Chapter 7: Net Prent Value and Capital Budgeting
7.3 Cash Flow Chart:
| | Year 0 | Year 1 | Year 2 | Year 3 | Year 4 |
1. | Sales revenue | 怀疑英文- | $7,000 | $7,000 | $7,000 | $7,000 |
2. viviction | Operating costs | 大量的英语- | 2,000 | 2,000 | 2,000 | 2,000 |
3. | Depreciation | 夏天怎么保养皮肤- | 2,500 | 2,500 | 2,500 | 2,500 |
4. | Income before tax [1-(2+3)] | - | 2,500 | 2,500 | 2,500 | 2,500 |
5. | Taxes at 34% | - | 850 | 850 | 850 | 850 |
英语歌曲大全6. | Net income [4-5] | 0 | 1,650 | 1,650 | 1,650 | 1,650 |
7. | Cash flow from operation [1-2-5] | 0 | 4,150 | 4,150 | 4,150 | 4,150 |
8. | Initial Investment | -$10,000 | - | - | - | - |
9. | Changes in net working capital | -200 | -50 | -50 | 100 | 200 |
10. | in the circleTotal cash flow from investment [9+10] | -10,200 | -50 | -50 | 100 | 200 |
11. | Total cash flow ranknow[7+10] | -$10,200 | $4,100 | $4,100 | $4,250 | $4,350 |
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a. Incremental Net Income [from 6]:
Year 0 0 | Year 1 $1,650 | Year 2 $1,650 | Year 3 $1,650 | Year 4 $1,650 |
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b. Incremental cash flow [from 11]:
Year 0 -$10,200 | Year 1 $4,100 | Year 2 $4,100 | 吸血鬼日记插曲Year 3 跨境电商培训班$4,250 | Year 4 $4,350 |
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c. The prent value of each cash flow is simply the amount of that cash flow discounted back from the date of payment to the prent. For example, discount the cash flow in Year 1 by 1 period (1.12), and discount the cash flow that occurs in Year 2 by 2 periods (1.12)2. Note that since the Year 0 cash flow occurs today, its prent value does not need to be adjusted.
PV(C0) = -$10,200
PV(C1) = $4,100 / (1.12) = $3,661
PV(C2) = $4,100 / (1.12)2 = $3,268
PV(C3) = $4,250 / (1.12)3 = $3,025
PV(C4) = $4,350 / (1.12)4 = $2,765
NPV = PV(C0) + PV(C1) + PV(C2) + PV(C3) + PV(C4) = $2,519
The calculations could also have been performed in a single step:
NPV = -$10,200 + $4,100 / (1.12) + $4,100 / (1.12)2 + $4,250 / (1.12)3 + $4,350 / (1.12)4
= $2,519
埃及少女 The NPV of the project is $2,519.
7.36Find the net prent value (NPV) of each option. The firm will choo the option with the higher NPV. Remember to take into account both the maintenance costs and depreciation tax shields associated with both the old and new machines. Note that the replacement machine will be bought in five years regardless of the option chon and therefore is not incremental to this decision.
Option 1
Sell old machine and purcha new machine now.
To find the cash flow from lling the old machine, consider both the sales price and the net book value of the machine. Since the firm will be lling the old machine ($2,000,000) for more than its net book value ($1,000,000), the resultant capital gain will be subject to corporate taxes.
After-Tax Salvage Value = Sale Price – TC(Sale Price – Net Book Value)
= $2,000,000 – 0.34($2,000,000 - $1,000,000)
= $1,660,000
PV(Salvage Value) = $1,660,000
The new machine is purchad today (year 0) and does not need to be discounted.
PV(New Machine) = -$3,000,000
To find the prent value of the new machine’s maintenance costs, u a five-year annuity, discounted at 12 percent. Remember to account for taxes.
PV(Maintenance Costs) = (1 – 0.34)(-$500,000)A50.12
= -$1,189,576
The firm will also recognize a depreciation tax shield from the new machine. The annual depreciation expen is $600,000 (= $3,000,000 / 5 years).
Annual Depreciation Tax Shield = TC * Depreciation per year
= 0.34 * $600,000
= $204,000
The prent value of the depreciation tax shields can be found by using a five-year annuity, discounted at 12 percent.
PV(Depreciation Tax Shield) = C1 ATr
= $204,000 A50.12
= $735,374
The new machine will be sold at the end of its economic life. Since the resale price ($500,000) is higher than the net book value ($0), the sale of the machine is subject to ca
pital gains taxes. Since the sale occurs at the end of year 5, discount the after-tax salvage value back 5 periods.
After-Tax Salvage Value = Sale Price – TC(Sale Price – Net Book Value)
= $500,000 – 0.34($500,000 – 0)
= $330,000
PV(Salvage Value) = $330,000 / (1.12)5
= $187,251
NPV(Option 1) = $1,660,000 - $3,000,000 - $1,189,576 + $735,374 + $187,251
= -$1,606,950
The net prent value (NPV) of lling the old machine and purchasing the new machine now is
-
$1,606,950.
Option 2
Sell old machine in five years and purcha new machine in five years.
The company will have to make the scheduled maintenance costs for the old machine. U a five-year annuity, discounted at 12 percent to find the prent value of the costs. Remember to account for taxes.
PV(Maintenance Costs) = (1 – 0.34)(-$400,000)A50.12
= -$951,661
The firm will continue to recognize depreciation on the old machine. The annual depreciation expen is $200,000 per year, and the firm will recognize a depreciation tax shield. The prent value of the tax shield is found by using a five-year annuity, discounted at 12 percent.
