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
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