Lecture 3

MIN 100Investment Analysis

Roy Endré DahlUniversity of Stavanger

E-mail: [email protected]

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mailto:[email protected]

Early dialogue• We need to elect a student representative who will help

organize the early dialogue in this course. • The early dialogue will answer 5 questions:

1. Teaching and assesment methods2. Curriculum3. Use of it’s learning4. Working conditions5. Other conditions that could be improved

• You will be given 10 minutes during the next lecture to discuss these questions, and the representative will fill out a form reporting on the 5 questions.

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0-3

MIN 100 – Investment AnalysisWeek / date Chapters / Topic Note

35 – 29.08.2011 1-3 / Introduction and basic concepts.

Part 1: Overview

37 – 12.09.2011 4-5 / Net present value, bonds, markets

Part 2: Valuation and Capital budgeting

38 – 19.09.2011 6-7 / Stocks, NPV and other investment rules

39 – 26.09.2011 8-9 / Cash flow and capital budgeting, decision tree, sensitivity, Monte Carlo

40 – 03.10.2011 10-11 / Return and Risk, expected return, CAPM

Part 3: Risk and Return

41 Mandatory assignment

42 – 17.10.2011 11-12 / CAPM, Risk, Cost of Capital

43 – 24.10.2011 13-14 / Financing, capital structure, Modigliani & Miller

Part 4: Capital Structure and Dividend Policy

44 – 31.10.2011 15-16 / Use of debt, leverage, dividends

45 – 07.11.2011 17 / Financial and Real Options. Part 5: Special topics

Stock Valuation

Chapter 6

McGraw-Hill/Irwin

• Comprehend that stock prices depend on future dividends and dividend growth

• Compute stock prices using the dividend growth model

• Understand how growth opportunities affect stock values

• Appreciate the PE ratio• Know how stock markets work

Key Concepts and Skills

6.1 The Present Value of Common Stocks6.2 Estimates of Parameters in the Dividend

Discount Model6.3 Growth Opportunities6.4 Price-Earnings Ratio6.5 Some Features of Common and Preferred

Stock6.6 The Stock Markets

Chapter Outline

Opening Case The education dilemma

• http://www.tu.no/jobb/article289898.ece• http://www.tu.no/jobb/article288563.ece• http://www.tu.no/jobb/article263597.ece• http://www.tu.no/jobb/article267679.ece

7

http://www.tu.no/jobb/article289898.ece




Opening CaseAker Drilling

8

• The value of any asset is the present value of its expected future cash flows.

• Stock ownership produces cash flows from: – Dividends – Capital Gains

• Valuation of Different Types of Stocks– Zero Growth– Constant Growth– Differential Growth

6.1 The PV of Common Stocks

• Assume that dividends will remain at the same level forever

• Since future cash flows are constant, the value of a zero growth stock is the present value of a perpetuity:

Case 1: Zero Growth

RP

RRRP

Div

)1(

Div

)1(

Div

)1(

Div

0

33

22

11

0

321 DivDivDiv

Suppose Big Deal Company will pay an annual dividend of $2.00 per common share that will never increase or decrease.

The market rate of return is 8.5%. What is the maximum amount you should be willing pay

for a common share of Big Deal Corporation?

Formula for Zero Growth Model: P = Div / R

Solution: P = $2.00 / .085 P = $23.53

Zero Growth Example

Case 2: Constant Growth

)1(DivDiv 01 g

Since future cash flows grow at a constant rate forever, the value of a constant growth stock is the present value of a growing perpetuity:

gRP

1

0

Div

Assume that dividends will grow at a constant rate, g, forever, i.e.,

2012 )1(Div)1(DivDiv gg

3023 )1(Div)1(DivDiv gg

...

• Suppose Big D, Inc., just paid a dividend of $.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk level, how much should the stock be selling for?

• P0 = Div / (R – g)• P0 = .50(1+.02) / (.15 - .02) = $3.92

Constant Growth Example

It is critical to understand that in the constant growth model calculations are based on the next dividend

If a situation only provides information on the last dividend it must be increased by the growth rate to arrive at the next dividend

If a situation provides the value of the next dividend, then the data necessary for the calculation is known and need not be derived.

An analyst must discriminate whether they have information about the next or last dividend and proceed with calculation accordingly

A Word About Dividends in the Constant Growth Model

Assume that dividends will grow at different rates in the foreseeable future and then will grow at a constant rate thereafter.

To value a Differential Growth Stock, we need to:◦ Estimate future dividends in the foreseeable

future.◦ Estimate the future stock price when the stock

becomes a Constant Growth Stock (case 2).◦ Compute the total present value of the estimated

future dividends and future stock price at the appropriate discount rate.

Case 3: Differential Growth

• This graph demonstrates the dividend profile for a company with differential growth

Graphic: Differential Dividend Growth


)(1DivDiv 101 g

· Assume that dividends will grow at rate g1 for N years and grow at rate g2 thereafter.

