Net Present Value and Other Investment Criteria

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Investment Criteria

Business 2039

1K. Hartviksen

This Chapter - Topics

Net Present ValuePayback Period

Multiple IRRsMutually Exclusive y

Discounted PaybackAverage Accounting

yInvestments (NPV vs. IRR)g g

ReturnInternal Rate of

Profitability Indexcapital rationing

Return

2K. Hartviksen

Long-Term Investments

When a firm considers a new project, corporate acquisition, plant expansion or asset acquisition that will produce income over the course of manywill produce income over the course of many years…this is called capital budgeting.It is imperative that in the analysis of such projects p y p jthat we consider the timing, riskiness and magnitude of the incremental, after-tax cashflows that the project is expected to generate for the firmis expected to generate for the firm.

Payback Method

This is a simple approach to capital budgeting that is d i d t t ll h it ill t k tdesigned to tell you how many years it will take to recover the initial investment.It is often used by financial managers as one of a setIt is often used by financial managers as one of a set of investment screens, because it gives the manager an intuitive sense of the project’s risk.

Payback Example

Initial cost = 100000AT cash flow benefits = 60000Useful life(years) = 5Cost of Capital = N/A

CumulativeCashflow After-tax incremental CF PV Factor Cash FlowsInitial cost -100000 -$100,000ATCF ti b fit 60000 $40 000ATCF operating benefit 60000 -$40,000ATCF operating benefit 60000 $20,000ATCF operating benefit 60000 ATCF operating benefit 60000 ATCF operating benefit 60000ATCF operating benefit 60000ATCF operating benefit 60000

Payback period = 1.7 years

Discounted Payback Example

A T cash flow benefits = 60000Useful life(years ) = 5Cos t of Capital = 0.1 Cum ulative

P V DiscountedY ear Cashflow A fter-tax inc rem ental CF P V Fac tor Cash F lows Cash flows

0 Init ial cos t -100000 1 -$100,000 -$100,0001 A TCF operating benefit 60000 0.9090909 $54,545 -$45,4552 A TCF operating benefit 60000 0 8264463 $49 587 $4 1322 A TCF operating benefit 60000 0.8264463 $49,587 $4,1323 A TCF operating benefit 60000 0.7513148 $45,079 $49,2114 A TCF operating benefit 60000 0.6830135 $40,981 $90,1925 A TCF operating benefit 60000 0.6209213 $37,255 $127,4476 A TCF operating benefit 60000 0.5644739 $33,868 $161,316

P ayback period (years )= 1.916671708

Discounted Payback Graphed

NPV$$ Discounted Payback

Point

Years

Discounted Payback

Overcomes the lack of consideration of the time value of money…ycan help us see the pattern of cashflows beyond the payback pointbeyond the payback point.If carried to the end of the project’s useful life will tell us the project’s NPVuseful life…will tell us the project s NPV (if you are using the firm’s WACC)

Net Present Value

NPV = -PV of initial cost + PV of incremental after-tax benefits= if greater than 0 - accept= if equal to 0 indifferent= if equal to 0 - indifferent= if less than 0 - reject

Firm’s Cost of Capital

At this point in the course, you will be given the firm’s cost of capitalcost of capitalthe firm’s cost of capital determines the minimum rate of return that would be acceptable for a capital p pproject.The weighted average cost of capital (WACC) is the relevant discount rate for NPV analysisrelevant discount rate for NPV analysis.

NPV ExampleI iti l t 100000Initial cost = 100000AT cash flow benefits = 60000Useful life(years) = 6Cost of Capital = 0.12

Year Cashflow After-tax incremental CF PV Factor Present Value0 Initial cost -100000 1 -$100,0001 ATCF operating benefit 60000 0.892857 $53,5712 ATCF operating benefit 60000 0 797194 $47 8322 ATCF operating benefit 60000 0.797194 $47,8323 ATCF operating benefit 60000 0.71178 $42,7074 ATCF operating benefit 60000 0.635518 $38,1315 ATCF operating benefit 60000 0.567427 $34,0466 ATCF operating benefit 60000 0.506631 $30,398p g ,

NPV = $146,684

NPV ExampleInitial cost = 100000AT cash flow benefits = 60000Useful life(years) = 6Cost of Capital = 0

Year Cashflow After-tax incremental CF PV Factor Present Value0 Initial cost -100000 1 -$100,0001 ATCF operating benefit 60000 1 $60,0002 ATCF ti b fit 60000 1 $60 0002 ATCF operating benefit 60000 1 $60,0003 ATCF operating benefit 60000 1 $60,0004 ATCF operating benefit 60000 1 $60,0005 ATCF operating benefit 60000 1 $60,0006 ATCF operating benefit 60000 1 $60 0006 ATCF operating benefit 60000 1 $60,000

NPV = $260,000

NPV Example

Initial cost = 100000AT cash flow benefits = 60000Useful life(years) = 6Cost of Capital = 0.05

Year Cashflow After-tax incremental CF PV Factor Present Value0 Initial cost -100000 1 -$100,0001 ATCF ti b fit 60000 0 952381 $57 1431 ATCF operating benefit 60000 0.952381 $57,1432 ATCF operating benefit 60000 0.907029 $54,4223 ATCF operating benefit 60000 0.863838 $51,8304 ATCF operating benefit 60000 0.822702 $49,3625 ATCF operating benefit 60000 0 783526 $47 0125 ATCF operating benefit 60000 0.783526 $47,0126 ATCF operating benefit 60000 0.746215 $44,773

