Chapter 6 Principles of Corporate Finance Eighth Edition Making Investment Decisions With the Net Present Value Rule Slides by Matthew Will Copyright ©

Chapter 6

Principles of

Corporate FinanceEighth Edition

Making Investment Decisions With the Net Present Value

Rule Slides by

Matthew Will

Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved

McGraw-Hill/Irwin


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Topics Covered

What To DiscountIM&C ProjectEquivalent Annual CostsProject Interaction

– Optimal Timing– Fluctuating Load Factors


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What To Discount

Only Cash Flow is Relevant


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What To Discount

Estimate Cash Flows on an Incremental BasisDo not confuse average with incremental payoffsInclude all incidental effectsDo not forget working capital requirementsInclude opportunity costs Forget sunk costsBeware of allocated overhead costs

Treat inflation consistently

Points to “Watch Out For”


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Be consistent in how you handle inflation!!Use nominal interest rates to discount

nominal cash flows.Use real interest rates to discount real cash

flows.You will get the same results, whether you

use nominal or real figures

Inflation

INFLATION RULEINFLATION RULE


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Inflation

Example

You own a lease that will cost you $8,000 next year, increasing at 3% a year (the forecasted inflation rate) for 3 additional years (4 years total). If discount rates are 10% what is the present value cost of the lease?

1 real interest rate = 1+nominal interest rate1+inflation rate


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Inflation

Example - nominal figures

99.429,26$

78.59708741,82=8000x1.034

56.63768487.20=8000x1.033

92.68098240=8000x1.032

73.727280001

10% @ PVFlowCash Year

4

3

2

10.182.87413

10.120.84872

10.18240

1.108000


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Inflation

Example - real figures

Year Cash Flow [email protected]%

1 = 7766.99

2 = 7766.99

= 7766.99

= 7766.99

80001.03

7766.991.068

82401.03

8487.201.03

8741.821.03

2

3

4

7272 73

6809 92

3 6376 56

4 5970 78

26 429 99

7766 991 068

7766 991 068

7766 991 068

2

3

4

.

.

.

.

..

..

..

= $ , .


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IM&C’s Guano Project

Revised projections ($1000s) reflecting inflation

0 1 2 3 4 5 6 7

1 Capital Investment 10,000 (1,949) 2 Accumulated depreciation 1,583 3,167 4,750 6,333 7,917 9,500 - 3 Year-end book value 10,000 8,417 6,833 5,250 3,667 2,083 500 - 4 Working capital 550 1,289 3,261 4,890 3,583 2,002 - 5 Total book value (3+4) 10,000 8,967 8,122 8,511 8,557 5,666 2,502 - 6 Sales 523 12,887 32,610 48,901 35,834 19,717 7 Cost of goods sold 837 7,729 19,552 29,345 21,492 11,830 8 Other Costs 4,000 2,200 1,210 1,331 1,464 1,611 1,772 9 Depreciation 1,583 1,583 1,583 1,583 1,583 1,583

10 Pretax profit (6-7-8-9) (4,000) (4,097) 2,365 10,144 16,509 11,148 4,532 1,449 11 Tax at 35% (1,400) (1,434) 828 3,550 5,778 3,902 1,586 507 12 Profit after tax (10-11) 2,600 (2,663) 1,537 6,595 10,731 7,246 2,946 942

Period


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Cash flow analysis ($1000s)

0 1 2 3 4 5 6 71 Sales 523 12,887 32,610 48,901 35,834 19,717 2 Cost of goods sold 837 7,729 19,552 29,345 21,492 11,830 3 Other costs 4,000 2,200 1,210 1,331 1,464 1,611 1,772 4 Tax on operations (1,400) (1,434) 828 3,550 5,778 3,902 1,586

5Cash flow from operations (1-2-3-4) (2,600) (1,080) 3,120 8,177 12,314 8,829 4,529

6 Change in working capital (550) (739) (1,972) (1,629) 1,307 1,581 2,002 7 Capital investment and (10,000) 1,442 8 Net cash flow (5+6+7) (12,600) (1,630) 2,381 6,205 10,685 10,136 6,110 3,444 9 Present value at 20% (12,600) (1,358) 1,654 3,591 5,153 4,074 2,046 961

Period

Net Present value= +3520 (sum of 9)


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NPV using nominal cash flows

$3,520,000or 520,3

20.1

444,3

20.1

110,6

20.1

136,10

20.1

685,10

20.1

205,6

20.1

381,2

20.1

630,1600,12

76

5432

NPV


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Details of cash flow forecast in year 3 ($1000s)


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Tax depreciation allowed under the modified accelerated cost recovery system (MACRS) (Figures in percent of depreciable investment)

