Last Study Topics

• How To Value Common Stock• Valuing Common Stock• Capitalization Rates• Returns Measurements

Today’s Topics

• FCF and PV• NPV and its Competitors• The Payback Period• The Book Rate of Return• Internal Rate of Return

FCF and PV

• Free Cash Flows (FCF) should be the theoretical basis for all PV calculations.

• FCF is a more accurate measurement of PV than either Div or EPS.

• The market price does not always reflect the PV of FCF.

• When valuing a business for purchase, always use FCF.

FCF and PVValuing a Business

The value of a business is usually computed as the discounted value of FCF out to a valuation horizon (H).

• The valuation horizon is sometimes called the terminal value and is calculated like PVGO.

HH

HH

r

PV

r

FCF

r

FCF

r

FCFPV

)1()1(...

)1()1( 22

11

FCF and PVValuing a Business

HH

HH

r

PV

r

FCF

r

FCF

r

FCFPV

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11

PV (free cash flows) PV (horizon value)

FCF and PVExample

Given the cash flows for Concatenator Manufacturing Division, calculate the PV of near term cash flows, PV (horizon value), and the total value of the firm. r=10% and g= 6%

66613132020202020(%) growth .EPS

1.891.791.681.59.23-.20-1.39-1.15-.96-.80- FlowCash Free

1.891.781.681.593.042.693.462.882.402.00Investment

3.783.573.363.182.812.492.071.731.441.20Earnings

51.3173.2905.2847.2643.2374.2028.1740.1400.1200.10ValueAsset

10987654321

Year

FCF and PVExample - continued

Given the cash flows for Concatenator Manufacturing Division, calculate the PV of near term cash flows, PV (horizon value), and the total value of the firm. r=10% and g= 6%

.

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FCF and PVExample - continued

Given the cash flows for Concatenator Manufacturing Division, calculate the PV of near term cash flows, PV (horizon value), and the total value of the firm. r=10% and g= 6%

.

$18.8

22.4-3.6

value)PV(horizonPV(FCF)s)PV(busines

Why Net Present Value Leads to Better Investment

Decisions than Other Criteria

Wajid S Ahmed

Chapter 5

McGraw Hill/Irwin

Introduction

• Vegetron’s chief financial officer (CFO) is wondering how to analyze a proposed $1 million investment in a new venture called project X;

• Your response should be as follows: “First, forecast the cash flows generated by project X over its economic life.

• Second, determine the appropriate opportun -ity cost of capital

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• Third, use this opportunity cost of capital to discount the future cash flows of project X;

• Fourth, calculate net present value (NPV) by subtracting the $1 million investment from PV. Invest in project X if its NPV is greater than zero.– Why NPV is so important!

Continue

• What is best for Vegetron stockholders – Maximization of their wealth.

• Lets see the following table;

Continue

• Clearly project X is worthwhile if its present value, PV, is greater than $1 million, that is, if net present value is positive;

• By calculating the present value of project X, we are replicating the process by which the common stock of firm X would be valued in capital markets;

• And, ultimately show up in Vegetron’s market value;

Continue

• The opportunity cost of taking the project is the return shareholders could have earned had they invested the funds on their own;

• When we discount the project’s cash flows by the expected rate of return on comparable financial assets, we are measuring how much investors would be prepared to pay for your project;

NPV and Cash Transfers• Every possible method for evaluating

projects impacts the flow of cash about the company as follows.

Cash

Investment opportunity (real

asset)Firm Shareholder

Investment opportunities

(financial assets)

Invest Alternative: pay dividend to shareholders

Shareholders invest for themselves

NPV’s Competitors

• we will now look at three of the alternatives.– They are:– 1. The book rate of return.– 2. The payback period.– 3. The internal rate of return.

• But, Three Points to Remember about NPV!

NPV’s 3-Points

• First, the NPV rule recognizes that a dollar today is worth more than a dollar tomorrow, because the dollar today can be invested to start earning interest immediately;

• Second, net present value depends solely on the forecasted cash flows from the project and the opportunity cost of capital;

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• Third, because present values are all measured in today’s dollars, you can add them up;

• Therefore, if you have two projects A and B, the net present value of the combined investment is;

– NPV(A +B) = NPV(A) + NPV(B)

NPV depends on CFs

• Net present value depends only on the project’s cash flows and the opportunity cost of capital;

• When companies report to shareholders, they report book—that is, accounting—income and book assets; book income gets most of the immediate attention;

Continue• The book rate of return may not be a good

measure of true profitability. It is also an average across all of the firm’s activities;

– Book rate of return = book income book assets

• The average profitability of past investments is not usually the right hurdle for new investments;

Payback

• The payback period of a project is the number of years it takes before the cumulative forecasted cash flow equals the initial outlay.