210112 )(1Div)(1DivDiv gg

NNN gg )(1Div)(1DivDiv 1011

)(1)(1Div)(1DivDiv 21021 ggg NNN

...

...


)(1Div 10 g

Dividends will grow at rate g1 for N years and grow at rate g2 thereafter

210 )(1Div g

Ng )(1Div 10 )(1)(1Div

)(1Div

210

2

gg

gN

N

…0 1 2

…N N+1

…


We can value this as the sum of: a T-year annuity growing at rate g1

plus the discounted value of a perpetuity growing at rate g2 that starts in year T+1

T

T

A R

g

gR

CP

)1(

)1(1 1

1

TB R

gRP

)1(

Div

2

1T


Consolidating gives:

TT

T

R

gR

R

g

gR

CP

)1(

Div

)1(

)1(1 2

1T

1

1

Or, we can “cash flow” it out.

What is the stock worth? The discount rate is 12%.

A Differential Growth Example

A common stock just paid a dividend of $2. The dividend is expected to grow at 8% for 3 years, then it will grow at 4% in perpetuity.

With the Formula

3

3

3

3

)12.1(

04.12.)04.1()08.1(2$

)12.1(

)08.1(1

08.12.

)08.1(2$

P

3)12.1(

75.32$8966.154$ P

31.23$58.5$ P 89.28$P

With Cash Flows

08).2(1$ 208).2(1$…

0 1 2 3 4

308).2(1$ )04.1(08).2(1$ 3

16.2$ 33.2$

0 1 2 3

08.

62.2$52.2$

89.28$)12.1(

75.32$52.2$

)12.1(

33.2$

12.1

16.2$320

P

75.32$08.

62.2$3 P

The constant growth phase beginning in year

4 can be valued as a growing perpetuity at

time 3.

Where does g come from?

g = Retention ratio × Return on retained earnings

Example: Suppose a company has a retention ratio of 70% and earns an ROE of 12%. What is the Growth Rate, g?

g = .70 X .12g = .084 = 8.4%

6.2 Estimates of Parameters

The value of a firm depends upon its growth rate, g, and its discount rate, R.

The discount rate can be broken into two parts. ◦ The dividend yield ◦ The growth rate (in dividends)

AKA: Capital Gains Yield

In practice, there is a great deal of estimation error involved in selecting R.◦ Cases calling for special skepticism:

Stocks not paying dividends Stocks with g expected to equal or exceed R

Where Does R Come From?

• Start with the DGM:

• Note that D1 /P0 is the dividend yield and g is the capital gains yield.

Using the DGM to Find R

gP

D g

P

g)1(D R

g-R

D

g - R

g)1(DP

0

1

0

0

100

Rearrange and solve for R:

• Imagine that a Solar Corp.’s last dividend was $.65 per share. Solar’s dividends are growing at a rate of 4% and the current price per share is $11.25. What is the market R implicit in Solar’s price?

• R=(D1 / P0) +g• R = [(.65 x 1.04) / 11.25] + .04• R= .10 or 10%

Example: Using DGM to Find R

• Dividends may not be a firm’s only cash payout

• Recently many firms have repurchased shares, another form of payout

• Using the Dividend Growth Model, the price of a share will be higher if considering total payout rather than just dividends

Total Payout

• A firm forecasts income of $4.00 per share and will payout 30% as dividends, 30% as share repurchase and will retain the rest. Its growth rate is 5% and required return is 10%. What is the price of a share?

• Dividend Growth Model: P0 = (4.00 X .30) / (.1 - .05) = $24.00– Notice that the price is based on dividend ( 30% of earnings)

growth only• Total Payout Model: P0 = (4.00 X .60) / (.1 - .05) = $48.00

– Notice that the price is based on total payout ( 60% of earnings = 30% for dividends and 30% for share repurchase) growth

Example: Total Payout Valuation

• Growth opportunities are opportunities to invest in positive NPV projects.

• The value of a firm can be conceptualized as the sum of the value of a firm that pays out 100% of its earnings as dividends plus the net present value of the growth opportunities (NPVGO).

6.3 Growth Opportunities

NPVGOR

EPSP

• Two conditions must exist if a company is to grow:– It must not pay out all of its earnings as

dividends; and,– It must invest in projects with a positive NPV

Prerequisites to Growth

• Why don’t firms with no dividends have stock price of $0?

• Such firms believe their earnings are better used to pursue growth opportunities

• Investors pay a stock price that conforms to their own calculus of the NPVGO of the no-payout firm

• The dividend growth model does not work in valuing this firm– The differential growth model can, but evaluating the

timing of changes in growth is tricky

The No-Payout Firm

Opening Case The education dilemma

• http://www.tu.no/jobb/article289898.ece• http://www.tu.no/jobb/article288563.ece• http://www.tu.no/jobb/article263597.ece• http://www.tu.no/jobb/article267679.ece

33





Many analysts frequently relate earnings per share to price.

