lecture 05-06 other investment criteria(1)

8/17/2019 Lecture 05-06 Other Investment Criteria(1)

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Professor Sang Byung [email protected]

Other investment criteria



Last class

• Finish the remainder of Lecture 03• Compounding frequencies

• Investment criteria• NPV rule

• Fisher Separation theorem



Today

•

Problem set #1 review

• Other investment criteria

• Internal rate of return (IRR)

• Payback period

• Profitability index

• How do CFOs make capital budgeting decision?

• Problem set #2

• Will be posted at 7 PM today on Blackboard

• Due by Feb 8th (Monday) 11:59 PM CST



NPV rule

•NPV rule• Accept projects with NPV>0

• Reject otherwise

• Competitors of the NPV rule

• Internal rate of return (IRR)

•Payback period

• Average accounting return



Internal rate of return

•

Definition• The rate of return such that the NPV = 0

• That is, IRR solves

0 =

(1 )

1

1 …

• For example, = −100 and = 110

= −100 110

1 = 0

= 110/100 − 1 = 10%



IRR: Example

• You can purchase a machine for $4,000. Thismachine will generate $2,000 and $4,000 in

cash flows for the following two years.

• What is the IRR on the investment?

= −4000 2000

1

4000

1 = 0



NPV profile

•

NPV profile• The graph that

illustrates a project's

NPV against various

discount rates• y-axis: NPV

• x-axis: discount rate

• For example,

• r = 0% NPV = $2,000

• r = 50% NPV = -$889



How to compute IRR?

•How to compute the IRR in practice?1. Trial-and-error (time consuming…)

2. Use a financial calculator

3. Use excel IRR function – IRR(values,guess)4. Use excel Goal-seek

• Let’s see how we can do this using excel!



Interpretation of IRR

•Return?• People like to think of IRR as the rate of return on their

investment.

• This is incorrect!

• In fact, IRR = actual return on investment only

if you can reinvest the intermediate cash flows

at IRR.

• Remember IRR is just the rate that makes the NPV equal to zero

• It can be very different from the discount rate or the

reinvestment rate.



IRR = ROI?

•In the previous example,

• At year 2, we receive

•

$4,000• $2,000 1 0.2808 = $2561.6 (assuming we can reinvest at IRR)

• Initial investment $4,000 $6,561.6 after two years

• $4,000 1 = $6,561.6

• Return on the investment (ROI) =,.

, − 1 = 0.2808 =



IRR = ROI?

•

IRR = HPR?

• Yes! Because we assume that we can reinvest theintermediate cash flow $2,000 at IRR.

• However, this assumption might be unrealistic!

• For example, what if the discount rate today and the futurereinvestment rate are just 5%?

• ROI = ,+,(.),

− 1 = 0.2349 <

• Then, what is the significance of IRR?

•The IRR rule!



IRR rule

•NPV rule• Accept projects with NPV > 0

• Reject otherwise

• IRR rule

• Accept projects with IRR > r (discount rate)

•

Reject otherwise



• In many cases,

• The NPV rule and the IRR rule give us the same result!

IRR rule and NPV rule

Accept

Reject

NPV> 0IRR > r

NPV< 0

IRR < r



IRR rule and NPV rule

•

Why the two rules generate the same result?• IRR rule: accept an investment project if the opportunity

cost of capital (discount rate) is less than the IRR.

• If the discount rate is smaller than 28%, NPV > 0

• If the discount rate is equal to 28%, NPV = 0

• If the discount rate is larger than 28%, NPV < 0

• When do they give the same results?

• Whenever the NPV profile shows a smoothly decreasingfunction!

• That is, when the NPV smoothly decreases when the

discount rate increases.



When the two rules are same?

• Suppose future cash flows are all nonnegative.

• i.e. ≥ 0 where = 1,2,3, …

=

( 1 )

1

1 …

• If becomes larger,

•

(+),

+ ,

+ , … get smaller, so the NPV gets smaller.

• When do NPV and IRR give the same answer?

• When NPV is a decreasing function of discount rate

• When future cash flows are all nonnegative

• More generally, when cash flows start out negative and switch to positive



When the two rules are different?

1. When the signs of future cash flows are mixed• For example, positive for the first few and then negative

• In this case, NPV is not decreasing in discount rate.

1) IRR can give the wrong answer.2) Sometimes there are multiple IRRs.

3) There are cases where no IRR exists.

• In contrast, the NPV rule is always right!

2. When choosing from among mutually

exclusive projects



Simple example

•For example, = 100, = −110, = 5%• The IRR rule

0 = 100 −110

1

=110

100− 1 = 10% > 5% ()

• The NPV rule

= 100 −110

1.05 = −4.76 < 0 ()



Two exactly opposite projects

•Two opposite projects

• Different results

• IRR rule: accept both projects (which is bad)

• NPV rule: accept Project 1.

IRR NPV at 5%

Project 1 -$4,000 $2,000 $4,000 28% $1,532.88

Project 2 $4,000 -$2,000 -$4,000 28% -$1,532.88



Multiple IRRs

• Example

• Assume a 10% discount rate.

