8/3/2019 lock_sol

1/31

Capital Budgeting Decision Rules

What real investments should

firms make?

8/3/2019 lock_sol

2/31

Alternative Rules in Use Today NPV

IRR Profitability Index

Payback Period Discounted Payback Period

Accounting Rate of Return

8/3/2019 lock_sol

3/31

NPV Analysis The recommended approach to any significant

capital budgeting decision is NPV analysis.

NPV = PV of the incremental benefits PV ofthe incremental costs.

When evaluating independent projects, take aproject if and only if it has a positive NPV.

When evaluating interdependent projects, take thefeasible combination with the highest total NPV.

The NPV rule appropriately accounts for theopportunity cost of capital and so ensures theproject is more valuable than comparable

alternatives available in the financial market.

8/3/2019 lock_sol

4/31

Lockheed Tri-Star As an example of the use of NPV analysis we

will use the Lockheed Tri-Star case.

To examine the decision to invest in the Tri-Star project, we first need to forecast thecash flows associated with the Tri-Starproject for a volume of 210 planes.

Then we can ask: What is a valid estimate ofthe NPV of the Tri-Star project at a volume of210 planes as of 1967.

8/3/2019 lock_sol

5/31

Lockheed Tri-Star Key Points

Pre-production costs estimated at $900 million

incurred between 1967 and 1971.

Total of 210 planes delivered from 1972-1977

Revenues of $16 million per unit, 25% of revenue

received 2 years in advance of delivery.

Production costs of $14 million (at 210 units coulddecline to $12.5 million at 300) from 1971-1976.

Discount rate of 10% per year.

8/3/2019 lock_sol

6/31

Tri-Star Cash Flows 210 planes (1972-1977)

Planes per year = 210/6=35

Production Costs (1971-1976) 35($14M)=$490M per year

Dont forget the preproduction costs of $900M

Revenues (1970-1977) Total Revenues 35($16M)=$560M per year Deposits=0.25($560M)=$140M (2 yrs in advance)

Net Revenues=$560-$140=$420M on delivery

8/3/2019 lock_sol

7/31

Year 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977

Pre

Prod.

-100 -200 -200 -200 -200

Costs -490 -490 -490 -490 -490 -490Dep. 140 140 140 140 140 140Revs. 420 420 420 420 420 420

TotalCash

Flow

-100 -200 -200 -60 -550 70 70 70 70 -70 420

TriTri--Star Cash FlowsStar Cash Flows

(210 Planes)(210 Planes)

8/3/2019 lock_sol

8/31

Tri-Star NPV @10% in 1967

Million

NPV

584$

)10.1(

420

)10.1(

70

)10.1(

70

)10.1(

70

)10.1(

70

)10.1(

70

)10.1(

550

)10.1(

60

)10.1(

200

)10.1(

200

100

109876

5432

!

!

8/3/2019 lock_sol

9/31

Accounting Profits at 210 Production revenues are $16M per plane and

production costs are $14M per plane. Profit is $2Mper plane.

210$2M = $420M production profits. $420M vs.$900M preproduction costs is breakeven?

Suppose production cost is $12.5M per plane(learning curve hits early). Profit per plane is $3.5M.A

t 210 planes this is $735M production profit. Now take the extreme low-end of the $800M - $1B

preproduction cost range.

Suddenly you have breakeven. Smart huh?

8/3/2019 lock_sol

10/31

Tri-Star NPV 1967 ($Millions)

Units Sold Average

Unit Cost

Accounting

Profit

NPV

323 $12.25 $311 -$195

400 $12.00 $700 -$12

400 $11.75 $800 $42

500 $11.00 $1,600 $441

8/3/2019 lock_sol

11/31

Year 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977

Pre

Prod.