The price-earnings ratio is calculated as the current stock price divided by annual EPS.◦ The Wall Street Journal uses last 4 quarter’s

earnings

6.4 Price-Earnings Ratio

EPS

shareper Priceratio P/E

Interpreting the P/E ratio• Historically a company has a fair price if the P/E ratio is between 10

– 17.• Below 10:

– The company’s earnings are thought to be in decline, and the company’s future might be in question.

– Or, current earnings are substantially above historical earnings (e.g. through asset sales).

• Over 17:– The stock is overvalued or the earnings have increased since the last

earnings figure was published.– Or, the stock is a growth company where earnings are expected to

increase in the future.• Over 25:

– High expected future growth in earnings (e.g. Facebook).– May be a speculative bubble.

S&P 500 Average P/E ratio

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Opening case revisitedAker Drilling

• Is the price paid by Transocean a fair price?• Normally you can find the P/E-ratio of any company by

looking at the qoutes delivered by the stock exchange. The P/E ratio would then be calculated by using historical earnings, number of outstanding shares and the share price:

• However, Aker Drilling has only been listed on the Oslo Stock Exchange since february/march 2011, and the historical earnings is not available directly in the quotes.

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• As a listed company on the stock exchange, Aker Drilling needs to provide quarterly financial reports.

• The latest report is from August 12th, and reports an earnings per share (EPS) equal to 0.10 USD for the first 6 months.

• By assuming that the last 6 months will provide the same EPS, the EPS for Aker Drilling for one year would be 0.20 USD = 1.08 NOK.

• Which will provide us with this PE ratio:

PE = 26.50 / 1.08PE = 24.5

• This is relatively high and indicates an optimistic Transocean which signals high confidence in future revenues.

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• The PE ratio is a valuable tool to compare companies.– Aker Drilling: 24.5– Transocean: -2.35 (9.7 in 2010)– Seadrill: 13.0 (9.6)– Songa Offshore: 8.4 (3.5)– Fred Olsen Energy: 9.2 (6.4)– Statoil: 9.0 (6.2)– DNO Int.: 13.6 (10.7)

• Technology industry:– Telenor: 14.2 (22.0 in 2011)– Nokia: -2.44 (8.0)– Microsoft: 15.6 (9.9)– Apple: 16.5 (25.5)– Google: 20.9 (19.0)

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More P/E analysis• The estimates for Transocean is

given in the figure to the right. How can we explain the change in P/E ratio?

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According to the formula, the P/E can increase due to either (1) a decrease in EPS or (2) an increase in price per share. - (2) is not plausible in this case, as the price per share must be set as given in

this 3-year scenario due to market equilibrium.- (1) EPS may decrease by either an increase in number of shares (new issuing

of shares), and since Transocean is not planning to issue new shares, the only option left is reduced earnings.

Thus, a higher P/E ratio does not necessarily mean that the company is making more money.

P/E ratio – the story of Renewable Energy Corporation (REC)

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First public offering (IPO) sets P/E = 30

Extreme optimism.P/E > 70

Pessimism.P/E = 3.8

First public offering (IPO) sets P/E = 70

Optimism/Realism?P/E ca. 35

• Voting rights (Cumulative vs. Straight)• Proxy voting• Classes of stock• Other rights

– Share proportionally in declared dividends– Share proportionally in remaining assets

during liquidation– Preemptive right – first shot at new stock

issue to maintain proportional ownership if desired

6.5 Features of Common Stock

• Dividends– Stated dividend must be paid before

dividends can be paid to common stockholders.

– Dividends are not a liability of the firm, and preferred dividends can be deferred indefinitely.

– Most preferred dividends are cumulative – any missed preferred dividends have to be paid before common dividends can be paid.

• Preferred stock generally does not carry voting rights.

Features of Preferred Stock

• Dealers vs. Brokers• New York Stock Exchange (NYSE)

– Largest stock market in the world– License Holders (formerly “Members”)

• Entitled to buy or sell on the exchange floor• Commission brokers• Specialists• Floor brokers• Floor traders

– Operations– Floor activity

6.6 The Stock Markets

• Not a physical exchange – computer-based quotation system

• Multiple market makers• Electronic Communications Networks• Three levels of information

– Level 1 – median quotes, registered representatives

– Level 2 – view quotes, brokers & dealers– Level 3 – view and update quotes, dealers

only• Large portion of technology stocks

NASDAQ

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Apple Inc. trades at NASDAQ with the stock ticker AAPL. It traded on September 2nd 2011 at $374.05, down 1.83% from the day before.

Bid defines what the highest price the buyers are willing to offer (and at what volume).Ask specify what the lowest price a seller is willing to sell at (and at what volume).The difference (Ask – Bid) is called the spread.

