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Chapter 6: Analyzing Investment Projects

Copyright © Prentice Hall Inc. 2000. Author: Nick Bagley, bdellaSoft, Inc.

ObjectiveExplain Capital Budgeting

Develop Criteria

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Chapter 6 Contents

The Nature of Project Analysis

Where do Investments Ideas come from?

The NPV Investment Rule

Estimating a Project.s Cash Flows

Cost of Capital Sensitivity Analysis

Analyzing Cost-Reducing Projects

Projects with Different Lives

Ranking Mutually Exclusive Projects

Inflation & Capital Budgeting

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Objectives

To show how to use discounted cash flow analysis to make decisions such as: Whether to enter a new line of

business Whether to invest in equipment to

reduce costs

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Types of Investment Projects

New Products Cost Reduction Replacing of Existing Assets

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Where Do Investment Ideas Come from

Surveys of Customers R&D Department Competition Production Divisions

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The NPV Rule

Invest if the proposed project’s NPV is positive

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Example: Generic Jeans Company

The company is considering whether to produce a new line of jeans called Protojeans. The Cash Flow forecasts read as follows:

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Cash Flow Forecasts

Year Cash Flows(in thousands of dollars)

0 -$100

1 $50

2 $40

3 $30

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Protojean Projects

If we discount each year’s cash flow at a rate of 8% per year we will have:

Year Cash Flows(,000)

PV of CF at 8%

CumulativePV

0 -100 -100.00000 -100.0000

1 50 46.29630 -53.70370

2 40 34.29355 -19.41015

3 30 23.81497 4.4082

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NPV as a Function of Discount Rate

-200

-150

-100

-50

0

50

100

150

200

250

0% 5% 10% 15% 20%

Discount Rate

NP

V

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Example: Compusell Corporation

The PC1000 project, a new type of personal computer.

The next table shows the estimated annual sales revenue, operating costs, and profit for the PC1000:

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Net Cash Inflow from Operations

Cash Flow= Revenue-Cash Expenses- Taxes Cash Flow= Revenue-Total Expenses- Taxes+Noncash Expenses = Net Income+Noncash Expenses

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Assumptions (Table in $'000)Cost of capital 15.00%Tax rate 40.00%Unit sales in year 1 4,000Sales growth rate 0.00%Unit price $5,000Unit Price Growth 0.00%Fixed Start 3,100,000Fixed Growth 0.00%Variable pcent 75.00%Depreciation schedule 400,000 NPV = 1236Start working capt 2,200,000Investment schedule 2,800,000Working Cap Sch 2,200,000

Year 0 1 2 3 4 5 6 7CF ForecastSales revenue 20,000 20,000 20,000 20,000 20,000 20,000 20,000ExpensesFixed Costs (cash) 3,100 3,100 3,100 3,100 3,100 3,100 3,100Variable costs 15,000 15,000 15,000 15,000 15,000 15,000 15,000Depreciation 400 400 400 400 400 400 400Operating Profit 1,500 1,500 1,500 1,500 1,500 1,500 1,500Taxes 600 600 600 600 600 600 600Net Profit 900 900 900 900 900 900 900Operating CF 1,300 1,300 1,300 1,300 1,300 1,300 1,300Working cap move 2200 -2,200Investment in P&E 2,800 0 0 0 0 0 0Invest CF 5,000 0 0 0 0 0 0 -2,200Net CF -5,000 1,300 1,300 1,300 1,300 1,300 1,300 3,500PV(NCF) -5000 1130 983 855 743 646 562 1316

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Assumptions (Table in $'000)Cost of capital 25.00%Tax rate 40.00%Unit sales in year 1 4,000Sales growth rate 0.00%Unit price $5,000Unit Price Growth 0.00%Fixed Start 3,100,000Fixed Growth 0.00%Variable pcent 75.00%Depreciation schedule 400,000 NPV = -429Start working capt 2,200,000Investment schedule 2,800,000Working Cap Sch 2,200,000