-200

Costs -490 -490 -490 -490 -490 -490Dep. 140 140 140 140 140 140Revs. 420 420 420 420 420 420

TotalCash

Flow

0 0 0 140 -550 70 70 70 70 -70 420

TriTri--Star Cash Flows 1970Star Cash Flows 1970

(210 Planes)(210 Planes)

8/3/2019 lock_sol

12/31

1970 Tri1970 Tri--Star NPV @10%Star NPV @10%

Million

NPV

18$

)10.1(

420

)10.1(

70

)10.1(

70

)10.1(

70

)10.1(

70

)10.1(

70

)10.1(

550140

76

5432

!

!

8/3/2019 lock_sol

13/31

Tri Star Post Mortem Accounting breakeven approximately 275 planes

$16M - $12.5M = $3.5M per plane $3.5Mv275 = $962M profit versus $960M in actual

development costs known in 1970 This more realistic breakeven level announced subsequent

to the guarantees being granted.

NPV breakeven approximately 400 planes Total free world market demand for wide-body aircraft

approximately 325 planes Optimistic estimate: total demand 775 and 40% of that is 310

Lockheed share price $64 Jan 1967 drops to $11 Jan 1971 ($64-$11)(11.3 Million shares)=-$599 Million

Compare to -$584 Million NPV

8/3/2019 lock_sol

14/31

Internal Rate of Return Definition: The discount rate that sets the NPV of a

project to zero (essentially project YTM) is theprojects IRR.

IRR asks: What is the projects rate of return?

Standard Rule: Accept a project if its IRR is greaterthan the appropriate market based discount rate,reject if it is less. Why does this make sense?

For independent projects with normal cash flowpatterns IRR and NPV give the same conclusions.

IRR is completely internal to the project. To use therule effectively we compare the IRR to a market rate.

8/3/2019 lock_sol

15/31

IRR Normal Cash Flow Pattern

Consider the following stream of cash flows:

Calculate the NPV at different discount rates

until you find the discount rate where theNPV of this set of cash flows equals zero.

Thats all you do to find IRR.

0 1 2 3

-$1,000 $400 $400 $400

8/3/2019 lock_sol

16/31

IRR NPV Profile Diagram Evaluate the NPV at various discount rates:

Rate NPV0 $200

10 -$5.3

20 -$157.4

At r = 9.7%,

NPV = 0

-200

-150

-100

-50

0

50

100

150

200

250

0 10 20

Discount Rate

NPV

8/3/2019 lock_sol

17/31

The Merit to the IRR Approach The IRR (as with the YTM) is an

approximation to the return generated over

the life of a project on the initial investment. As with NPV, the IRR is based on incremental

cash flows, does not ignore any cash flows,and (by comparison to the appropriate

discount rate, r) take proper account of thetime value of money and risk.

In short, it can be useful.

8/3/2019 lock_sol

18/31

Pitfalls of the IRR Approach Multiple IRRs

There can be as many solutions to the IRR

definition as there are changes of sign in the timeordered cash flow series.

Consider:

This can (and does) have two IRRs.

0 1 2

-$100 $230 -$132

8/3/2019 lock_sol

19/31

Pitfalls of IRR cont

Disc.Rate 0.00% 10.00% 15.00% 20.00% 40.00%

NPV -$2.00 $0.00 $0.19 $0.00 -$3.06

IRR1 IRR2

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

0 10 15 20 40

Discount Rate

N

PV

8/3/2019 lock_sol

20/31

Pitfalls of IRR cont

-0.5

0

0.5

1

1.5

2

2.5

3

0 10 15 20 40

Discount Rate

NPV

8/3/2019 lock_sol

21/31

Pitfalls of IRR cont Mutually exclusive projects:

IRR can lead to incorrect conclusions

about the relative worth of projects. Ralph owns a warehouse he wants to fix

up and use for one of two purposes:A. Store toxic waste.

B. Store fresh produce.

Lets look at the cash flows, IRRs and NPVs.

8/3/2019 lock_sol

22/31

Mutually Exclusive Projects and IRR

Project Year 0 Year 1 Year 2 Year 3

A -10,000 10,000 1,000 1,000B -10,000 1,000 1,000 12,000

Project NPV @0% NPV @10% NPV@15%

IRR

A $2000 $669 $109 16.04%

B $4000 $751 -$484 12.94%

8/3/2019 lock_sol

23/31

At low discount rates, B is better. At high discountrates, A is better.

