Chapter 2: Capital Budgeting Principles and Techniques



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CHAPTER 3: PROBLEMS


1. TelCo must decide whether to replace a computer system with a new model. TelCo forecasts net before tax cost savings from the new computer over five years as given below (in $000). It has a 12 percent cost of capital, a 35 percent tax rate, and uses straight line depreciation.


Year

1

2

3

4


5

($)


350

350

300


300


300



a. The new computer costs $1 million but TelCo is eligible for a 15 percent investment tax credit (ITC) in the first year. The ITC reduces Telco’s taxes by an amount equal to 15 percent of the equipment’s purchase price. In addition, the old computer can be sold for $450,000. If the old computer originally cost $1.25 million and is three years old (depreciable, not economic, life is five years), what is the net investment required in the new system? Assume that there was no ITC on the old computer and that both computers are being depreciated to a zero salvage value.
Answer: All figures are in thousands. The net investment in the machine can be found by the following equation:

Net Inv = Cost - Salv(Old) + Tax from sale of Old = 1000 - 450 - 0.35(50) = $532.50.

The book value of the old machine was $500, but it can be sold for $450, at a $50 loss. The writeoff is worth 0.35(50) = $17.50 to the company. This reduces the effective investment in the new machine.

b. Estimate the incremental operating cash flows associated with the new system.
Answer: The incremental cash flows can be found by calculating:
Incr Cash Flow = After Tax Savings + t * (Net Depreciation)
c. If the new computer’s salvage value at the end of five years is projected to be $100,000, should TelCo purchase it?
Answer: If the computer has a salvage value after 5 years, and is sold at that time, the book value will be zero, and the company will have to pay a tax of 0.35 * 100 = $35 at that time. This changes the marginal cash flow to 265 + 100 - 35 = $330 in year 5.
The present value of the marginal cash flows (at 12%) is $899.19. The net present value is 899.19 - 532.50 = $366.70. The new computer should be purchased.
2. New diesel locomotives will cost a railroad $600,000 each and can be depreciated straight-line over their five-year life. Using a diesel instead of a coal-fired steam locomotive will save $12,000 annually in operating expenses. Railroads have a required rate of return of 10 percent and a tax rate of 40 percent.
a. What is the maximum price a railroad would be willing to pay for a coal-fired steam locomotive? (Hint: Set up the cash flows for a coal-fired locomotive at a price of P, including depreciation, and then compare them to the incremental cash flows associated with a diesel costing $600,000.)
Answer: PVIFAr=10%,n=5 = 3.790787.

Consider the decision to switch from coal-fired steam locomotives to diesel locomotives. We will find the indifference point by assuming that the net present value of the switching decision is zero.

All figures are reported in thousands. The incremental cost is (600 ─ P). Annual incremental cash flows = (1─t)(Savings) + t(Incr Depr). = 0.6(12) + 0.4(120 ─ 0.2P) = 55.2 ─ 0.08P. The present value of the incremental cash flows is PVIFA´(55.2 ─ 0.08P) or 209.251442 ─ 0.303263P. Setting this expression equal to 600 ─ P, we solve for P = $560.826. This makes NPV = 0.

b. Will your answer to (a) change if the railroad has enormous tax-loss carryforwards that put it in a zero taxpaying position for the foreseeable future?
Answer: Enormous tax loss carryforwards make the effective tax rate equal to zero. Therefore, the annual incremental cash flow is $12, and its present value is 12 ´ 3.790787 = 45.4894. Setting this equal to the marginal cost of (600 ─ P), we get P = $554,511. The value of the cost savings obtained by the purchase of diesel locomotives is higher, since the savings are not taxed. This makes the diesel relatively more valuable in this instance.
3. Varico produces HO scale trains, including a diesel locomotive that sells 100,000 units annually. Each unit requires an electric motor. Presently these are purchased once a week from a local manufacturer for $10 apiece. However, a foreign firm has offered to sell Varico a container of 100,000 motors of like quality for only $9.50 apiece. Given an interest rate of 15 percent, what should Varico do?
Answer: By buying 100,000 motors today, the firm will have average inventory on hand of 50,000 during the year. The opportunity cost of maintaining this inventory equals





Average Number of Units on Hand

x

Price Per Unit

x

Interest Rate






=


50,000

x

$9.50

x

0.15

=

$1,250

By buying weekly, the firm incurs no interest expense. Thus, the real cost of buying 100,000 motors today is $950,000 + $71,250 = $1,021,250. This exceeds the $1M that it costs to buy motors at $10 apiece on a weekly basis.