Year 0 1 2 3 4 5 6 7CF ForecastSales revenue 20,000 20,000 20,000 20,000 20,000 20,000 20,000ExpensesFixed Costs (cash) 3,100 3,100 3,100 3,100 3,100 3,100 3,100Variable costs 15,000 15,000 15,000 15,000 15,000 15,000 15,000Depreciation 400 400 400 400 400 400 400Operating Profit 1,500 1,500 1,500 1,500 1,500 1,500 1,500Taxes 600 600 600 600 600 600 600Net Profit 900 900 900 900 900 900 900Operating CF 1,300 1,300 1,300 1,300 1,300 1,300 1,300Working cap move 2200 -2,200Investment in P&E 2,800 0 0 0 0 0 0Invest CF 5,000 0 0 0 0 0 0 -2,200Net CF -5,000 1,300 1,300 1,300 1,300 1,300 1,300 3,500PV(NCF) -5000 1040 832 666 532 426 341 734

Was 15%

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Assumptions (Table in $'000)Cost of capital 15.00%Tax rate 30.00%Unit sales in year 1 4,000Sales growth rate 0.00%Unit price $5,000Unit Price Growth 0.00%Fixed Start 3,100,000Fixed Growth 0.00%Variable pcent 75.00%Depreciation schedule 400,000 NPV = 1860Start working capt 2,200,000Investment schedule 2,800,000Working Cap Sch 2,200,000

Year 0 1 2 3 4 5 6 7CF ForecastSales revenue 20,000 20,000 20,000 20,000 20,000 20,000 20,000ExpensesFixed Costs (cash) 3,100 3,100 3,100 3,100 3,100 3,100 3,100Variable costs 15,000 15,000 15,000 15,000 15,000 15,000 15,000Depreciation 400 400 400 400 400 400 400Operating Profit 1,500 1,500 1,500 1,500 1,500 1,500 1,500Taxes 450 450 450 450 450 450 450Net Profit 1,050 1,050 1,050 1,050 1,050 1,050 1,050Operating CF 1,450 1,450 1,450 1,450 1,450 1,450 1,450Working cap move 2200 -2,200Investment in P&E 2,800 0 0 0 0 0 0Invest CF 5,000 0 0 0 0 0 0 -2,200Net CF -5,000 1,450 1,450 1,450 1,450 1,450 1,450 3,650PV(NCF) -5000 1261 1096 953 829 721 627 1372

Was 40%

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Assumptions (Table in $'000)Cost of capital 15.00%Tax rate 40.00%Unit sales in year 1 4,000Sales growth rate 5.00%Unit price $5,000Unit Price Growth 0.00%Fixed Start 3,100,000Fixed Growth 0.00%Variable pcent 75.00%Depreciation schedule 400,000 NPV = 2885Start working capt 2,200,000Investment schedule 2,800,000Working Cap Sch 2,200,000

Year 0 1 2 3 4 5 6 7CF ForecastSales revenue 20,000 21,000 22,050 23,153 24,310 25,526 26,802ExpensesFixed Costs (cash) 3,100 3,100 3,100 3,100 3,100 3,100 3,100Variable costs 15,000 15,750 16,538 17,364 18,233 19,144 20,101Depreciation 400 400 400 400 400 400 400Operating Profit 1,500 1,750 2,013 2,288 2,578 2,881 3,200Taxes 600 700 805 915 1,031 1,153 1,280Net Profit 900 1,050 1,208 1,373 1,547 1,729 1,920Operating CF 1,300 1,450 1,608 1,773 1,947 2,129 2,320Working cap move 2200 -2,200Investment in P&E 2,800 0 0 0 0 0 0Invest CF 5,000 0 0 0 0 0 0 -2,200Net CF -5,000 1,300 1,450 1,608 1,773 1,947 2,129 4,520PV(NCF) -5000 1130 1096 1057 1014 968 920 1699