Day’s Range tells us today’s highest and lowest price.52wk Range tells us the highest and lowest price during the last year.

Volume specify the number of shares traded the last day.

Market cap gives us the market value of the company (number of shares * price of share)

P/E Ratio is given with regards to the average PE the last twelve months (ttm = trailing twelve months)

Earnings per share, EPS (ttm), is given with earnings reported for the last twelve months.

Dividends specify last dividend paid. For Apple this was 0, and therefore there is no yield to calculate.

Closing CaseValuating Ragan Engines

• East Coast Yachts are considering buying a supplier in order to make more profit. The company Ragan Engines is not publicly traded and is owned by two persons holding 125 000 stocks each.

• We know the following about the firm:– EPS = $ 4.20– Dividend = $ 157 500 to each stock holder.– ROE = 20%– Required return = 16%

48


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Number of shares 250 000 Earnings pr share (EPS) 4,20 Dividend 315 000 Dividend pr share 1,26 Return on Equity (ROE) 20 %Required return 16 %

1) Calculate value pr share by using company information

Total earnings 1 050 000 =EPS * Number of sharesPayout rate 30 % =Dividend / Total earningsRetention rate 70 % =1 - Payout rateGrowth rate 14 % =ROE * Retention RateDividends next year 359 100 =Dividend * (1 + Growth Rate)Equity Value 17 955 000 =Dividends / (Required return - Growth rate)

Value pr share 71,82

Equity value is calculated as a growing perpetuity, using dividends as the constant cash flow and required return as discount rate and growth rate.

According to this valuation, Ragan Engines is valued at $17 955 000 and East Coast Yachts should pay $71.82 pr share.


• While Ragan Engines have an industry advantage today, East Coast Yachts believe the industry will catch up within 5 years and the growth rate will after this be reduced to industry standard.

• In addition, to get a fair valuation, they will use industry standard as the required return.

• Industry numbers follow from the table below:

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EPS DPS Stock price

ROE R

Blue Ribband Motors Corp. $ 1,15 $ 0,34 $ 18,25 13,00 % 15,00 %Bon Voyage Marine, Inc. 1,45 0,42 15,31 16,00 % 18,00 %Nautilus Marine Engines 1,85 0,60 28,72 N/A 14,00 %Ragan Engines 4,20 1,26 unknown 20,00 % 16,00 %Industry average $ 0,80 $ 0,45 $ 20,76 14,50 % 15,67 %

2) Calculate value pr share by using industry information

Industry EPS 1,48=Average of competitor's EPSIndustry Payout ratio 30,3 %=Industry DPS / Industry EPSIndustry Retention ratio 69,7 %=1-Industry Payout ratioIndustry Growth rate 10,1 %=Industry ROE * Undustry Retention Ratio

Growth rate year 1-5 14 %Number of shares 250 000

Year Dividends1 359 100,00 2 409 374,00 3 466 686,36 4 532 022,45 5 606 505,59 6 667 769,47 NOTE: From year 6, use industry growth rate

Stock value in Year 5 11 991 098,82 =Dividends / (Required return - Growth rate)Total stock value today 7 299 104,48 =NPV of Dividends in year 1-5 + NPV of stock value in year 5



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Equity value is calculated as a growing perpetuity, using dividends as the constant cash flow and required return as discount rate and growth rate.

EPS DPS Stock $ ROE RBlue Ribband Motors Corp. $ 1,15 $ 0,34 $ 18,25 13,00 % 15,00 %Bon Voyage Marine, Inc. 1,45 0,42 15,31 16,00 % 18,00 %Nautilus Marine Engines 1,85 0,60 28,72 N/A 14,00 %Ragan Engines 4,20 1,26 unknown 20,00 % 16,00 %Industry average $ 0,80 $ 0,45 $ 20,76 14,50 % 15,67 %

Total value is the sum of the present value of all dividends paid in year 1-5, plus the present value of the stock value in year 5.Share value is now lowered considerably, and East Coast Yachts should pay $29.20 pr share.


• One more method to valuate Ragan Engines is by using the formula for the P/E ratio.

• We do not know the price of the share, but we do know the earnings pr share (EPS) = 4.20, and the industry average P/E = $20.76 / $1.48 = 14.00.

• This gives us:

Price pr share = P/E * EPS = 14.00 * 4.20 = 58.80

• This is between our previous estimates.• Finally, we may compare the industry average P/E with the estimated P/E in

our previous valuations of Ragan Engines:1: P/E = 71.82 / 4.20 = 17.12: P/E = 29.20 / 4.20 = 6.95

52

Extra Case: StatoilUsing DGM to find R

• By looking into a company’s report we can find key figures which will help us estimate the implicit required return R by shareholders.

• This can be valuable information when valuating the company at a later time or comparing against other companies in the same industry. E.g. to compare risk assesment by shareholders.

