Goal of the Lecture:

Understand how to properly value a potential corporate investment.

Basic Capital Basic Capital BudgetingBudgeting

I. Profit Evaluation of Investment Projects

II. Five Steps

a. Project Identification

b. Estimate of Cash Flows

c. Determine Risk and Discount Rate (CAPM)

d. Formulate Selection Criteria

e. Control and Post Completion Audit

III. Types of Projects

a. Expansion

b. Replacement

c. Regulatory (Government Required)

IV. Types of Decision Scenarios

a. Screen for All Acceptable Projects

b. Mutually Exclusive

c. Capital Rationing

ACCEPT-REJECT CRITERIA - A PROJECT ACCEPT-REJECT CRITERIA - A PROJECT SHOULD ENHANCE SHARE VALUESHOULD ENHANCE SHARE VALUE

V. Project Selection Criteria - Alternate Methods

• Payback Method

• Net Present Value (NPV)

• Internal Rate of Return (IRR)

ILLUSTRATIVE PROBLEM:Suppose firm ABC has a share price of $10. The firm may invest $500,000 in a machine that costs $100,000 each year in operating expenses for its 10 year life. The machine produces a product that it sells for $200,000 each year. Should the investment be made if k = 10%? What should be the price of the shares once the new project is accepted if there are 100,000 shares?

PV of Annual Profits = PV of Annual Revenue - Cost

PV = ($200,000 - $100,000)

= [=PV(0.10, 10, -100000, 0)] = $614,500

But the machine costs $500,000 so net profit = $114,500

Share Price = $10 + ($114,500) / (100,000 shares) = 11.14

What would you do if the machine costs $700,000?

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Payback MethodPayback Method““Number of years it takes a firm to recover its initial investment.”Number of years it takes a firm to recover its initial investment.”

I. Payback Method - Accept project if

Payback < Maximum

Payback = Investment/Cash Flow Per Year

(If cash flows are annuities, otherwise, find the point in time when the cash flows sum up to the investment

amount)

II. Example: Suppose a $1.0M project yields net operating cash flows of $150,000 per year for 10 years. What is its payback?

$1,000,000/$150,000 = 6.67 Years

If the Firm’s Maximum Payback is > 6.67, then

Accept, Otherwise Reject

Second Method - Could have added cash flows as follows:

$150,000 + $150,000 + $150,000 + $150,000 +

$150,000 + $150,000 + [$100,000 / $150,000] = 6.67

Firm Sets Maximum or Flexible Payback Period

Advantages:

a. Simple to Calculate and Understand

b. Adjust for Risk by Shortening Payback Period

Disadvantages:

a. Ignores Timing of Cash Flows (no discounting) and ignores Cash Flows After Payback Point

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-100 70 20 30 20

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-100 30 70 20 20

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-100 100 5 5 5

b. Payback Maximum is Arbitrary

Net Present Value - NPVNet Present Value - NPV““The NPV is determined by discounting cash inflows back toThe NPV is determined by discounting cash inflows back to

the present at k and then subtracting the initial investment.”the present at k and then subtracting the initial investment.”

I. Net Present Value (NPV) - Accept Project If NPV > 0

NPV = CF0 +

Note: k is given or must be determined.

Advantage: NPV gives the correct decision more often.

Disadvantage: Not intuitive and hard to explain to non-finance managers.

II. Example: Suppose you have a project that costs $100,000 and yields cash flows of

$50,000 in each of 3 years.

What is the NPV if k =5, 10, 15, 20, 25, and 30%?

NPV= -$100,000 + [=PV(0.05, 3, -50000, 0)] = $36,750

NPV= -$100,000 + [=PV(0.10, 3, -50000, 0)] = $24,350

NPV= -$100,000 + [=PV(0.15, 3, -50000, 0)] = $11,415

NPV= -$100,000 + [=PV(0.20, 3, -50000, 0)] = $ 5,300

NPV= -$100,000 + [=PV(0.25, 3, -50000, 0)] = $ -2,400

NPV= -$100,000 + [=PV(0.30, 3, -50000, 0)] = $ -9,200

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I. Internal Rate of Return - Accept Project If IRR >

Hurdle

NPV = 0 = - Initial Investment +

or

In. Investment =

Advantages: Considers time value, like NPV.