Was 0%

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Assumptions (Table in $'000)Cost of capital 15.00%Tax rate 40.00%Unit sales in year 1 4,000Sales growth rate 0.00%Unit price $5,000Unit Price Growth 0.00%Fixed Start 3,100,000Fixed Growth 0.00%Variable pcent 85.00%Depreciation schedule 400,000 NPV = -3757Start working capt 2,200,000Investment schedule 2,800,000Working Cap Sch 2,200,000

Year 0 1 2 3 4 5 6 7CF ForecastSales revenue 20,000 20,000 20,000 20,000 20,000 20,000 20,000ExpensesFixed Costs (cash) 3,100 3,100 3,100 3,100 3,100 3,100 3,100Variable costs 17,000 17,000 17,000 17,000 17,000 17,000 17,000Depreciation 400 400 400 400 400 400 400Operating Profit -500 -500 -500 -500 -500 -500 -500Taxes -200 -200 -200 -200 -200 -200 -200Net Profit -300 -300 -300 -300 -300 -300 -300Operating CF 100 100 100 100 100 100 100Working cap move 2200 -2,200Investment in P&E 2,800 0 0 0 0 0 0Invest CF 5,000 0 0 0 0 0 0 -2,200Net CF -5,000 100 100 100 100 100 100 2,300PV(NCF) -5000 87 76 66 57 50 43 865

Was 75%

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Assumptions (Table in $'000)Cost of capital 15.00%Tax rate 40.00%Unit sales in year 1 4,000Sales growth rate 0.00%Unit price $5,000Unit Price Growth 0.00%Fixed Start 3,500,000Fixed Growth 0.00%Variable pcent 75.00%Depreciation schedule 400,000 NPV = 237Start working capt 2,200,000Investment schedule 2,800,000Working Cap Sch 2,200,000

Year 0 1 2 3 4 5 6 7CF ForecastSales revenue 20,000 20,000 20,000 20,000 20,000 20,000 20,000ExpensesFixed Costs (cash) 3,500 3,500 3,500 3,500 3,500 3,500 3,500Variable costs 15,000 15,000 15,000 15,000 15,000 15,000 15,000Depreciation 400 400 400 400 400 400 400Operating Profit 1,100 1,100 1,100 1,100 1,100 1,100 1,100Taxes 440 440 440 440 440 440 440Net Profit 660 660 660 660 660 660 660Operating CF 1,060 1,060 1,060 1,060 1,060 1,060 1,060Working cap move 2200 -2,200Investment in P&E 2,800 0 0 0 0 0 0Invest CF 5,000 0 0 0 0 0 0 -2,200Net CF -5,000 1,060 1,060 1,060 1,060 1,060 1,060 3,260PV(NCF) -5000 922 802 697 606 527 458 1226

Was $3,100,000

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Assumptions (Table in $'000)Cost of capital 15.00%Tax rate 40.00%Unit sales in year 1 4,000Sales growth rate 2.00%Unit price $5,000Unit Price Growth -3.00%Fixed Start 3,100,000Fixed Growth 8.00%Variable pcent 75.00%Depreciation schedule 400,000 NPV = -797Start working capt 2,200,000Investment schedule 2,800,000Working Cap Sch 2,200,000

Year 0 1 2 3 4 5 6 7CF ForecastSales revenue 20,000 19,788 19,578 19,371 19,165 18,962 18,761ExpensesFixed Costs (cash) 3,100 3,348 3,616 3,905 4,218 4,555 4,919Variable costs 15,000 14,841 14,684 14,528 14,374 14,222 14,071Depreciation 400 400 400 400 400 400 400Operating Profit 1,500 1,199 879 538 174 -214 -629Taxes 600 480 351 215 70 -86 -252Net Profit 900 719 527 323 104 -129 -377Operating CF 1,300 1,119 927 723 504 271 23Working cap move 2200 -2,200Investment in P&E 2,800 0 0 0 0 0 0Invest CF 5,000 0 0 0 0 0 0 -2,200Net CF -5,000 1,300 1,119 927 723 504 271 2,223PV(NCF) -5000 1130 846 610 413 251 117 836