53

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StatoilNumbers provided by http://www.statoil.com/annualreport2010/en/Pages/frontpage.aspx

Share value as of 31.12.2011 153,50 NOK/Share

Number of shares 3 182 112 843,00 Earnings pr share (EPS) 24,70 NOK/Share

Dividend 20 683 733 479,50 NOK

Dividend pr share 6,50 NOK/Share

Total Equity 285,20 BillionNet income (return or profit) 78,40 billionReturn on Equity (ROE) 27,5 %Required return 25,3 %

1) Calculate value pr share by using company information

Total earnings 78 598 187 222 =EPS * #sharesPayout ratio 26,3 % =Dividend / Total earningsRetention ratio 73,7 % =1 - Payout rateGrowth rate 20,3 % =ROE * Retention RateDividends next year 24 873 307 900 =Dividend * (1 + Growth Rate)Equity Value 488 454 321 401 =Dividends / (Required return - Growth rate)


When using the number provided by the annual report, the implied required return by shareholders is 25.3%. This can be used to compare risk assesments for different companies and industries.

Net Present Value and Other Investment Rules

Chapter 7

McGraw-Hill/Irwin

Ability to compute and interpret an investment’s payback and discounted payback

(Competence in calculating and interpreting accounting rates of return)

Facility in computation and interpretation of the internal rate of return and profitability index

Fluency in describing the advantages and disadvantages of each valuation method specified above.

Ability to compute and interpret the net present value and explain why it is the best decision criterion

Key Concepts and Skills

7.1 Why Use Net Present Value?7.2 The Payback Period Method7.3 The Discounted Payback Period Method7.4 (The Average Accounting Return

Method)7.5 The Internal Rate of Return7.6 Problems with the IRR Approach7.7 The Profitability Index7.8 The Practice of Capital Budgeting

Chapter Outline

Opening CaseOil Field

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Opening caseOil field investment

59

Revenues Investment Operational cost Tariffs Exploration cost

Reduced exploration costs

Reducedinvestments

Reduced tariffs

Reduced operational costs

Swift decision-makingFast-track developments

Accelerated ramp-upof production

Improved regularity and capacity utilisationExtension of plateau production

Higher prices

Increased recovery

Extended tailend production

Net Present Value (NPV) = Total PV of future project Cash Flows - the Initial Investment

Estimating NPV:1. Estimate future cash flows: how much? and when?2. Estimate discount rate3. Estimate initial costs

Minimum Acceptance Criteria: Accept if NPV > 0 Ranking Criteria: Choose the highest NPV

7.1 Net Present Value & Its Rules

• Suppose Big Deal Co. has an opportunity to make an investment of $100,000 that will return $33,000 in year 1, $38,000 in year 2, $43,000 in year 3, $48,000 in year 4, and $53,000 in year 5. If the company’s required return is 12% should they make the investment?

Net Present Value: Example

Answer: YES! The NPV is greater than $0. Therefore, the investment does return at least the required rate of return.

Year Cash Flow PV of Cash Flow0 $ -100 000.00 $ -100 000.00 1 $ 33 000.00 $ 29 464.29 2 $ 38 000.00 $ 30 293.37 3 $ 43 000.00 $ 30 606.55 4 $ 48 000.00 $ 30 504.87 5 $ 53 000.00 $ 30 073.62

Net Present Value $ 50 942.69

• Accepting positive NPV projects benefits shareholders.NPV uses cash flowsNPV uses all relevant cash flows of the

projectNPV discounts the cash flows properly

• Reinvestment assumption: the NPV rule assumes that all cash flows can be reinvested at the discount rate.

Why Use Net Present Value?

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

• Payback Period = number of years to recover initial costs

• Minimum Acceptance Criteria: – Set by management; a predetermined time

period• Ranking Criteria:

– Set by management; often the shortest payback period is preferred

7.2 The Payback Period Method

• Disadvantages:– Ignores the time value of money– Ignores cash flows after the payback period– Biased against long-term projects– Requires an arbitrary acceptance criteria– A project accepted based on the payback

criteria may not have a positive NPV• Advantages:

– Easy to understand– Biased toward liquidity

The Payback Period Method

• Suppose Big Deal Co. has an opportunity to make an investment of $100,000 that will return $33,000 in year 1, $38,000 in year 2, $43,000 in year 3, $48,000 in year 4, and $53,000 in year 5. If the company require the investment to be paid back within 3 years should it take this opportunity?

Example: Payback Period

Answer: YES! According to the payback method, the investment will be paid back after 3 years, and hence give a profit according to the company’s investment rules.

Year Cash Flow Payback0 $ -100 000.00 $ -100 000.00 1 $ 33 000.00 $ -67 000.00 2 $ 38 000.00 $ -29 000.00 3 $ 43 000.00 $ 14 000.00 4 $ 48 000.00 $ 62 000.00 5 $ 53 000.00 $ 115 000.00

Payback Period 3 years

• Consider a project with an investment of $50,000 and cash inflows in years 1,2, & 3 of $30,000, $20,000, $10,000

• The timeline above clearly illustrates that payback in this situation is 2 years. The first two years of return = $50,000 which exactly “pays back” the initial investment

Example: Payback Method

• How long does it take the project to “pay back” its initial investment, taking the time value of money into account?