4. To capitalize on consumers’ concerns about healthful food, Specific Foods, Inc., is considering a new cereal, Veggie Crisp, which contains small bits of cooked vegetables with bran flakes. As part of its cash flow analysis, the finance department has made the following forecasts of demand and cost:

a. Sales revenue for the first year will be $200,000 and increase to $1,000,000 the next year. Revenue will then grow by 15 percent a year for the next four years, remain the same in the seventh year, and then decline by 15 percent a year for the next three years, when the product will be terminated.

b. Cost of goods sold will be 60 percent of sales.

c. Advertising and general expenses will be $10,000 a year.

d. Equipment will be purchased today for $1,250,000 and will be depreciated over the ten-year project using the straight-line method. Installation cost today is $25,000, and this is depreciated over five years, also on a straight-line basis. The equipment has no salvage value. Other initial costs (which are expensed, not depreciated) total $875,000. There is no investment tax credit.

(i). Calculate net income and operating cash flow using a 35 percent tax rate.
Answer: The income and cash flow statement ($000’s) appears below (rounded mercilessly: Total PV is accurate to decimal places shown)


Year

1

2

3

4

5

6

7

8

9

10

Sales

200

1000

1150

1323

1521

1749

1749

1487

1264

1074

CGS

120

600

690


794

913

1049

1049

892

758

644

Adv/Gen

10

10

10

10

10

10

10

10

10

10

Depr (Equip)

125

125

125

125

125

125

125

125

125

125

Depr(Inst)

5

5

5

5

5

0


0

0

0

0

OCF

91

299

338

383

434

492

492

424

366

317

PV(r=10%)

83

247

254

261

270

278

252

198

155

122

Tax rate = 35% Total PV = $2120.065  


b. Find the net present value of the project using a 10 percent cost of capital.

Answer: Cost today = 1250 + 25 + 875(1 ─ 0.35) = $1843.750.

NPV($000’s) = 2120.065 ─ 1843.750 = $276.315.


The project should be accepted.
c. In an effort to adjust for inflation, the finance department has produced an alternative estimate of cash flows. The product price will remain the same, but advertising and general expenses will grow by 5 percent a year from its initial level of $10,000. In addition, the cost of goods sold will grow by 20 percent a year from its initial level of $600,000 until year 6, remain the same in year 7, and then decline by 15 percent a year through year 10. What is the project’s net present value under these assumptions?
Answer: Under the new cash flow estimates, the project should be rejected:


Year

1

2

3

4

5

6

7

8

9

10

Sales

200

1000

1150

1323

1521

1749

1749

1487

1264


1074

CGS

120

600

720

864

1037

1244

1244

1058

899

764

Depr(Equip)

10

11

11

12

12

13

13

14

15

16

Depr(Inst)































OCF





























PV(r=10%)






























┌─────────┬─────────────────────────────────────────────┐

│Year │ 1 2 3 4 5 6 7 8 9 10 │

│Sales │200 1000 1150 1323 1521 1749 1749 1487 1264 1074 │

│CGS │120 600 720 864 10371244 1244 1058 899 764 │

│Adv/Gen │ 10 11 11 12 12 13 13 14 15 16 │

│Depr(Equip) │ 125 125 125 125 125 125 125 125 125 125 │

│Depr(Inst) │ 5 5 5 5 5 0 0 0 0 0 │

│OCF │ 91 299 318 336 352 364 363 314 271 235 │

│PV(r=10%) │ 83 247 239 229 219 205 186 146 115 91 │

└─────────┴───────────────────────────────────┘

Tax rate = 35% Total PV = $1760.160

NPV($000’s) = 1760.160 ─ 1843.750 = ─$83.590.

