7-0 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Corporate Finance Ross Westerfield...

7-1

McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited

Corporate Finance Ross Westerfield Jaffe Sixth Edition

7Chapter Seven

Net Present Value and Capital Budgeting

Prepared by

Gady JacobyUniversity of Manitoba

and

Sebouh AintablianAmerican University of Beirut

7-2


Chapter Outline

7.1 Incremental Cash Flows

7.2 The Majestic Mulch and Compost Company: An Example

7.3 Inflation and Capital Budgeting

7.4 Investments of Unequal Lives: The Equivalent Annual Cost Method

7.5 Summary and Conclusions

7-3


7.1 Incremental Cash Flows

• Cash flows matter—not accounting earnings.

• Sunk costs don’t matter.

• Incremental cash flows matter.

• Opportunity costs matter.

• Side effects like cannibalism and erosion matter.

• Taxes matter: we want incremental after-tax cash flows.

• Inflation matters.

7-4


Cash Flows—Not Accounting Earnings

• Consider depreciation expense.

• You never write a cheque made out to “depreciation.”

• Much of the work in evaluating a project lies in taking accounting numbers and generating cash flows.

7-5


Incremental Cash Flows

• Sunk costs are not relevant

– Just because “we have come this far” does not mean that we should continue to throw good money after bad.

• Opportunity costs do matter. Just because a project has a positive NPV does not mean that it should also have automatic acceptance. Specifically if another project with a higher NPV would have to be passed up we should not proceed.

• Side effects matter.

– Erosion and cannibalism are both bad things. If our new product causes existing customers to demand less of current products, we need to recognize that.

7-6


Estimating Cash Flows

• Cash Flows from Operations

– Recall that:

Operating Cash Flow = EBIT – Taxes + Depreciation

• Net Capital Spending

– Don’t forget salvage value (after tax, of course).

• Changes in Net Working Capital

– Recall that when the project winds down, we enjoy a return of net working capital.

7-7


Interest Expense

• Later chapters will deal with the impact that the amount of debt that a firm has in its capital structure has on firm value.

• For now, it’s enough to assume that the firm’s level of debt (hence interest expense) is independent of the project at hand.

7-8


7.2 The Majestic Mulch and Compost Company (MMCC): An ExampleCosts of test marketing (already spent): $250,000.

The proposed factory site (which we own) has no resale value.

Cost of the tool making machine: $800,000 (CCA calculations are based on a class 8, 20-percent rate).

Production (in units) by year during 8-year life of the machine: 6,000, 9,000, 12,000, 13,000, 12,000, 10,000, 8,000, and 6,000.

Price during first year is $100; price increases 2-percent per year thereafter.

Production costs during first year are $64 per unit and increase at the annual inflation rate of 5-percent per year thereafter.

Fixed production costs are $50,000 each year.

Working capital: initially $40,000, then 15-percent of sales at the end of each year. Falls to $0 by the project’s end.

7-9


Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8Income: (1) Sales revenues 600,000$ 918,000$ 1,248,480$ 1,379,570$ 1,298,919$ 1,104,081$ 900,930$ 689,211$

The Worksheet for Cash Flows of the MMCC

Recall that production (in units) by year during 8-year life of the machine is given by: (6,000, 9,000, 12,000, 13,000, 12,000, 10,000, 8,000, 6,000).

Price during first year is $100 and increases 2% per year thereafter.

Sales revenue in year 5 = 12,000×[$100×(1.02)4] = $1,298,919.

(All cash flows occur at the end of the year.)

7-10


Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8Income: (1) Sales revenues 600,000$ 918,000$ 1,248,480$ 1,379,570$ 1,298,919$ 1,104,081$ 900,930$ 689,211$ (2) Operating costs 434,000 654,800 896,720 1,013,144 983,509 866,820 736,129 590,327

The Worksheet for Cash Flows of the MMCC (continued)

Again, production (in units) by year during 8-year life of the machine is given by: (6,000, 9,000, 12,000, 13,000, 12,000, 10,000, 8,000, 6,000).

Variable costs during first year (per unit) are $64 and (increase 5% per year thereafter). Fixed costs are $50,000 each year.

Production costs in year 2 = 12,000×[$64×(1.05)4] + 50,000= $983,509.