Year(s) 3-Year 5-Year 7-Year 10-Year 15-Year 20-Year

1 33.33 20 14.29 10 5 3.752 44.45 32 24.49 18 9.5 7.223 14.81 19.2 17.49 14.4 8.55 6.684 7.41 11.52 12.49 11.52 7.7 6.185 11.52 8.93 9.22 6.93 5.716 5.76 8.92 7.37 6.23 5.287 8.93 6.55 5.9 4.898 4.45 6.55 5.9 4.529 6.56 5.9 4.46

10 6.55 5.9 4.4611 3.29 5.9 4.4612 5.9 4.4613 5.91 4.4614 5.9 4.4615 5.91 4.4616 2.99 4.46

17-20 4.4621 2.23

Tax Depreciation Schedules by Recovery-Period Class


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Tax Payments ($1000s)

0 1 2 3 4 5 6 71 Sales 523 12,887 32,610 48,901 35,834 19,717 2 Cost of goods sold 837 7,729 19,552 29,345 21,492 11,830 3 Other Costs 4,000 2,200 1,210 1,331 1,464 1,611 1,772 4 Tax depreciation 2,000 3,200 1,920 1,152 576 5 Pretax profit (1-2-3-4) (4,000) (4,514) 748 9,807 16,940 11,579 5,539 1,949 6 Taxes at 35% (1,400) (1,580) 262 3,432 5,929 4,053 1,939 682

Period


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Revised cash flow analysis ($1000s)

0 1 2 3 4 5 6 71 Sales 523 12,887 32,610 48,901 35,834 19,717 2 Cost of goods sold 837 7,729 19,552 29,345 21,492 11,830 3 Other costs 4,000 2,200 1,210 1,331 1,464 1,611 1,772 4 Tax (1,400) (1,580) 262 3,432 5,929 4,053 1,939 682

5Cash flow from operations (1-2-3-4) (2,600) (934) 3,686 8,295 12,163 8,678 4,176 (682)

6 Change in working capital (550) (739) (1,972) (1,629) 1,307 1,581 2,002

7Capital investment and disposal (10,000) 1,949

8 Net cash flow (5+6+7) (12,600) (1,484) 2,947 6,323 10,534 9,985 5,757 3,269

9Present Value= +3802 (sum of 9) (12,600) (1,237) 2,047 3,659 5,080 4,013 1,928 912

Period

Net present value= +3802 (sum of 9)


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Equivalent Annual Cost

Equivalent Annual Cost - The cost per period with the same present value as the cost of buying and operating a machine.


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Equivalent Annual Cost - The cost per period with the same present value as the cost of buying and operating a machine.

Equivalent annual cost =present value of costs

annuity factor


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Example

Given the following costs of operating two machines and a 6% cost of capital, select the lower cost machine using equivalent annual cost method.

Year

Machine 1 2 3 4 PV@6% EAC

A 15 5 5 5 28.37 10.61

B 10 6 6 21.00 11.45



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Timing

Even projects with positive NPV may be more valuable if deferred.

The actual NPV is then the current value of some future value of the deferred project.

tr

t

)1(

date of as valuefutureNet NPVCurrent


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Timing

Example

You may harvest a set of trees at anytime over the next 5 years. Given the FV of delaying the harvest, which harvest date maximizes current NPV?

9.411.915.420.328.8 valuein change %

109.410089.477.564.450($1000s) Net FV

543210

YearHarvest


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Timing

Example - continuedYou may harvest a set of trees at anytime over the next 5 years. Given the FV of delaying the harvest, which harvest date maximizes current NPV?

5.581.10

64.41 year in harvested if NPV


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Timing

Example - continuedYou may harvest a set of trees at anytime over the next 5 years. Given the FV of delaying the harvest, which harvest date maximizes current NPV?

5.581.10

64.41 year in harvested if NPV

67.968.367.264.058.550($1000s) NPV

543210

YearHarvest


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Fluctuating Load Factors

$30,00015,0002machines twoofcost operating PV

$15,0001,500/.10pachineper cost operating PV

$1,5007502machineper cost Operating

units 750machineper output Annual

MachinesOld Two


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$27,000500,132machines twoofcost operating PV

$13,500750/.106,000pachineper cost operating PV

$7507501machineper cost Operating

000,6$machineper cost Capital

units 750machineper output Annual

Machines New Two


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000,26..$..............................machines twoofcost operating PV

$16,000.10/000,16,000$10,000,000/.101machineper cost operating PV

$1,000000,11$1,0005002machineper cost Operating

000,6$0machineper cost Capital

units 1,000units 500machineper output Annual

Machine New OneMachine Old One


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Web Resources

www.investopedia.com/calculator/NetPresentValue.aspx

www.finalyst.com/

www.toolkit.cch.com/text/P06_6530.asp

Click to access web sitesClick to access web sites

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Chapter 6 Principles of Corporate Finance Eighth Edition Making Investment Decisions With the Net Present Value Rule Slides by Matthew Will Copyright ©

Documents

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s reflecting inflation

discount estimate cash

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