5. In building a new facility for producing trucks, International Truck (IT) must estimate the total investment required. In the current year, IT estimates it will acquire land for the plant at $1,000,000 and modify existing plant equipment for $123,000. Next year, construction will begin and require $866,000, and further plant modifications will require $344,000. In addition, new equipment worth $140,000 will be purchased (with a 10 percent investment tax credit). The new equipment will require $250,000 of installation expense. Finally, in the next year, construction will be completed at a cost of $750,000; installation charges will total $229,000; and building modifications will require $350,000. Lastly, more new equipment will be purchased for $230,000 (with a 10 percent ITC). With a cost of capital of 10 percent, what is the present value of the initial investment required for the plant?

Answer:


Year 0 1 2

Land 1,000,000

Modification 123,000

Construction 866,000 750,000

Modification 344,000 350,000

New Equipment 126,000* 207,000*

Installation 250,000 229,000

Totals 1,123,000 1,586,000 1,536,000

PV (10%) 1,123,000 1,441,818 1,269,421

Total PV $3,834,239

*Net of investment tax credit

6. Yankee Atomic Electric Co. announced in 1992 that it would decommission its Yankee Rowe nuclear plant at an estimated cost of $247 million. The cost includes:


i. $32 million to maintain the plant until 2000, when dismantling will begin. These expenses will accrue at the rate of $4 million a year.

ii. $56.5 million for the cost of building a facility to store its spent fuel until it is shipped in 2000 to a permanent repository. This storage facility will be depreciated straight-line over its eight-year estimated life.

iii. $158.5 million for the cost of dismantling the plant in 2000 and disposing of its nuclear wastes.

At the same time, Yankee Atomic estimated that decommissioning the plant in 1992, eight years earlier than its planned retirement in 2000, will save it $116 million ($14.5 million a year) before tax by enabling the utility to purchase cheaper electricity than Yankee Rowe could provide. In addition, Yankee Atomic said it had accumulated $72 million in a decommissioning fund required by the Nuclear Regulatory Commission.

a. What is the present value of Yankee’s $247 million decommissioning cost. Assume a cost of capital equal to 12 percent and a 34 percent tax rate.


Answer: . In order to answer this question we must make some assumptions regarding the timing of the various cash flows. Assume that the maintenance and storage facility costs begin immediately in 1992. The costs associated with the storage facility include an initial outlay of $56.5 million and subsequent depreciation tax shields worth $2,471,875 annually (0.35 ? $56,500,000/8) beginning in 1993 and continuing through 2000. All cash flows are assumed to occur at the beginning of the year, that is, the 1992 cash flows are expected to occur immediately and so on. As shown in the bottom row of this table, the present value of these net costs discounted at 12% is $160 million.

Year Maintenance Storage Facility Dismantling/Disposal Costs Total Cash Flows


1992 56,500,000 56,500,000

1993 4,000,000 (2,471,875) 1,528,125

1994 4,000,000 (2,471,875) 1,528,125

1995 4,000,000 (2,471,875) 1,528,125

1996 4,000,000 (2,471,875) 1,528,125

1997 4,000,000 (2,471,875) 1,528,125

1998 4,000,000 (2,471,875) 1,528,125

1999 4,000,000 (2,471,875) 1,528,125

2000 4,000,000 (2,471,875) 158,500,000 160,028,125

Present value @ 12% $128,106,666

b. Taking into account the savings on the purchase of cheaper electricity, and the $72 million already set aside, how much additional money does Yankee Atomic have to set aside in 1992 to have enough money to pay for the decommissioning expense?


Answer: The following table takes into account the savings on the purchase of cheaper electricity. Not that the annual after tax fuel savings of $9,245,000 ($14.5 million net of tax at 35%, or $14,500,000 ? 0.65) show up with a negative sign because it is a cost reduction. The net present value of these costs as shown on the bottom line is $81.3 million. Yankee Atomic has to set aside an additional $9.3 million in 1992 to make up the shortfall ($81.3 million   $72 million).