7-11


Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8Income: (1) Sales revenues 600,000$ 918,000$ 1,248,480$ 1,379,570$ 1,298,919$ 1,104,081$ 900,930$ 689,211$ (2) Operating costs 434,000 654,800 896,720 1,013,144 983,509 866,820 736,129 590,327 (3) 80,000 144,000 115,200 92,160 73,728 58,982 47,186 37,749 CCA

CCA calculations are based on a class 8, 20% rate (shown at right)

The machine cost $800,000.

CCA charge in year 5 =$368,640×(.20) = $73,728.

Beginning EndingYear UCC CCA UCC

1 400,000$ 80,000$ 320,000$ 2 720,000 144,000 576,000 3 576,000 115,200 460,800 4 460,800 92,160 368,640 5 368,640 73,728 294,912 6 294,912 58,982 235,930 7 235,930 47,186 188,744 8 188,744 37,749 150,995

Annual CCA



7-12




Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8Income: (1) Sales revenues 600,000$ 918,000$ 1,248,480$ 1,379,570$ 1,298,919$ 1,104,081$ 900,930$ 689,211$ (2) Operating costs 434,000 654,800 896,720 1,013,144 983,509 866,820 736,129 590,327 (3) 80,000 144,000 115,200 92,160 73,728 58,982 47,186 37,749

(4) 86,000 119,200 236,560 274,266 241,682 178,278 117,615 61,136

(5) Taxes at 40% 34,400 47,680 94,624 109,707 96,673 71,311 47,046 24,454

(6) Net Income 51,600 71,520 141,936 164,560 145,009 106,967 70,569 36,682

[(1) – (2) - (3)]

CCA

EBIT

7-13




Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8Investments: (7) NWC (year end) 40,000$ 90,000$ 137,700$ 187,272$ 206,936$ 194,838$ 165,612$ 135,139$ 0$

(8) Change in NWC (40,000) (50,000) (47,700) (49,572) (19,664) 12,098 29,226 30,473 135,139 (9) Equipment (800,000)

(10) Aftertax salvage 150,000 (11) Total cash flow (840,000) (50,000) (47,700) (49,572) (19,664) 12,098 29,226 30,473 285,139

of investment[(8) + (9) + (10)]

7-14


Incremental After Tax Cash Flows (IATCF) of the MMCC

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8(1) Sales 600,000$ 918,000$ 1,248,480$ 1,379,570$ 1,298,919$ 1,104,081$ 900,930$ 689,211$

revenues(2) Operating 434,000$ 654,800$ 896,720$ 1,013,144$ 983,509$ 866,820$ 736,129$ 590,327$

costs(3) 34,400 47,680 94,624 109,707 96,673 71,311 47,046 24,454

(4) 131,600 215,520 257,136 256,720 218,737 165,949 117,755 74,430

(5) Total CF of (840,000) (50,000) (47,700) (49,572) (19,664) 12,098 29,226 30,473 285,139

Investment(6) IATCF (840,000) 81,600 167,820 207,564 237,056 230,835 195,175 148,228 359,570

Taxes

OCF

[(4) + (5)]

[(1) - (2) - (3)]


NPV@10% $500,135

NPV@10% $188,042

NPV@15% $2,280

NPV@20% ($137,896)

IRR 15.07%

If the project’sdiscount rate is above 15.07%, it should not be accepted (since

NPV > 0).

7-15


7.3 Inflation and Capital Budgeting

• Inflation is an important fact of economic life and must be considered in capital budgeting.

• Consider the relationship between interest rates and inflation, often referred to as the Fisher relationship:(1 + Nominal Rate) = (1 + Real Rate) × (1 + Inflation Rate)

• For low rates of inflation, this is often approximated as Real Rate Nominal Rate – Inflation Rate

• While the nominal rate in the U.S. has fluctuated with inflation, most of the time the real rate has exhibited far less variance than the nominal rate.

• When accounting for inflation in capital budgeting, one must compare real cash flows discounted at real rates or nominal cash flows discounted at nominal rates.

7-16


Example of Capital Budgeting under Inflation

Canadian Electronics Inc. (CEI) has an investment opportunity to produce a new stereo colour TV.

The required investment on January 1 of this year is $32 million. CCA calculations are based on a class 8, 20% rate. The firm is in the 34% tax bracket.