• Decision rule: Accept the project if it pays back on a discounted basis within the specified time.

• By the time you have discounted the cash flows, you might as well calculate the NPV.

7.3 The Discounted Payback Period

• Suppose Big Deal Co. has an opportunity to make an investment of $100,000 that will return $33,000 in year 1, $38,000 in year 2, $43,000 in year 3, $48,000 in year 4, and $53,000 in year 5. If the company’s required return is 12% and predetermined payback period is 3 years should they make the investment?

Example: Discounted Payback Period

Answer: NO! At the end of three years the project has still not broken even or “ paid back”. Therefore, it must be rejected.

Year Cash Flow PV of Cash Flow Payback0 $ -100 000.00 $ -100 000.00 $ -100 000.00 1 $ 33 000.00 $ 29 464.29 $ -70 535.71 2 $ 38 000.00 $ 30 293.37 $ -40 242.35 3 $ 43 000.00 $ 30 606.55 $ -9 635.80 4 $ 48 000.00 $ 30 504.87 $ 20 869.07 5 $ 53 000.00 $ 30 073.62 $ 50 942.69

Discounted Payback Period 4 years

• Another attractive, but fatally flawed, approach

• Ranking Criteria and Minimum Acceptance Criteria set by management

7.4 Average Accounting Return

Investment of ValueBook Average

IncomeNet AverageAAR

• Disadvantages:– Ignores the time value of money– Uses an arbitrary benchmark cutoff rate– Based on book values, not cash flows and

market values• Advantages:

– The accounting information is usually available

– Easy to calculate

Average Accounting Return

• IRR: the discount rate that sets NPV to zero

• Minimum Acceptance Criteria: – Accept if the IRR exceeds the required

return• Ranking Criteria:

– Select alternative with the highest IRR• Reinvestment assumption:

– All future cash flows assumed reinvested at the IRR

7.5 The Internal Rate of Return

• Disadvantages:– Does not distinguish between investing and

borrowing– IRR may not exist, or there may be multiple

IRRs – Problems with mutually exclusive

investments

• Advantages:– Easy to understand and communicate

Internal Rate of Return (IRR)

• Suppose Big Deal Co. has an opportunity to make an investment of $100,000 that will return $33,000 in year 1, $38,000 in year 2, $43,000 in year 3, $48,000 in year 4, and $53,000 in year 5. If the company require a minimum of 12% return on the investment, should it take this opportunity?

• When calculating Internal Rate of Return (IRR), we want to find the discount rate that will result in an NPV = 0.

• It can be solved in Excel by the IRR-formula, or graphically by calculating NPV over a series of discount rates.

Example: Internal Rate of Return

• Suppose Big Deal Co. has an opportunity to make an investment of $100,000 that will return $33,000 in year 1, $38,000 in year 2, $43,000 in year 3, $48,000 in year 4, and $53,000 in year 5. If the company require a minimum of 12% return on the investment, should it take this opportunity?


Answer: YES! The project’s IRR is 29.3% which is higher than the required rate of return.

Year Cash Flow0 $ -100 000.00 1 $ 33 000.00 2 $ 38 000.00 3 $ 43 000.00 4 $ 48 000.00 5 $ 53 000.00

Internal Rate of Return (IRR) 29.3%


75

0 % 2 % 4 % 6 % 8 % 10 % 12 % 14 % 16 % 18 % 20 % 22 % 24 % 26 % 28 % 30 % 32 % 34 % 36 % 38 % 40 % $-40,000.00

$-20,000.00

$-

$20,000.00

$40,000.00

$60,000.00

$80,000.00

$100,000.00

$120,000.00

$140,000.00

Internal Rate of Return

NPV

IRR = 29.3%

7.6 Problems with IRR

Multiple IRRs

Are We Borrowing or Lending

The Scale Problem

The Timing Problem

IRR Pitfall 1 – Borrowing or lending?

• In this scenario, both projects seems to be ok according to IRR. However, when discounting at 10% the lender gets a positive NPV, while the borrower has a negative NPV.

• When borrowing money the NPV of the project increases as the discount rate increases, since money today becomes increasingly and relatively more valuable.

• This is contrary to the normal relationship between NPV and discount rates.

Cash Flow 1 Cash Flow 2 IRR NPV @10%Lending -1000 1500 50 % 363,64Borrowing 1000 -1500 50 % - 363,64

IRR Pitfall 1 – Borrowing or lending?