Year Maintenance Storage Facility Dismantling/Disposal Costs After tax Fuel Savings Total Cash Flows

1992 56,500,000 56,500,000

1993 4,000,000 (2,471,875) (9,425,000) (7,896,875)

1994 4,000,000 (2,471,875) (9,425,000) (7,896,875)

1995 4,000,000 (2,471,875) (9,425,000) (7,896,875)

1996 4,000,000 (2,471,875) (9,425,000) (7,896,875)

1997 4,000,000 (2,471,875) (9,425,000) (7,896,875)

1998 4,000,000 (2,471,875) (9,425,000) (7,896,875)

1999 4,000,000 (2,471,875) (9,425,000) (7,896,875)

2000 4,000,000 (2,471,875) 158,500,000 (9,425,000) 150,603,125

Present value @ 12% $81,286,661



c. What other factors might you consider in calculating the cost of decommissioniong?

Answer: Given the ever stiffening environmental laws, it would make sense to take into account the likelihood that cleanup standards–and hence costs–will rise over time. At the same time, it would make sense to try to lock politicians into the decommissioning program so that it would be grandfathered in the event of tougher laws.

7. Oldham Industries is considering replacing a 5 year old machine with an original life of 10 years, a cost of $100,000, and a zero salvage value, with a new and more efficient machine. The new machine will cost $200,000 installed and will have a 10 year life. The new machine will increase sales by $25,000 and decrease scrap cost by $10,000 per year. The old machine can be sold currently at $50,000, and Oldham’s marginal tax rate is 50 percent. Assume straight line depreciation and a 10 percent investment tax credit for both the old and the new machines. A prorated portion of any investment tax credit must be returned to the IRS for equipment sold before the end of its depreciable life; that is, if half the equipment’s life remains, then half the ITC is reclaimed by the IRS. Assume depreciation is taken on 100 percent of the cost of equipment.

a. What is the initial cash outflow generated by the machine replacement?

Answer:


b. What are the annual operating cash flows generated by this project?

Answer:

c. What is the net present value of this replacement project, given a 12 percent cost of capital?



Answer:

8. Molecugen has developed a new kind of cardiac diagnostic unit. Owing to the highly competitive nature of the market, the sales department forecasts demand of 5,000 units in the first year and a decrease in demand of 10 percent a year after that. After five years, the project will be discontinued with no salvage value. The marketing department forecasts a sales price of $15 a unit. Production estimates operating cost of $5 a unit, and the finance department estimates general and administrative expenses of $15,000 a year. The initial investment in land is $10,000, and other nondepreciable setup costs are $10,000.

a. Is the new project acceptable at a cost of capital of 10 percent? (Note: Use straight line depreciation over the life of the project and a tax rate of 35 percent.)


Answer: Demand Growth ─10% Price Growth 0%

┌─────────┬────────────────────────────────────┐

│Year │ 1 2 3 4 5 │

│Demand │ 5000 4500 4050 3645 3281 │

│Sales Price │ 15.00 15.00 15.00 15.00 15.00 │

│Revenue │ 75,000 67,500 60,750 54,675 49,208 │

│Costs │ 25,000 22,500 20,250 18,225 16,403 │

│Expenses │ 15,000 15,000 15,000 15,000 15,000 │

│NOI │ 22,750 19,500 16,575 13,943 11,573 │

└─────────┴────────────────────────────────────┘

Total PV = 65,960 NPV = 45,960 (Acceptable)

b. If the marketing department had forecast a decline of 15 percent a year in demand, would the project be acceptable?