This investment will have no resale value at the end of the project (in four years).

The price of the product on January 1 will be $400 per unit. The price will stay constant in real terms.

Labour costs will be $15 per hour on January 1. The will increase at 2% per year in real terms.

Energy costs will be $5 per TV; they will increase 3% per year in real terms.

The inflation rate is 5%.

Revenues are received and costs are paid at year-end.

7-17



The riskless nominal discount rate is 4%. The real discount rate for costs and revenues is 8%. Calculate the NPV.

Year 1 Year 2 Year 3 Year 4

Physical Production (units)

100,000 200,000 200,000 150,000

Labour Input (hours)

2,000,000 2,000,000 2,000,000 2,000,000

Energy input, physical units

200,000 200,000 200,000 200,000

7-18


Present Value of the Tax Shield on CCA• The PV of CCA tax shield is a perpetuity, with an

adjustment for

– the 1st year 50-percent rule

– the sale of the asset at the time when the project is terminated

• The PV of CCA tax shield is given by:

n

ccShieldTaxCCA

kdk

TdS

k

k

dk

TdCPV

1

1

1

5.01

S = Min[resale value of assets, original price of assets]

C = original price of the assets

d = depreciation rate that applies to the asset class

d = discount rate

n = the time when assets are sold

7-19



• The depreciation tax shield is a risk-free nominal cash flow, and is therefore discounted at the nominal riskless rate.

• Cost of investment today: C = $32,000,000Project life: n = 4 yearsClass 8 depreciation rate: d = 20%Asset resale value: S = 0

Finally: k = 0.04 and TC = 0.34

• The PV of CCA tax shield is given by:

308,892,8$

04.1

1

2.04.

34.2.0

04.1

04.5(.1

2.04.

34.2.000,000,324

ShieldTaxCCAPV

7-20



• Risky Real Cash Flows– Price: $400 per unit with zero real price increase– Labour: $15 per hour with 2% real wage increase– Energy: $5 per unit with 3% real energy cost increase

• Year 1 After-tax Real Risky Cash Flows:After-tax revenues =

$400 × 100,000 × (1-.34) = $26,400,000After-tax labour costs =

$15 × 2,000,000 × 1.02 × (1-.34) = $20,196,000After-tax energy costs =

$5 × 2,00,000 × 1.03 × (1-.34) = $679,800After-tax net operating CF =

$26,400,000 - $20,196,000 - $679,800 =$5,524,200

7-21



$5,524,200 $31,499,886 $31,066,882 $17,425,007

-$32,000,000

0 1 2 34

868,590,69$

)08.1(

007,425,17$

)08.1(

882,066,31$

)08.1(

886,499,31$

)08.1(

200,524,5$32$

CFsrisky

432CFsrisky

PV

mPV

Year One After-tax revenues = $400 × 100,000 × (1-.34) = $26,400,000

Year One After-tax labour costs = $15 × 2,000,000 × 1.02 × (1-.34) = $20,196,000

Year One After-tax energy costs = $5 × 2,00,000 × 1.03 × (1-.34) = $679,800

Year One After-tax net operating CF =$5,524,200

7-22



The project NPV can now be computed as the sum of the PV of the cost, the PV of the risky cash flows discounted at the risky rate, and the PV of the risk-free CCA tax shield cash flows discounted at the risk-free discount rate.

NPV = -$32,000,000 + $69,590,868 + $8,892,308 = $46,483,176

7-23


7.4 Investments of Unequal Lives: The Equivalent Annual Cost Method• There are times when application of the NPV rule can lead

to the wrong decision. Consider a factory that must have an air cleaner. The equipment is mandated by law, so there is no “doing without.”

• There are two choices:

– The “Cadillac cleaner” costs $4,000 today, has annual operating costs of $100 and lasts for 10 years.

– The “cheaper cleaner” costs $1,000 today, has annual operating costs of $500 and lasts for five years.

• Which one should we choose?

7-24


7.4 Investments of Unequal Lives: The Equivalent Annual Cost MethodAt first glance, the cheap cleaner has the lower NPV (r = 10%):

46.614,4)10.1(

100$000,4$

10

1Cadillac

tt

NPV

39.895,2)10.1(

500$000,1$

5

1cheap

tt

NPV

This overlooks the fact that the Cadillac cleaner lasts twice as long.