It is a rate of return; easier than NPV to explain.

Disadvantage: Ignores project scale; reinvestment at IRR.

Unreliable if cash flows change signs more than once.

II. Example: Suppose the initial investment is $1.0M and annual cash flows are $150,000 for 10 years. Find IRR?

[=Rate(10, -150000, 1000000, 0)]

=> IRR = 8.14%

Note: If required (or hurdle) rate is 10%, we would reject this project.

Internal Rate of Return - IRRInternal Rate of Return - IRR““The IRR Is the Rate that Causes the Net Present Value to The IRR Is the Rate that Causes the Net Present Value to Equal Zero: Set the Initial Investment Equal to the Present Equal Zero: Set the Initial Investment Equal to the Present Value of the Future Cash Flows and Find k = IRR.”Value of the Future Cash Flows and Find k = IRR.”

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IRR with Unequal Cash Flows

The Excel function “Rate” gets you the IRR but only if the cash flows are all equal. Suppose you that you have the following cash flows, where year 0 refers to the date of the initial investment (an outflow).

Year Cash Flow

0 -65

1 40

2 30

3 20

In Excel, just enter each of these numbers in separate cells, say B1, B2, B3, and B4.

Then in another cell of the spreadsheet type in [=IRR(B1:B4)], without the square brackets and you should get 20.82%. (or 21% if your cell is formatted with zero decimal places).

For more detail see page 60-61 of the text or go to Excel and select Help and search for IRR.

NPV Avoids Some of IRR WeaknessesNPV Avoids Some of IRR Weaknesses

WEAKNESSES

1. Multiple IRRs0 1 2------------------------------

CFs -80 500 -500

IRR = 25% and 400%

QUESTION: How can you check whether these two IRR’s are correct? Substitute & Calculate NPV =>0

QUESTION: Suppose the hurdle rate is 10%. Should we accept the project?

Instead use NPV with 10%

NPV = - 80 + .500/(1.1) - .500/(1.1)2

= - 80,000 + 454,545 - 413,243 = - 38.678

=> reject

If we reject at 10% we should reject at higher rates like 25%.

2. Mutually exclusive investments -scale problem.

PROBLEM: Suppose you have the following investments which are mutually exclusive. Which do you choose if you use IRR? If NPV?

TIME Project A Project B

0 -100 -101 50 52 50 53 50 54 50 5

[=Rate(4, -50, 100, 0)] = [=Rate(4, -5, 10, 0)]

IRR = 35% for both A and B

Assume k = 11% then:

NPVA = -100 + [=PV(0.11, 4, -50, 0)] = 55.0

NPVB = -10 + [=PV(0.11, 4, -5, 0)] = 5.50

IRR is inferior if there are scale differences because you make more total profit from Project A.

PROBLEM: Suppose you must choose between A and B below and the required rate is 9%. Which do you choose using IRR? NPV? :

TIME A B0 -35,000 -35,0001 20,000 5,0002 15,000 10,0003 10,000 15,0004 4,000 25,000

IRR 20% 16%NPV(5%) 9582 12357NPV(9%) 6529 7297NPV(15%) 2595 1066

Here IRR always chooses A because it assumes reinvestment of intermediate CFs at IRR.

NPV chooses B at low interest rates and A at high interest rates. So as the k approaches the calculated IRR in value we see that they give similar results. This is because the NPV assumes intermediate CFAT's are invested at k, and IRR assumes they are invested at IRR.

The NPV numbers above were computed using the Excel NPV formula. For example, the first NPV number 9582 is:

9582 = NPV(0.05, 20000, 15000, 10000, 4000) - 35000

QUESTION: Why has the project A become more attractive from an NPV standpoint when k increases to 15%?

