Mod 14 - ROI

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Michael R. Roberts

William H. Lawrence Professor of Finance

The Wharton School, University of Pennsylvania

Return on Investment

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Last TimeDiscounted Cash Flow (DCF) Decision making Free cash flow Forecast drivers

Forecasting free cash flow Sensitivity analysis Decision criteria

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9

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This TimeReturn on investment IRR versus NPV

IRR

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REC LL

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The internal rate of return of an asset is theone discount rate such that the NPV of theassets free cash flows equals zero.

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;

The internal rate of return of an asset is theone discount rate such that the NPV of theassets free cash flows equals zero.

NPV =CF

1

1+ IRR( )+

CF2

1+ IRR( )2 +

CF3

1+ IRR( )3 + ...+

CFT

1+ IRR( )T =0

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The IRR Decision Rule says accept allprojects whose IRR > R, reject all projectswhose IRR < R where Ris the hurdle rate

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Rates of return are popular measures usedfor making decisions

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0%20%

40%60%

80%

Internal rate of return

Net present value

Payback

Discounted payback

Accounting rate of return

Profitability index

? @2*A3)B 9CC#B D-3 .-3'*) 2>? (*21E13 'F 1'*('*2.3

G>2>13H IA+?3>13 F*'= .-3 G34?B!"#$%&' ") *+%&%,+&' -,"%".+,/

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K-2. ?' L*+A2.3 IMN+.) O+*=8 P2) .-3) Q'R SL2N4

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!

Lesson: The IRR rule leads to thesame decisions accept or reject asthe NPV rule if all negative cash flows

precede all positive cash flows

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Examples of CF sequences where IRRand NPV rules will coincide:-, +, +, +, +-, -, -, +, +, +, +, +, +-, -, -, -, - , +

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X

Examples of CF sequences where IRRand NPV rules may not coincide:-, +, -, +, -, +

+, +, +, +, +, +, -, -, -, --, +, +, +, +, -

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Can we compare projects using IRR?

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Y

Comparing Projects

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Wharton wants to upgrade IT systemand overhaul network infrastructure

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#C

Wharton wants to upgrade IT systemand overhaul network infrastructure

Puts out request for proposals (RFP)

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Bid #1 from Cisco

Generate $60 million in cost savingsover three years for up front cost of$100 million

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##

Bid #1 from CiscoGenerate $60 million in cost savingsover three years for up front cost of$100 million

If Whartons cost of capital is 12%,what is your assessment of this bid?

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Bid #1 from Cisco


Cash flows first:

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#9


0 = !100+60

1+ IRR( )+

60

1+ IRR( )2 +

60

1+ IRR( )3

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Bid #1 from Cisco


IRR > Rand CFs signs proper!Looks good!

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NPV =!100+60

1+ 0.12( )+

60

1+ 0.12( )2 +

60

1+ 0.12( )3

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Bid #1 from Cisco


NVP > 0!Looks good!

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Bid #1a from CiscoSame cost savings ($60 mil over threeyears) but costs spread over time: $20mil today, $35 mil over three years

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Bid #1a from Cisco

Same cost savings ($60 mil over threeyears) but costs spread over time: $20mil today, $35 mil over three years

Cash flows first:

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Cash flows first:

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Bid #1a from Cisco


Cash flows first:

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#J


0 = !20+25

1+ IRR( )+

25

1+ IRR( )2 +

25

1+ IRR( )3

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Bid #1a from Cisco


Bid #1a IRR (112%) > Bid #1 IRR (36%)

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#!


NPV =!20+25

1+ 0.12( )+

25

1+ 0.12( )2 +

25

1+ 0.12( )3

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Bid #1a from Cisco


Bid #1 NPV ($44.11) > Bid #1a NPV ($40.05)

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#X

What is going on?

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NPV!Bid #1 is better

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#Y

NPV!Bid #1 is better

IRR!Bid #1a is better

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A closer look

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9C

A closer look

Bid 1a incorporates a loan from Cisco

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A closer look

Bid 1a incorporates a loan from CiscoWhat is the interest rate?

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9#

A closer look

80 =35

1+R( )+

35

1+R( )2 +

35

1+R( )3 !R= 15%

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A closer look

0 = !80+35

1+ IRR( )+

35

1+ IRR( )2 +

35

1+ IRR( )3" IRR= 15%

Note: This is also the IRRof the loan

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99

A closer look

Note: This is also the Yield-to-Maturityof the loan

80=35

1+YTM( )+

35

1+YTM( )2 +

35

1+YTM( )3 !YTM = 15%

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A closer look

Is this high or low?

80=35

1+YTM( )+

35

1+YTM( )2 +

35

1+YTM( )3!YTM = 15%

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A closer look

Loan interest rate (15%) > Cost of Capital (12%)

80=35

1+YTM( )+

35

1+YTM( )2 +

35

1+YTM( )3 !YTM = 15%

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Lesson: IRR increased because initialinvestment fell more than future cash flows.

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9;

Lesson: IRR increased because initialinvestment fell more than future cash flows.

(Intuition: Small payoffs on a smaller

investment can generate very large returnsbecause of division by small numbers.)

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Lesson: NPV fell because Cisco is lendingyou money at an interest rate that is greaterthan your cost of capital.

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Lesson: IRR can mislead when decidingamong projects.

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Lesson: NPV wi l l not mislead incomparisons. The larger the NPV, thegreater the value

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9J

DDITION L BIDS

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9!

How would you rank the bids according

to the IRR and the NPV criterion?

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9X

IRR: #3 > #2 > #1

NPV: #1 > #2 > #3

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9Y

Intuition:Huawei has small upfront cost!IRR "Juniper has front-loaded CFs!IRR "

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Lesson: IRR does not address differencesin scale.

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:C

Lesson: IRR does not address differencesin scale.

Would you rather earn 100% on a $1

investment or 10% on a $1,000,000investment?

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Intuition:Junipers bid is like Ciscos with anembedded loan

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Intuition:Junipers bid is like Ciscos with anembedded loanwith a 23% interest rate!

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Summary

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:9

Lessons

The internal rate of return of an asset isthe one discount rate such that the NPVof the assets free cash flows equalszero.

The IRR Decision Rule says accept all

projects whoseIRR

>R

, reject allprojects whose IRR < R where R is thehurdle rate

NPV =CF

1

1+ IRR( )+

CF2

1+ IRR( )2 +

CF3

1+ IRR( )3 + ...+

CFT

1+ IRR( )T =0

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Lessons IRR Rule can mislead decision making

when cash flow signs are anything otherthan all negatives before all positives

IRR Rule can mislead decision makingwhen comparing projects even when

cash flow signs are proper.IRR does not account for differences in

scale

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Lessons

IRR should be used in conjunctionwith NPV analysis

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Coming up next Fixed Income Securities

Institutional environment

Valuation

Risk analysis

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Mod 14 - ROI

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