0 % 6 % 12 % 18 % 24 % 30 % 36 % 42 % 48 % 54 % 60 % 66 % 72 % 78 % 84 % 90 % 96 %

-600.00

-400.00

-200.00

-

200.00

400.00

600.00

NPV LendingNPV Borrowing

IRR Pitfall 2 - Multiple Rates of Return• Certain cash flows can generate NPV=0 at two different discount rates.• The following cash flow generates NPV=$ 0 at both IRR% of (-44%) and

+11.6%.

• Notice that Excel returns the error #NUM! when trying to calculate the IRR of this cash flow, since the IRR is not unique.

Cash flow 0 Cash flow 1 CF 9 CF 10 IRR NPV @10%Project 1 -60 12 ... 12 -15 #NUM! -3,33

-50 %-41 %-32 %-23 %-14 % -5 % 4 % 13 % 22 % 31 % 40 % 49 %

kr -1,000.00

kr -800.00

kr -600.00

kr -400.00

kr -200.00

kr 0.00

kr 200.00

kr 400.00

kr 600.00

NPV Project 1

IRR Pitfall 2 – Multiple rates of return• It is possible to have no IRR and a positive NPV.

• You can guarantee against multiple IRRs by having only positive cash flows after the first initial investment.

339500,2000,3000,1

%10@Project 210

NoneC

NPVIRRCCC

IRR Pitfall 3 - Scale problem• IRR sometimes ignores the magnitude of the project, and the

following example illustrates this.• You have to decide between two film projects.• Due to the high risk in movie industry the discount rate is set to

25%.

• According to IRR, the small budget movie will be chosen, since the IRR is bigger, 300% > 160%.

• However, the earnings for the large budget is bigger. How can you by using IRR, show that the large budget is the best investment?

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Investment Cash flow 1 NPV @25% IRR

Small budget

-10 million 40 million 22 million 300 %

Large budget

-25 million 65 million 27 million 160 %

IRR Pitfall 3 - Scale problem• By using incremental IRR, you can show that the large budget

provides extra return compared to the small budget movie:

• We know that this includes the IRR of the first 10 million investment. In addition we get 66.67% return on the extra 15 million invested, which is higher than the discount rate at 25%. Therefore the incremented investment should be taken.

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Investment Cash flow 1 NPV @25% IRR

Small budget -10 million 40 million 22 million 300 %

Large budget -25 million 65 million 27 million 160 %

Incremental (large – small)

-15 million 25 million 5 million 66,67 %

IRR Pitfall 3 - Scale Problem

Would you rather make 100% or 50% on your investments?

What if the 100% return is on a $1 investment, while the 50% return is on a $1,000 investment?

• We have usually assumed independent projects: accepting or rejecting one project does not affect the decision of the other projects.

• Our concern has been if the project has exceeded a MINIMUM acceptance criteria.

• There might be scenarios where we have Mutually Exclusive Projects: only ONE of several potential projects can be chosen, e.g., acquiring an accounting system.

• Then we need to RANK all alternatives, and select the best one. When using IRR the timing may provide a problem when comparing two or more projects.

Pitfall 4 –Timing problem

• Consider the following two projects:

• Because of the late payment in project B, this project has the lowest IRR. However, as seen from the NPVs, project B has the highest NPV when discounted at a lower rate, and we therefore need to find out when project A is better than B and vice versa.

• The crossover rate will tell us at what discount rate NPV A = NPV B.

Pitfall 4 –Timing problem

NPV

CF 1 CF 2 CF 3 CF 4 IRR @ 0% @ 10% @ 15%

Project A -10000 10000 1000 1000 16,04 % 2 000,00 668,67 109,31

Project B -10000 1000 1000 12000 12,94 % 4 000,00 751,31 -484,10

Pitfall 4 – Timing problem

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0.00 % 2.00 % 4.00 % 6.00 % 8.00 % 10.00 % 12.00 % 14.00 % 16.00 % 18.00 % 20.00 % 22.00 % 24.00 %

-3,000.00

-2,000.00

-1,000.00

-

1,000.00

2,000.00

3,000.00

4,000.00

5,000.00

NPV Project ANPV Project B

Crossover rate = 10.55%

IRR B = 12.94%

IRR A = 16.04%

Calculating the Crossover Rate

Compute the IRR for either project “A-B” or “B-A”

0.00 % 3.75 % 7.50 % 11.25 %15.00 %18.75 %22.50 %

kr -2,500.00

kr -2,000.00

kr -1,500.00

kr -1,000.00

kr -500.00

kr 0.00

kr 500.00

kr 1,000.00

kr 1,500.00

kr 2,000.00

kr 2,500.00

NPV Project A - BNPV Project B - A

10.55% = IRR

Cash Flow 1 Cash Flow 2 Cash Flow 3 Cash Flow 4 IRRProject A -10000 10000 1000 1000 16,04 %Project B -10000 1000 1000 12000 12,94 %Project A - B 0 9000 0 -11000 10,55 %Project B - A 0 -9000 0 11000 10,55 %

• NPV and IRR will generally give the same decision.