Answer: Demand Growth ─15%

┌─────────┬────────────────────────────────────┐

│Year │ 1 2 3 4 5 │

│Demand │ 5000 4250 3613 3071 2610 │



│Revenue │ 75,000 63,750 54,188 46,059 39,150 │

│Costs │ 25,000 21,250 18,063 15,353 13,050 │

│NOI │ 22,750 17,875 13,731 10,209 7,215 │

└─────────┴────────────────────────────────────┘

Total PV = 57,224 NPV = 37,224 (Acceptable)

c. If the marketing department had forecast a decline in sales price of 10 percent a year, along with the 15 percent annual decline in demand predicted in (b), would the project be acceptable?


Answer: . Demand Growth ─15% Price Growth ─10%

┌─────────┬──────────────────────────────┐

│Year │ 1 2 3 4 5 │

│Demand │ 5000 4250 3613 3071 2610 │

│Sales Price │ 15.00 13.50 12.15 10.94 9.84 │

│Revenue │ 75,000 57,375 43,892 33,577 25,687│

│Costs │ 25,000 21,250 18,063 15,353 13,050│

│Expenses │ 15,000 15,000 15,000 15,000 15,000│

│NOI │ 22,750 13,731 7,039 2,096 ─1,536│

└─────────┴───────────────────────────── ┘

Total PV = 37,796 NPV = 17,796 (Acceptable)

d. If prices decline by 10 percent a year, the marketing department estimates that demand will be a constant 5,000 units a year. Is the project acceptable?

Answer:


Demand Growth 0% Price Growth ─10%

┌─────────┬───────────────────────────────────┐

│Year │ 1 2 3 4 5 │

│Demand │ 5000 5000 5000 5000 5000 │

│Sales Price │ 15.00 13.50 12.15 10.94 9.84 │

│Revenue │ 75,000 67,500 60,750 54,675 49,208 │

│Costs │ 25,000 25,000 25,000 25,000 25,000 │

│Expenses │ 15,000 15,000 15,000 15,000 15,000 │

│NOI │ 22,750 17,875 13,488 9,539 5,985 │


└─────────┴──────────────────────────────────── ┘

Total PV = 55,819 NPV = 35,819 (Acceptable)

9. Salterell Textiles is considering replacing the looming equipment in its North Carolina mill. The original purchase price was $79,300 two years ago. The machine has a useful life of ten years and is being depreciated using the straight-line method. The old equipment can be sold today for $10,800. The new equipment costs $80,500 and has an eight-year life. Its salvage value is expected to be $8,000. The new equipment is expected to increase output and sales revenue by $9,000 a year (after tax) and reduce costs by $7,500 (after tax).

a. With a tax rate of 25 percent and a 14 percent cost of capital, what should Salterell’s decision be?


Answer: NPV = PV(Revenue & Savings) + NPV(New Machine) + NPV(Old)

NPV(Revenue & Savings) = (9000 + 7500) ´ PVIFr=14%,n=8

= 16,500 ´ 4.6389 = $76,541.25. (after tax)

NPV(New Machine) = ─Cost + PV(Depr) + PV(After tax salvage)

= ─80,500 + 0.25 ´ 10,062.50 ´ 4.6389 + 8000(0.75)(0.3506 = PVIF)

= ─$66,726.67.

NPV(Old Machine) = [After Tax Sales Proceeds] ─ PV(Depr)

= [10,800 ─ 0.25(10,800 ─ 63,440*)] ─ 7930 ´ 0.25 ´ 4.6389

= $14,763.45.

Overall NPV = $76,541.25 ─ 62,830.27 + 14,763.45 = $24,578.

b. Would a 10 percent ITC change the analysis?


Answer: A 10% Investment Tax Credit would reduce current taxes by 0.10(80,500) = $8050. The effective NPV of the New Machine is increased to ─58,676.67, and the overall NPV is increased to $32,628.

c. If an inflation rate of 7 percent a year must be incorporated into the decision, is the project acceptable?



Answer: An inflation rate of 7% will increase nominal revenues, costs and salvage values, but will not affect depreciation or after-tax value of the sale of an existing asset (assuming the 7% inflation rate was already included in the nominal discount rate). As such, the inclusion of inflation will only make the net present value picture rosier.