• NPV = $0.2529

• IRR -- there are two discount rates that make NPV = 0.

0 = −3 1

1.035

1

1.035 ⋯

1

1.035 –

6.5

1.035

0 = −3 1

1.1954

1

1.1954 ⋯

1

1.1954 –

6.5

1.1954

• Both 3.5% and 19.54% are IRRs.

Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10

-$3 $1 $1 $1 $1 $1 $1 $1 $1 $1 -$6.5



Multiple IRRs

•NPV profile



No IRR

•For example, = 1,000, = −3,000, = 2,500

• NPV at 10% = 339

•

IRR does not exist



Mutually exclusive projects

•

Suppose that we have two projects:

• Which one should we choose?

•

Project 1 -- because its has the higher NPV!• However, Project 2 has the higher IRR.

• IRR is unreliable in ranking projects!

IRR NPV at 10%

Project 1 -$20,000 $35,000 75% $11,818

Project 2 -$10,000 $20,000 100% $8,182



Another example

•Consider the two projects:

• Note that Project 2 generates cash flows forever.

• Different results

• NPV rule Project 2

• IRR rule Project 1

… IRR NPV at 10%

Project 1 -$9K $6K $5K $4K 0 0 … 33% $3,592

Project 2 -$9K $1.8K $1.8K $1.8K $1.8K $1.8K …. 20% $9,000



Why is this happening?

Project 1

Project 2



Payback period

•How long does it take the project to “pay back”its initial investment?

•

Payback period= # of years to recover the initial period

• The Payback rule

• Accept a project if its payback period is less than some

specified cutoff period.



Example (revisited)

•

Consider again the two projects.

• Payback period

• Project 1 -- 2 years

• Project 2 -- 5 years

• The payback rule with a cutoff period of 3 years

•Choose Project 1

… IRR NPV at 10%

Project 1 -$9K $6K $5K $4K 0 0 … 33% $3,592

Project 2 -$9K $1.8K $1.8K $1.8K $1.8K $1.8K …. 20% $9,000



Another example

•

Examine the following the following threeprojects and note the mistake we make if we

insisted on only taking projects with a payback

period of 2 years or less.



Answer

• Project A

• NPV = $2,624.34

• IRR = 51.08%

• 3-year payback period

• Project B

• NPV = -$57.85

• IRR = 8.19%

• 2-year payback period

• Project C

• NPV = $49.59

• IRR = 12.27%

•

2-year payback period



Payback rule

•

What is it bad?• It ignores all cash flows after the cutoff date.

• It gives equal weight to all cash flows before the cutoff

date.

• Why do many companies still use it?

• Simple

• Easy way to communicate an idea of project profitability

• Small firms with limited access to capital may worry

about their future ability to raise capital.



Discounted payback rule

•

Discount cash flows before computing thepayback period!

•

Pros: this rule will never accept a negative NPVproject!

•

Cons: it still takes no account of cash flowsafter the cutoff date.

• The discounted payback rule will reject Project A.



When resources are limited

•

So far, we have assumed that there is nolimitation on capital.

•

What if we have a limited budget but severalprojects to choose from — which projects should

we choose?

• This situation is called capital rationing.



Profitability index

•

The profitability index (PI) method provides atool for choosing among various project

combinations:

=

• The highest weighted average PI (WAPI)

indicates which project or which combinationof projects to choose.



Example

•

You are the CFO of a company with fourprojects (A, B, C, and D). The company has

only $300,000 available for investment. Which

projects do you choose?

E h j ’ PI



Each project’s PI

•

First, calculate each project’s PI.

W i ht d PI (WAPI)



Weighted average PI (WAPI)

= 1.15 ×200

300 0 ×

100

300 = 0.77

= 1.13 × 125300

1.11 × 175300

= 1. 12

= 1.13 ×125

300 1.08 ×

150

300 0 ×

25

300 = 1.01

Ch bi ti



Choose a combination

• Select project(s) with the highest WAPI:

• WAPI(A) = 0.77

• WAPI(BC) = 1.12

• WAPI(BD) = 1.01

H d CFO k d i i ?



How do CFOs make decisions?

•

“How do CFOs Make Capital Budgeting andCapital Structure Decisions?” Journal of

Applied Corporate Finance by John Graham and

Campbell Harvey

S



Survey

•

Mailed to CFOs of all (1998) Fortune 500companies and also faxed 4,440 firms with

officers who are members of the Financial

Executives Institute

• About 100 questions

• 392 responses

C it l b d ti th d



Capital budgeting methods

Fi di



Findings

•

Companies more likely to use NPV or IRR if:• Large and publicly traded

• Highly levered

•

Utilities• Companies whose CEOs have MBAs

•

56.7% often used the payback period! Why?• Simplicity?

• Useful for firms that are severely financially constrained

and can’t raise money easily

lecture 05-06 other investment criteria(1)

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