20 percent discount rate.5.... I cannot figure out how the present value equals $1,842,000, which is partially the reason I feel I cannot solve the rest of this problem.

Cash Inflow: 26000 * 5 = 130000

Depreciation:
Year One Depreciation = $100,000 x 0.2000 = $20000
Year Two Depreciation = $100,000 x 0.3200 = $32000
Year Three Depreciation = $100,000 x 0.1920 = $19200
Year Four Depreciation = $100,000 x 0.1152 = $11520
Year Five Depreciation = $100,000 x 0.1152 = $11520
Year Six Depreciation = $100,000 x 0.0576 = $5760

Taxable income:
Year 1: 26000 – 20000 = 6000
Year 2: 26000 – 32000 = -6000
Year 3: 26000 – 19200 = 6800
Year 4: 26000 – 11520 = 14480
Year 5: 26000 – 11520 = 14480
Year 6: 0 – 5760 = 5760

Taxes:
Year 1: 26000 – 20000 = 6000 * .35 = 2100
Year 2: 26000 – 32000 = -6000 * .35 = -2100
Year 3: 26000 – 19200 = 6800 * .35 = 2380
Year 4: 26000 – 11520 = 14480 * .35 = 5068
Year 5: 26000 – 11520 = 14480 * .35 = 5068
Year 6: 0 – 5760 = 5760 * .35 = 2016

Cash Flow:
Year 1: 26000 –2100 = 23900
Year 2: 26000 – (-2100) or 26000 + 2100 = 28100
Year 3: 26000 – 2380 = 23620
Year 4: 26000 – 5068 = 20932
Year 5: 26000 – 5068 = 20932
Year 6: 0 – 2016 = 2016
Total cash flow: 119140
-100000 + 119140 = 9531.20

PV = (23900 / 1.08) + (28100 / 1.08)^2 + (23620 / 1.08)^3 + (20932 / 1.08)^4 + (20932 / 1.08)^5 + (20932 / 1.08)^6 = 22129.63 + 24091.22 + 18750.32 + 15385.64 + 13604.36 + 13190.71 = 107151.88
NPV = -100000 + 107151.88 + ???

Thanks
 
marie27 said:
A project requires an initial investment of $100,000 and is expected to produce a cash inflow before tax of $26,000 per year for five years. Company A has substantial accumulated tax losses and is unlikely to pay taxes in the foreseeable future. Company B pays corporate taxes at a rate of 35 percent and can depreciate the investment for tax
purposes using the five-year MACRS tax depreciation schedule. Suppose the opportunity cost of capital is 8 percent. Ignore inflation.

a. Calculate project NPV for each company.

PV = (26000 / 1.08) + (26000 / 1.08)^2 + (26000 / 1.08)^3 + (26000 / 1.08)^4 + (26000 / 1.08)^5 = 24074.07 + 22290.81 + 20639.64 + 19110.78 + 17695.16 = 103810.46
NPV = -100000 + 103810.46 = 3810.46
Company A: $3810.46


***This is where I need some help. I am quite confused as to what the next step is.
Am I totally missing something with this statement from the text: "Tax shield = depreciation x tax rate=  1,583 x .35 =554, or $554,000. The present value of the tax shields ($554,000 for six years) is $1,842,000 at a 20 percent discount rate.5.... I cannot figure out how the present value equals $1,842,000, which is partially the reason I feel I cannot solve the rest of this problem.

Cash Inflow: 26000 * 5 = 130000

Depreciation:
Year One Depreciation = $100,000 x 0.2000 = $20000
Year Two Depreciation = $100,000 x 0.3200 = $32000
Year Three Depreciation = $100,000 x 0.1920 = $19200
Year Four Depreciation = $100,000 x 0.1152 = $11520
Year Five Depreciation = $100,000 x 0.1152 = $11520
Year Six Depreciation = $100,000 x 0.0576 = $5760

Taxable income:
Year 1: 26000 – 20000 = 6000
Year 2: 26000 – 32000 = -6000
Year 3: 26000 – 19200 = 6800
Year 4: 26000 – 11520 = 14480
Year 5: 26000 – 11520 = 14480
Year 6: 0 – 5760 = 5760

Taxes:
Year 1: 26000 – 20000 = 6000 * .35 = 2100
Year 2: 26000 – 32000 = -6000 * .35 = -2100
Year 3: 26000 – 19200 = 6800 * .35 = 2380
Year 4: 26000 – 11520 = 14480 * .35 = 5068
Year 5: 26000 – 11520 = 14480 * .35 = 5068
Year 6: 0 – 5760 = 5760 * .35 = 2016

Cash Flow:
Year 1: 26000 –2100 = 23900
Year 2: 26000 – (-2100) or 26000 + 2100 = 28100
Year 3: 26000 – 2380 = 23620
Year 4: 26000 – 5068 = 20932
Year 5: 26000 – 5068 = 20932
Year 6: 0 – 2016 = 2016
Total cash flow: 119140
-100000 + 119140 = 9531.20

PV = (23900 / 1.08) + (28100 / 1.08)^2 + (23620 / 1.08)^3 + (20932 / 1.08)^4 + (20932 / 1.08)^5 + (20932 / 1.08)^6 = 22129.63 + 24091.22 + 18750.32 + 15385.64 + 13604.36 + 13190.71 = 107151.88
NPV = -100000 + 107151.88 + ???

Thanks
Click to expand...
No idea what "statement from text means" : hard to "read", plus talks in millions !

Your present value calculations are ok, except:
> PV = (23900/ 1.08) + (28100/ 1.08)^2 + (23620/ 1.08)^3 + (20932/ 1.08)^4 + (20932/ 1.08)^5 + (20932/ 1.08)^6
6th one should be 2016 / 1.08^6
 
No idea what "statement from text means" : hard to "read", plus talks in millions !--- This means that I copied it directly out of the textbook for interpretation. I don't understand how the author of the book came to the present value of $1,842,000.

Sorry it is difficult to read. Maybe this will be helpful, I tried to attach from excel but it keeps saying, "extension not allowed"...

0 1 2 3 4 5 6
Investment 100,000
Cash Inflow 26,000 26,000 26,000 26,000 26,000
Depreciation 20,000 32,000 19,200 11,520 11,520 5,760
Taxable Income 6,000 -6,000 6,800 14,480 14,480 -5,760
Tax 2,100 -2,100 2,380 5,068 5,068 -2,016
Cash Flow -100,000 23,900 28,100 23,620 20,932 20,932 2,016
NPV = ???


Thanks for the correction on the PV. With the correction you provided my new PV is 82991.6, however I am still unsure how to obtain NPV including the MACRS tax depreciation.
 
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