10. Ross Designs is thinking of replacing its seven-year-old knitting machine with a new one that can also emboss designs on cloth. This will allow Ross to sell its textiles, which currently wholesale for $1.20 a yard, for $0.07 a yard more. The embossing should also raise sales 15 percent, to 2.07 million yards annually. The new machine costs $320,000, has annual operating costs of $27,000, and is expected to last for eight years. Labor, materials, and other expenses are estimated to rise by $0.02, to $1.10 per yard. Working capital requirements should remain at 30 percent of sales. All working capital investments will be recaptured in eight years. The current machine was purchased for $190,000 and is being depreciated on a straight line basis assuming a 10 year life. Its economic life as of today, however, is estimated to be eight years, the same as that of the new machine. It can be sold for $70,000 today, or for an estimated salvage value of $5,000 in eight years. The new machine will be depreciated straight line over a five-year period, and has an estimated salvage value of $20,000 in eight years. The appropriate discount rate is estimated at 12 percent.

a. What is the change in operating cash flows for each year? What is their present value?



Answer: Here are the incremental cash flows associated with the new machine. The present value of these cash flows, discounted at 12%, is $416,409. Although it is not mentioned in the problem, the tax rate is assumed to be 35%. Note that the incremental depreciation varies from year to year, depending on the old and new depreciation schedules.

Year 1 2 3 4 5 6 7 8

2,628,900 2,628,900 2,628,900 2,628,900 2,628,900 2,628,900 2,628,900 2,628,900

Old sales revenue 2,160,000 2,160,000 2,160,000 2,160,000 2,160,000 2,160,000 2,160,000 2,160,000

Incremental sales revenue 468,900 468,900 468,900 468,900 468,900 468,900 468,900 468,900

Annual machine operating costs 27,000 27,000 27,000 27,000 27,000 27,000 27,000 27,000

Other costs (new) 2,277,000 2,277,000 2,277,000 2,277,000 2,277,000 2,277,000 2,277,000 2,277,000

Other costs (old) 1,944,000 1,944,000 1,944,000 1,944,000 1,944,000 1,944,000 1,944,000 1,944,000

Incremental other costs 333,000 333,000 333,000 333,000 333,000 333,000 333,000 333,000

Depreciation (new) 64,000 64,000 64,000 64,000 64,000

Depreciation (old) 19,000 19,000 19,000

Incremental depreciation 45,000 45,000 45,000 64,000 64,000

Incremental before tax profit 63,900 63,900 63,900 44,900 44,900 108,900 108,900 108,900

Incremental tax @ 35% 22,365 22,365 22,365 15,715 15,715 38,115 38,115 38,115

Incremental after tax profit 41,535 41,535 41,535 29,185 29,185 70,785 70,785 70,785

Incremental depreciation 45,000 45,000 45,000 64,000 64,000

Incremental operating cash flow 86,535 86,535 86,535 93,185 93,185 70,785 70,785 70,785

Present value @12% 77,263 68,985 61,594 59,221 52,876 35,862 32,020 28,589

Cumulative present value $77,263 $146,249 $207,842 $267,063 $319,939 $355,801 $387,820 $416,409

b. What are the net cash flows associated with the purchase of the new knitting machine and sale of the old one?


Answer: If Ross purchases the new machine, it will have an initial outlay of$320,000 and cash receipts of $70,000 from the sale of the old machine. After seven years of straight line depreciation, the old machine will have a book value of $57,000. Hence, Ross will have to pay tax of $4,550 on the recapture of $13,000 in excess depreciation ($13,000 x 0.35). Thus, Ross’s net cash outlay will be $254,550 ($320,000   70,000 + 4,550). At the end of eight years, Ross will sell its new machine for an estimated $20,000. However, since the book value will be 0, Ross will have to pay tax of $7,000 ($20,000 x 0.35) on the recaptured depreciation. This leaves Ross with a net cash inflow of $13,000 in eight years. There is one more impact of the purchase of the new machine: Ross loses the estimated $5,000 salvage value of the old machine at the end of year 8. At the same time, Ross avoids paying tax of $1,750 on the recaptured depreciation, leaving it with a net loss of $3,250. Hence, the net effect of the purchase of the new machine and sale of the old one on year 8 cash flows is a net increase in cash flow for that year of $9,750 ($13,000   $3,250). The purchase of the new machine also affects intermediate term cash flows through its effects on depreciation. However, these effects have already been incorporated into the operating cash flow analysis. The present value of Ross’s investment in the new machine is $250,612 ($254,550   $9,750/1.128)

c. What is the NPV of the investment in working capital?