Because you get larger cash flows earlier. At large interest rates, early cash flows become relatively more attractive

Present value of cash flows at 30% discount rate

At low discount rates (below 10%) project is preferred because it earns greater cash flows,55 vs. 49 for .

At high discount rates(30%) project is preferred because its large cash flows come earlier (are worth more)than those of project .

0 period 1st period 2nd period 3rd period 4th period

0 period 1st period 2nd period 3rd period 4th period

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9 6 5

7

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20

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10 10

15

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When Two Mutually Exclusive Projects Have When Two Mutually Exclusive Projects Have Different Life Spans, the Longer Project Will Different Life Spans, the Longer Project Will Have a Larger NPV, All Else Equal.Have a Larger NPV, All Else Equal.

Ways to Handle Unequal Project Lives

• Can use IRR

• Replacement chains - assume multiple replacements

• Assume long-lived asset is sold at the end of the short-lived asset’s life.

• Use equivalent annual annuity NPV

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Equivalent Annual NPV =

This method normalizes NPV for project years.It is the simplest and most effective method.

Example: Either of two molding machines that makes drinking glasses requires an initial investment of $2000. Model 3SR produces short glasses and has a 5-year life. Model 3TR produces tall glasses and has a 9-year life. CFs expected from the purchase of model 3SR and 3TR are $700 and $500 per year, respectively. If k =.13 and there is no resale value, which should be chosen?

NPVS = -2000 + [=PV(0.13, 5, -700, 0)] = 462

NPVT = -2000 + [=PV(0.13, 9, -500, 0)] = 566

ENPVS = 462/3.517 = 131 ENPVT = 566/5.132 = 110

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Capital RationingCapital Rationing““A situation in which a constraint exists on funds availableA situation in which a constraint exists on funds available

such that not all positive NPV projects will be accepted.”such that not all positive NPV projects will be accepted.”

I. Capital Rationing - Maximize the NPV Subject to Budget

Profit Index = PI =

Note: PI is a guide to choosing projects, it measures the NPV per dollar invested, i.e., PI = 1.5 means that

you get and NPV of 1.5 per $1 invested.

II. Example: Assume the following information. You have $600,000 to spend. Which should

you choose?

Project In. Invest. PV(CF) PI NPV

1. $300,000 $336,000 1.12 $36,000

2. $100,000 $120,000 1.20 $20,000

3. $100,000 $108,000 1.08 $ 8,000

4. $200,000 $230,000 1.15 $30,000

5. $200,000 $190,000 0.95 -$10,000

6. $300,000 $330,000 1.10 $30,000

Choose: Projects 1, 2, 4

Suppose that Project 4 costs $225,000 (PI = 1.02).

Which projects to choose now? Choose: 1, 6

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Options and Real Options

1. THE TWO BASIC OPTIONS - PUT AND CALL

• A call (put) is the right to buy (sell) an asset.

• Most other options are just combinations of these.

• Options are “derivatives” and other derivatives may include options

• The price of an option is called a “premium” because options are equivalent to insurance and the price of insurance is called a premium.

2. For most of this lecture we will assume that the option

a. Can only be exercised at maturity (called European). An American option, which is the most common type should behave similarly because, in most cases, American options are not exercised until maturity. They are almost always worth more left unexercised so very few are exercised. If they are never exercised before expiration, there should be no difference in value between an American and European option.

b. Pays no dividends – most options aren’t dividend protected so dividends will affect price.

CALL OPTION CONTRACT

Definition: The right to purchase 100 shares of a security at a specified exercise price (Strike) during a specific period.

EXAMPLE: A January 60 call on Microsoft (at 7 1/2)

This means the call is good until the third Friday of January and gives the holder the right to purchase the stock from the writer at $60 / share for 100 shares.

Cost is $7.50 / share x 100 shares = $750 premium or option contract price.

PUT OPTION CONTRACT

Definition: The right to sell 100 shares of a security at a specified exercise price during a specific period.

EXAMPLE: A January 60 put on Microsoft (at 14 1/2)

This means the put is good until the third Friday of January and gives the holder the right to sell the stock to the writer for $60 / share for 100 shares.