When we incorporate that, the Cadillac cleaner is actually cheaper.

7-25


7.4 Investments of Unequal Lives: The Equivalent Annual Cost Method

The Cadillac cleaner time line of cash flows:-$4,000 –100 -100 -100 -100 -100 -100 -100 -100 -100 -100

0 1 2 3 4 5 6 7 8 9 10

-$1,000 –500 -500 -500 -500 -1,500 -500 -500 -500 -500 -500

0 1 2 3 4 5 6 7 8 9 10

The “cheaper cleaner” time line of cash flows over 10 years:

20.693,4$)10.1(

500$

)10.1(

000,1$

)10.1(

500$000,1$

10

65

5

1cheap

tt

tt

NPV

46.614,4)10.1(

100$000,4$

10

1Cadillac

tt

NPV

7-26


Investments of Unequal Lives

• Replacement Chain

– Repeat the projects forever, find the PV of that perpetuity.

– Assumption: Both projects can and will be repeated.

• Matching Cycle

– Repeat projects until they begin and end at the same time—like we just did with the air cleaners.

– Compute NPV for the “repeated projects.”

• The Equivalent Annual Cost Method

7-27


Investments of Unequal Lives: EAC• The Equivalent Annual Cost Method

– Applicable to a much more robust set of circumstances than replacement chain or matching cycle.

– The Equivalent Annual Cost is the value of the level payment annuity that has the same PV as our original set of cash flows.

– NPV = EAC × ArT

– For example, the EAC for the Cadillac air cleaner is $750.98

10

1

10

1 )10.1(

98.750$46.614,4

)10.1(

100$000,4$

tt

tt

The EAC for the cheaper air cleaner is $763.80 which confirms our earlier decision to reject it.

7-28


Example of Replacement Projects

Consider a Belgian Dentist’s office; he needs an autoclave to sterilize his instruments. He has an old one that is in use, but the maintenance costs are rising and so he is considering replacing this indispensable piece of equipment.

New Autoclave– Cost = $3,000 today, – Maintenance cost = $20 per year– Resale value after 6 years = $1,200– NPV of new autoclave (at r = 10%):

6

6

1 )10.1(

200,1$

)10.1(

20$000,3$74.409,2$

tt

6

1 )10.1(

29.553$74.409,2$

tt

EAC of new autoclave = -$553.29

7-29



• Existing Autoclave

Year 0 1 2 3 45

Maintenance 0 200 275 325 450 500

Resale 900 850 775 700 600500

Total Annual Cost

Total Cost for year 1 = (900 × 1.10 – 850) + 200 = $340340 435

Total Cost for year 2 = (850 × 1.10 – 775) + 275 = $435

478

Total Cost for year 3 = (775 × 1.10 – 700) + 325 = $478

620

Total Cost for year 4 = (700 × 1.10 – 600) + 450 = $620Total Cost for year 5 = (600 × 1.10 – 500) + 500 = $660

660

Note that the total cost of keeping an autoclave for the first year includes the $200 maintenance cost as well as the opportunity cost of the foregone future value of the $900 we didn’t get from selling it in year 0 less the $850 we have if we still own it at year 1.

7-30



340 435 478 620 660

New Autoclave EAC of new autoclave = -$553.29

Existing AutoclaveYear 0 1 2 3 4

5Maintenance 0 200 275 325 450 500Resale 900 850 775 700 600

500Total Annual Cost•We should keep the old autoclave until it’s cheaper to buy a new one.

•Replace the autoclave after year 3: at that point the new one will cost $553.29 for the next year’s autoclaving and the old one will cost $620 for one more year.

7-31


7.5 Summary and Conclusions

• Capital budgeting must be placed on an incremental basis.

– Sunk costs are ignored

– Opportunity costs and side effects matter

• Inflation must be handled consistently

– Discount real flows at real rates

– Discount nominal flows at nominal rates

• When a firm must choose between two machines of unequal lives:

– the firm can apply either the matching cycle approach

– or the equivalent annual cost approach

7-0 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Corporate Finance Ross Westerfield...

Documents

Transcript of 7-0 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Corporate Finance Ross Westerfield...