Answer: The incremental working capital requirement is 30% of incremental sales, or $140,670 ($468,900 x 0.30). Ross will recapture this investment at the end of year 8. Hence, the net present value of its incremental working capital investment is $83,856 ($140,670   $140,670/1.128).

d. What is the NPV of the acquisition of the new knitting machine? Should Ross buy it?


Answer: Combining the answers to parts (a) (c) yields an NPV for the new knitting machine of $81,941 ($416,409   $250,612   $83,856).


e. Suppose that all prices and costs are in nominal terms and will increase at the rate of inflation, which is projected at 4 percent. How does the analysis in parts (a) through (d) change? The 12 percent discount rate is expressed in nominal terms as well.

Answer: Assuming growth in costs and sales of 4% annually yields a new present value of operating profits equal to $460,514, as shown below, an increase of $44,105 compared its value before.

Year 1 2 3 4 5 6 7 8

New sales revenue 2,628,900 2,734,056 2,843,418 2,957,155 3,075,441 3,198,459 3,326,397 3,459,453

Old sales revenue 2,160,000 2,246,400 2,336,256 2,429,706 2,526,894 2,627,970 2,733,089 2,842,413

Incremental sales revenue 468,900 487,656 507,162 527,449 548,547 570,489 593,308 617,040

Annual machine operating costs 27,000 28,080 29,203 30,371 31,586 32,850 34,164 35,530

Other costs (new) 2,277,000 2,368,080 2,462,803 2,561,315 2,663,768 2,770,319 2,881,131 2,996,377

Other costs (old) 1,944,000 2,021,760 2,102,630 2,186,736 2,274,205 2,365,173 2,459,780 2,558,171

Incremental other costs 333,000 346,320 360,173 374,580 389,563 405,145 421,351 438,205

Depreciation (new) 64,000 64,000 64,000 64,000 64,000

Depreciation (old) 19,000 19,000 19,000

Incremental depreciation 45,000 45,000 45,000 64,000 64,000

Incremental before tax profit 63,900 68,256 72,786 58,498 63,398 132,494 137,793 143,305

Incremental tax @ 35% 22,365 23,890 25,475 20,474 22,189 46,373 48,228 50,157

Incremental after tax profit 41,535 44,366 47,311 38,023 41,208 86,121 89,566 93,148

Incremental depreciation 45,000 45,000 45,000 64,000 64,000

Incremental operating cash flow86,535 89,366 92,311 102,023 105,208 86,121 89,566 93,148

Present value @12% 77,263 71,242 65,705 64,838 59,698 43,631 40,515 37,621

Cumulative present value $77,263 $148,506 $214,211 $279,049 $338,747 $382,378 $422,893 $460,514

At the same time, working capital requirements rise year by year at the rate of 4% annually. The present value of these increases net of their return at the end of year 8 is $94,374, as shown below. This figure is $10,518 more than its value of $83,856 under the no inflation scenario.

Year 0 1 2 3 4 5 6 7 8

Incremental working capital req 140,670 5,627 5,852 6,086 6,329 6,583 6,846 7,120 (185,112)

Present value @12% $140,670 $5,024 $4,665 $4,332 $4,022 $3,735 $3,468 $3,221  $74,764

Cumulative present value $140,670 $145,694 $150,359 $154,691 $158,713 $162,448 $165,917 $169,137 $94,374


The net effect of these changes is to increase the project NPV by $33,587 ($44,105   $10,518).





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