• Exceptions:– Non-conventional cash flows – cash flow signs

change more than once– Mutually exclusive projects

• Initial investments are substantially different• Timing of cash flows is substantially different

NPV versus IRR

• Minimum Acceptance Criteria: – Accept if PI > 1

• Ranking Criteria: – Select alternative with highest PI

7.7 The Profitability Index (PI)

Investent Initial

FlowsCash Future of PV TotalPI

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Capital rationing

• So far we have assumed that the company may pursue all investment projects with a positive NPV

• In real life, however, the company may face restrictions on capital access– Capital rationing

• Capital rationing may arise from imperfect capital markets– e.g., special demands from investors and analysts

• The problem is then to design a portfolio of projects which maximises total NPV

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Project ranking with capital rationing

• Consider the following three projects

• Assume a capital budget of NOK 10 M• Project I has the highest NPV at a 10% discount rate, but not larger

than the sum of projects J and K• We therefore need a tool which secure maximum NPV per NOK

invested.

Initial investment Cash Flow 1 Cash Flow 2 NPV @10%Project I -10 30 5 21.4 Project J -4 5 20 17.1 Project K -6 5 15 10.9

92

An NPV index for capital rationing

• The Profitability Index (PI) is calculated by:

• This yields for our projects I, J, and K

• We should therefore chose projects J and K which would provide a combined PI = 2.80 > PI Project I = 2.14

I0 NPV @10% PIProject I 10 21.4 2.14Project J 4 17.1 4.27Project K 6 10.9 1.82

• Disadvantages:– Problems with mutually exclusive

investments• Advantages:

– May be useful when available investment funds are limited

– Easy to understand and communicate– Correct decision when evaluating

independent projects

The Profitability Index

• Varies by industry:– Some firms use payback, others use accounting rate of return.

• The most frequently used technique for large corporations is IRR or NPV.

7.8 The Practice of Capital Budgeting

• Net present value– Difference between market value and cost– Accept the project if the NPV is positive– Has no serious problems– Preferred decision criterion

• Internal rate of return– Discount rate that makes NPV = 0– Take the project if the IRR is greater than the required return– Same decision as NPV with conventional cash flows– IRR is unreliable with non-conventional cash flows or mutually

exclusive projects• Profitability Index

– Benefit-cost ratio– Take investment if PI > 1– Cannot be used to rank mutually exclusive projects– May be used to rank projects in the presence of capital rationing

Summary – Discounted Cash Flow

• Payback period– Length of time until initial investment is recovered– Take the project if it pays back in some specified period– Doesn’t account for time value of money, and there is

an arbitrary cutoff period• Discounted payback period

– Length of time until initial investment is recovered on a discounted basis

– Take the project if it pays back in some specified period– There is an arbitrary cutoff period

Summary – Payback Criteria

Opening case revisitedOil field investment

97


Should the oil field be developed?Calculate the following:• Payback Period• Discounted Payback Period• Internal Rate of Return• Net Present Value• Profitability Index


Decision rule #1 - Net Present ValueNPV 1 360,51

Decision rule #2 - Payback periodYears to payback 11

Desicion rule #2 version 2 - Discounted Payback periodYears to payback 14

Decision rule #3 - Internal rate of returnIRR 14,5 %

Decision rule #4 - Profitability IndexInitial investment -5 086,75 Total PV 6 447,26 Profitability index 1,27

98

NPV > 0. The field should be developed.

If the decision rule is to accept investments with more than 11 years (or 14 years for discounted payback), then the investment should be started.

If the decision rule is to accept investments with more than 11 years (or 14 years for discounted payback), then the investment should be started.

If the alternative cost at the company is below 14.5% the investment will provide a bigger return than other projects.

PI > 1. The field should be developed.


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Reduced exploration costs

Reducedinvestments

Reduced tariffs

Reduced operational costs

Swift decision-makingFast-track developments

Accelerated ramp-upof production

Improved regularity and capacity utilisationExtension of plateau production

Higher prices

Increased recovery

Extended tailend production

There are a lot of uncertainties when estimating the value of an investment.And the longer the horizon, the higher the uncertainty is.

So far we have only used certain outcomes, but in our next lecture we will introduce probability

as we do sensitivity analysis, decision treesand monte carlo analysis.

How much can the oil price increase or decrease within 20 years?How big or small is the real size of the oil field?

How much can we increase the efficiency ratio by improved technology?…

And how will this effect the valuation of our project?

Lecture summary

• Chapter 6 – Stock Valuation– Present Value of Common Stocks– Dividend Growth Model (DGM)– P/E Ratio– Common vs. Preferred Stock– Stock Markets

• Chapter 7 – NPV and other Investment Rules– Net Present Value– Internal Rate of Return– (Discounted) Payback Method– Profitability Index

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Documents

Lecture 3