NPV = $204,542

NPV Example

Initial cost = 100000AT cash flow benefits = 60000Useful life(years) = 6Cost of Capital = 0.15

Year Cashflow After-tax incremental CF PV Factor Present Value0 Initial cost -100000 1 -$100,0001 ATCF ti b fit 60000 0 869565 $52 1741 ATCF operating benefit 60000 0.869565 $52,1742 ATCF operating benefit 60000 0.756144 $45,3693 ATCF operating benefit 60000 0.657516 $39,4514 ATCF operating benefit 60000 0.571753 $34,3055 ATCF operating benefit 60000 0 497177 $29 8315 ATCF operating benefit 60000 0.497177 $29,8316 ATCF operating benefit 60000 0.432328 $25,940

NPV = $127,069

NPV Example

Initial cost = 100000AT cash flow benefits = 60000Useful life(years) = 6Cost of Capital = 0.3

Year Cashflow After-tax incremental CF PV Factor Present Value0 Initial cost -100000 1 -$100,0001 ATCF ti b fit 60000 0 769231 $46 1541 ATCF operating benefit 60000 0.769231 $46,1542 ATCF operating benefit 60000 0.591716 $35,5033 ATCF operating benefit 60000 0.455166 $27,3104 ATCF operating benefit 60000 0.350128 $21,0085 ATCF operating benefit 60000 0 269329 $16 1605 ATCF operating benefit 60000 0.269329 $16,1606 ATCF operating benefit 60000 0.207176 $12,431

NPV = $58,565

NPV Example

Initial cost = 100000AT cash flow benefits = 60000Useful life(years) = 6Cost of Capital = 0.5581

Year Cashflow After-tax incremental CF PV Factor Present Value

0 Initial cost -100000 1 -$100,0001 ATCF ti b fit 60000 0 641807 $38 5081 ATCF operating benefit 60000 0.641807 $38,5082 ATCF operating benefit 60000 0.411917 $24,7153 ATCF operating benefit 60000 0.264371 $15,8624 ATCF operating benefit 60000 0.169675 $10,1815 ATCF operating benefit 60000 0 108899 $6 5345 ATCF operating benefit 60000 0.108899 $6,5346 ATCF operating benefit 60000 0.069892 $4,194

NPV = -$6

NPV Example

Initial cost = 100000AT cash flow benefits = 60000Useful life(years) = 6Cost of Capital = 0.7

Year Cashflow After-tax incremental CF PV Factor Present Value

0 Initial cost -100000 1 -$100,0001 ATCF ti b fit 60000 0 588235 $35 2941 ATCF operating benefit 60000 0.588235 $35,2942 ATCF operating benefit 60000 0.346021 $20,7613 ATCF operating benefit 60000 0.203542 $12,2124 ATCF operating benefit 60000 0.11973 $7,1845 ATCF operating benefit 60000 0 07043 $4 2265 ATCF operating benefit 60000 0.07043 $4,2266 ATCF operating benefit 60000 0.041429 $2,486

NPV = -$17,837

NPV ProfileNPV

$

IRR

Discount Rate0

Discount Rate

NPV Profiles

The slope of the NPV profile depends on the timing and magnitude of g gcashflows.Projects with cashflows that occur lateProjects with cashflows that occur late in the project’s life will have an NPV that is more sensitive to discount rateis more sensitive to discount rate changes.

IRR

The internal rate of return (IRR) is that discount rate that causes the NPV of the project to equal zero.If IRR > WACC, then the project is acceptable b it ill t t f tbecause it will return a rate of return on invested capital that is likely to be greater than the cost of funds used to invest in thethan the cost of funds used to invest in the project.

IRR ExampleTime Type of Cash Flow ATCF

0 Initial Project cost = -560001 Incremental ATCF Benefit= 50001 Incremental ATCF Benefit 50002 Incremental ATCF Benefit= 100003 Incremental ATCF Benefit= 150004 Incremental ATCF Benefit= 200004 Incremental ATCF Benefit 200005 Incremental ATCF Benefit= 25000

IRR = 8%

IRR Example

Time Type of Cash Flow ATCF ATCF ATCF0 Initial Project cost = -56000 -56000 -560001 Incremental ATCF Benefit= 5000 25000 100002 Incremental ATCF Benefit= 10000 20000 100003 Incremental ATCF Benefit= 15000 15000 100004 Incremental ATCF Benefit= 20000 10000 100005 Incremental ATCF Benefit= 25000 5000 10000

IRR = 8% 14% -4%

IRR vs. NPV

Both methods use the same basic decision inputs.pThe only difference is the assumed discount ratediscount rate.The IRR assumes intermediate cashflows are reinvested at IRR NPVcashflows are reinvested at IRR…NPV assumes they are reinvested at WACC

NPV ProfileNPV

$

IRR(B)IRR(A)

Discount Rate

( )

0

( )

Discount Rate

Profitability Index

Uses exactly the same decision inputs as NPV simply expresses the relative profitability of the

j t i t l ft t hfl b fitprojects incremental after-tax cashflow benefits as a ratio to the project’s initial cost.

PI = PV of incremental ATCF benefitsPV of initial cost of project

If PI>1, then we accept; because the PV of benefits exceeds the PV of costs.

Capital Rationing

The corporate practice of limiting the amount of funds dedicated to capital pinvestments in any one year.Is academically illogicalIs academically illogical.In the long-run could threaten a firm’s continuing existence through erosion ofcontinuing existence through erosion of its competitive position.