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Carry-forward, Carry-back

When Calculating capital gains for tax purposes, a firm nets out all capital losses in the same year. If capital losses exceed capital gains, the net capital loss may be carried back to reduce taxable capital gains in the three prior years. Under the carry-back feature, a firm files

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Carry-forward, Carry-back

A revised tax return and receives a refund of prior years’ taxes. For example, suppose Canadian Enterprises experienced a net capital loss of $1 million in 2000 and net capital gains of $300,000 in 1999, $200,000 in 1998, and $150,000 in 1997.

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Carry-forward, Carry-back

Canadian could carry back a total of $650,000 to get a refund on its taxes. The remaining $350,000 can be carried forward indefinitely to reduce future taxes on capital gains.

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Carry-forward, Carry-back

A similar carry-forward provision applies to operating losses. The carry-back period is three years and carry forward is allowed up to seven years.

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Table 6.4 Project Sensitivity to Sales Volume

Sales Units Net CF Operations NPV Project2000 200000 50050223000 550000 18847083604 1003009 04000 1300000 12356075000 2050000 43559226000 2800000 7476237

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Sensitivity of Project to Sale Volume

$500,000

$0

$500,000

$1,000,000

$1,500,000

$2,000,000

$2,500,000

$3,000,000

$2,000 $2,500 $3,000 $3,500 $4,000 $4,500 $5,000 $5,500 $6,000

Sales (Units)

Net

CF

fro

m O

per

atio

ns

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NPV Project

$6,000,000

$4,000,000

$2,000,000

$0

$2,000,000

$4,000,000

$6,000,000

$8,000,000

$10,000,000

2000 2500 3000 3500 4000 4500 5000 5500 6000

Sales (Units)

NP

V

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NPV v. Discount Rate

$3,000

$2,000

$1,000

$0

$1,000

$2,000

$3,000

$4,000

$5,000

$6,000

$7,000

0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50%

Rate

NP

V $

000

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Projects with Different Lives

Example: Two labor-saving equipment1) Costs $2 million, has an expected

life of 5 years2) Costs $4 million, lasts for 10 years Discount rate 10%

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Annualized capital Cost

The annual cash payment that has a present value equal to the initial outlay

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Projects with different lives

1) n=5, i=10, PV=-2000000, FV=0 PMT=$5275952) n=10, i=10, PV=-4000000, FV=0 PMT=$650982

So equipment 1) is the preferred one.

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Inflation and Capital Budgeting

RULE: There are two correct ways of computing NPV:

1. Use the nominal cost of capital to discount nominal cash flows.

2. Use the real cost of capital to discount real cash flows.

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Inflation and Capital Budgeting

Example: An investment with an initial outlay of $2 million, produces an annual after-tax real CF of $600000 for 5 years, the cost of capital is 10%. Inflation rate is 6% per year. We can summarize the information in the following table:

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Investment under 6% inflation

Year Real Cash Flow

Nominal CF(6% inflation)

1 600,000 636,000

2 600,000 647,160

3 600,000 714,610

4 600,000 757,486

5 600,000 802,935

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Inflation and…

1) By discounting the annual 600,000 by 10% we come to PV=$2,274,472. So that

NPV=$2,274,472-2,000,000=$274,472

2) By discounting the third column by 16.6% nominal rate we get the same PV and

NPV=$247,472

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Analyzing Cost-Reducing Projects

A firm is considering an investment proposal to automate its production process to save labor costs. It can invest $2 million now in equipment and save $700,000 per year in pretax labor costs. If the equipment has an expected life of 5 years and if the tax rate is (33+1/3)%, is this investment worthwhile?