Cost $14.25 / share x 100 shares = $1450 premium.

INTRINSIC AND TIME VALUE

•AN OPTION'S INTRINSIC VALUE IS ITS VALUE IF IT WERE EXERCISED IMMEDIATELY.

•AN OPTION'S TIME VALUE IS ITS COST ABOVE ITS INTRINSIC VALUE.

Microsoft Stock Price = 53.50 at the time - October 1987

QUESTION: Which Microsoft option has greater intrinsic value? - put

QUESTION: Which Microsoft option has greater time value? – put

a. For the Call - Time Value = 7.50 (the full premium) Intrinsic Value = 0 (Stock price < exercise price).

b. For the Put - Time Value = $8.00 = 14. 50 - (60 - 53.50) Intrinsic Value = (60 - 53.50) = 6.50.

QUESTION: Which option is a better deal?

REAL OPTIONS EXAMPLES

Call - option to buy another company or company's line.

Call - capital expenditures on R & D and marketing. Give an option to make further investments if promising.

Call - buy car at the end of the lease

Call - rain check at a grocery store

Put - abandonment

Put - agreement to buy company but only if loan losses are less than 50 million (WCIS).

Put - guarantees - government price supports - consider farmer's incentives

Related to NU’s Business

Call – Invest in the first few electric charging stations for electric cars

Call or Put – weather or temperature options

Call – new technology batteries

Put – consumers with solar cells can sell to NU

Call – consumers with solar sells have the right to buy from NU if they need power

Call – carbon pollution permits

Call – interruptible service – the right to turn off a businesses’ service

NET PRESENT VALUE RULE FOR PROJECT ACCEPTANCE MUST BE ADJUSTED IF OPTIONS ARE INVOLVED.

There are two types of options to consider for most projects

A. The call option to delay a project to the future when the project may have a larger NPV. A project that can be delayed effectively competes with itself in the future.

This call option is more valuable when a project can be delayed for a longer time (t), when a project’s (returns) are very risky (), and when interest rates (r) are high.

This could explain why it may be rational to delay a positive NPV project. Managers have often been criticized by governments for not investing in plant and equipment during recessions. Managers are not being indecisive or too risk-averse but simply evaluating projects based upon their option values which may be high during recessions.

The basic idea is that if you undertake a project now, you can’t undertake it in the future when it may have a higher NPV. The more likely a project could have a higher NPV in the future, the larger its option’s time value. If the project is accepted, its time value is lost.

Thus, time value must be considered in the project selection criteria. Thus instead of

NPVproject > 0

we use

NPVproject > time value of the option to delay > 0

Hence we should accept a project only when it has a relatively large NPV. A large NPV in options terms means that the market value or present value of the project’s cash flows greatly exceeds its exercise price (cost of the project). In other words - when its option is sufficiently “in the money” i.e., it has much intrinsic value.

B. When a project’s acceptance allows one to undertake additional projects in the future then we must make another adjustment to the NPV criteria above.

NPVproject + Value of option on extended projects > time value of option to delay

For example, if we delay building a new pentium chip-making plant, it may be cheaper in the future, all else equal. However, if not building the plant means we may forfeit the opportunity to build the next generation chip, then this extra option must be considered.

Example: You have a project that requires a $20 million investment. You expect the project to provide future cash flows with present value of $22 million. If the option to delay the project for two years is worth $9.5 million, should you accept the project now or wait? What if the project gives you the option to make future investments where this option is worth $8 million? Assume that the investment remains $20 million whenever it is made and the present value of future cash flows remains $22 million. Also assume that if you delay then you lose the option to make future investments.

Time value of the option to delay = 9.5 - (22 - 20) = 7.5

Since NPV = (22 -20) = 2 < 7.5 then wait.

If the project gives us the option to make future investments but only if we invest now, and this option is worth 8 then we would have

NPV + Option on Future Project = 2 + 8 = 10 > 7.5 - so now we would go ahead with the project.