But A always has the higher IRR. A common mistake

to make is choose A regardless of the discount rate. Simply choosing the project with the larger IRR would

be justified only ifthe project cash flows could bereinvested at the IRR instead of the actual marketrate, r, for the life of the project.

-1000

0

1000

2000

3000

4000

5000

0% 10% 15%

Discount Rate

NPV

A

B

8/3/2019 lock_sol

24/31

Summary of IRR vs. NPV IRR analysis can be misleading if you dont fully

understand its limitations. For individual projects with normal cash flows NPV and IRR

provide the same conclusion. For projects with inflows followed by outlays, the decision

rule for IRR must be reversed.

For Multi-period projects with several changes in sign of thecash flows multiple IRRs exist. Must compute the NPVs tosee what is appropriate decision rule.

IRR can give conflicting signals relative to NPV when rankingprojects.

I recommend NPV analysis, using others as backup.

8/3/2019 lock_sol

25/31

Profitability Index Definition: The present value of the cash

flows that accrue after the initial outlay

divided by the initial cash outlay. Rule: Take any/only the projects with a PI>1.

The PI does a benefit/cost (bang for the buck)analysis. Any time the PV of the future benefits islarger than the current cost PI > 1. When this istrue what is the NPV? Thus for independentprojects the rules make exactly the same decision.

0

1

)1/(

CF

rCF

PI

N

t

t

t!

!

8/3/2019 lock_sol

26/31

PI and Mutually Exclusive

Projects Example:

Project CF0 CF1 NPV @ 10% PI

A -$1,000 $1,500 $364 1.36

B -$10,000 $13,000 $1,818 1.18

Since you can only take one and not both the NPV rule saysB, the PI rule would suggestA. Which is right?

The projects are mutually exclusive so the NPV ofone is an opportunity cost to the other. We must

take B, in this respectAhas a negative NPV. PI treats scale strangely. It measures the bang per

buck invested. This is larger for Abut since weinvest more in B it will create more wealth for us.

8/3/2019 lock_sol

27/31

Payback Period Rule Frequently used as a check on NPV analysis

or by small firms or for small decisions.

Payback period is defined as the number of yearsbefore the cumulative cash inflows equal the initialoutlay.

Provides a rough idea of how long invested capitalis at risk.

Example: Aproject has the following cash flows Year 0 Year 1 Year 2 Year 3 Year 4

-$10,000 $5,000 $3,000 $2,000 $1,000

The payback period is 3 years. Is that good or

bad?

8/3/2019 lock_sol

28/31

Payback Period Rule Frequently used as a check on NPV analysis

or by small firms or for small decisions.

Payback period is defined as the number of yearsbefore the cumulative cash inflows equal the initialoutlay.

Provides a rough idea of how long invested capitalis at risk.

Example: Aproject has the following cash flows Year 0 Year 1 Year 2 Year 3 Year 4

-$10,000 $5,000 $3,000 $2,000 $1,000,000

The payback period is 3 years. Is that good or

bad?

8/3/2019 lock_sol

29/31

Payback Period Rule An adjustment to the payback period rule that is

sometimes made is to discount the cash flows andcalculate the discounted payback period.

This new rule continues to suffer from the problemof ignoring cash flows received after an arbitrarycutoff date.

If this is true, why mess up the simplicity of the rule?Simplicity is its one virtue.

At times the payback or discounted payback periodmay be valuable information but it is not often thatthis information alone makes for good decision-making.

8/3/2019 lock_sol

30/31

Average Accounting Return Definition: The average net income

after depreciation and taxes (before

interest) divided by the average bookvalue of the investment.

Rule: If the AAR is above some cutofftake the project.

This is essentially a measure of returnon assets (ROA).

8/3/2019 lock_sol

31/31

AAR Problems

Doesnt use cash flows but ratheraccounting numbers.

Ignores the time value of money.

Does not adjust for risk.

Uses an arbitrarily specified cutoff rate.