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Cost-Reducing Projects

We must compute the incremental cash flows due to the investment

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Incremental Cash flowsWithout

Investment

With

Investment

Difference

Due to Inv.

Revenue $5,000,000 $5,000,000 0

Labor Costs 1,000,000 300,000 -$700,000

Other cash expenses 2,000,000 2,000,000 0

Depreciation 1,000,000 1,400,000 $400,000

Pretax profit 1,000,000 1,300,000 $300,000

Income tax 333,333 433,333 $100,000

After-tax pr. 666,667 866,667 $200,000

Net CF $1,666,667 $2,266,667 $600,000

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Time Line

NPV =$2,274,472-$2,000,000 =$274,472

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Cost-reducing Projects (2)

Steiness Danish Ham, Inc., is contemplating buying a new machine that has an economic life of five years. The cost of machine is 1,242,000 krone and will be fully depreciated using the straight line method. At the end of five years it will have a market value of 138,000 krone.

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It is estimated that the new machine will save the company 345,000 krone per year due to reduced labor costs. Moreover, it will lead to a reduction in net working capital of 172,500 krone because of the higher yield from raw materials inventory. The net working

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Capital will be recovered by the end of the five years. If the corporate tax is 34% and the discount rate is 12%, what is the NPV of the project?

Working Capital

Working Capital=Current Assets – Current Liabilities

Current Assets: Inventories, Accounts Receivable

Current Liabilities: Accrued Expenses, Accounts Payable

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The Cash Flow Cycle

Ordered Arrives Finished Goods Sold Cash Received

Inventory Period Receivable Period

Payable Period Time Cash Cycle Time Invoice Received Cash Paid

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Solution: Incremental cash flows

Years 1 to 4 (in thousands krone)Revenue 0Labor costs -345Other cash expenses 0Depreciation 248.4Pretax profit 96.6Income taxes 32.844After-tax pr. 63.756

NCF 312.156

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Year 5

Labor costs -345Depreciation 248.4Pretax profit 96.6Income taxes 32.844After-tax pr. 63.756OCF 312.156Chg. in Working Cap. -172.5Salvage value 138Tax on Capital Gain .34*138Terminal Value 91.08NCF 230.736

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Year 0

Working Capital -172.5Investment in P&E 1,242 Investment CF 1,069.5 NCF 1,069.5

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Time Line

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553.912.1

736.2300645.9485.1069

12.1

736.230)3645.0)(3.2601(5.1069

12.1

736.230)12.11(

12.

156.3125.1069

)12.1(

656.277

)12.1(

156.312

)12.1(

156.312

)12.1(

156.312

12.1

156.3125.1069

5

5

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NPV

Comparing 2 projects with different lifetimes

You are evaluating two different pollution control options

1. A filtration System:Installation Cost $1.1 millionPretax AOC $60,000 Lifetime 5 years

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Comparing 2 projects with different lifetimes

2. A Precipitation SystemInstallation Cost $1.9 millionPretax AOC $10,000Lifetime 8 years

Discount rate: 12%Tax rate: 40%

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Incremental Cash Flow of two Projects

NCF=(1-t)(R-C-D)+D =(1-t)(R-C)+tDAs about Cost:Cost=-(1-t)C+tD

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Incremental Cash Flow of two Projects

Filtration System Precipitation System

After tax operating cost

-$36,000 -$6,000

Depreciation tax shield

$ 88,000 $95,000

Operating CF $ 52,000 $89,000

PV of operating CF $ 187,450 $ 442,116

Capital spending -$1,100,000 -$1,900,000

Total PV of costs -$912,550 -$1,457,884

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Incremental Cash Flow of two Projects

ACC: Annualized Capital Cost-912,550=ACC(F)*3.6048ACC(F)=-$253,149

-1,457,884=ACC(P)*4.9676ACC(P)=-$293,479

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