• The payback rule says only accept projects that “payback” in the desired time frame.

• This method is very flawed, primarily because it ignores later year cash flows and the the present value of future cash flows.

Payback

ExampleExamine the three projects and note the mistake we would make if we insisted on only taking projects with a payback period of 2 years or less.

050018002000-C

018005002000-B

50005005002000-A

10% @NPVPeriod

PaybackCCCCProject 3210

Payback

ExampleExamine the three projects and note the mistake we would make if we insisted on only taking projects with a payback period of 2 years or less.

502050018002000-C

58-2018005002000-B

2,624350005005002000-A

10% @NPVPeriod

PaybackCCCCProject 3210

The Payback Rule

• The payback rule with a cutoff period of three or more years would accept all three projects;

• Therefore, regardless of the choice of cutoff period, the payback rule gives answers different from the net present value rule;– The payback rule ignores all cash flows after the

cutoff date;– The payback rule gives equal weight to all cash

flows before the cutoff date;

continue

• In order to use the payback rule, a firm has to decide on an appropriate cutoff date;

• If it uses the same cutoff regardless of project life, it will tend to accept many poor short-lived projects and reject many good long-lived ones;

• What about the discounted-payback rule asks?

Internal Rate of Return

ExampleYou can purchase a turbo powered machine tool gadget for $4,000. The investment will generate $2,000 and $4,000 in cash flows for two years, respectively. What is the IRR on this investment?

Internal Rate of ReturnExample

You can purchase a turbo powered machine tool gadget for $4,000. The investment will generate $2,000 and $4,000 in cash flows for two years, respectively. What is the IRR on this investment?

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21

IRRIRRNPV

Internal Rate of ReturnExample

You can purchase a turbo powered machine tool gadget for $4,000. The investment will generate $2,000 and $4,000 in cash flows for two years, respectively. What is the IRR on this investment?

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000,4

)1(

000,2000,4

21

IRRIRRNPV

%08.28IRR

Internal Rate of Return

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

10 20 30 40 50 60 70 80 90 100

Discount rate (%)

NP

V (

,000

s)

IRR=28%

Summary

• FCF and PV• NPV and its Competitors• The Payback Period• The Book Rate of Return• Internal Rate of Return

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• Now, the internal rate of return rule is to accept an investment project if the opportunity cost of capital is less than the internal rate of return;– If the opportunity cost of capital is less than the 28

percent IRR, then the project has a positive NPV.– If it is equal to the IRR, the project has a zero NPV. – And if it is greater than the IRR, the project has a

negative NPV

Internal Rate of ReturnPitfall 1 - Lending or Borrowing?• With some cash flows (as noted below) the NPV of the

project increases s the discount rate increases. • This is contrary to the normal relationship between NPV

and discount rates.

364%5015001000

,364%5015001000

%10@Project 0

B

A

NPVIRRCC t

Project C• If the opportunity cost of capital is 10 percent,

that means the project is a good one. Or does it?

• Should we accept or reject? – The only way to find the answer is to look at the

net present value.

.7520%1,7284,3203,6001,000

NPV@10%IRRCCCC 3210

Internal Rate of ReturnPitfall 1 - Lending or Borrowing?• With some cash flows (as noted below) the NPV of the project increases

s the discount rate increases. • This is contrary to the normal relationship between NPV and discount

rates.

Discount Rate

NPV

Internal Rate of ReturnPitfall 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 (-

50%) and 15.2%.

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CCCCCCC

Internal Rate of ReturnPitfall 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 (-50%) and 15.2%. 1000

NPV

500

0

-500

-1000

Discount Rate

IRR=15.2%

IRR=-50%

Internal Rate of ReturnPitfall 3 - Mutually Exclusive Projects• IRR sometimes ignores the magnitude of the project.• The following two projects illustrate that problem.

818,1175000,35000,20

182,8100000,20000,10

%10@Project 0

F

E

NPVIRRCC t

Explanation

• If you follow the IRR rule, you have the satisfaction of earning a 100 percent rate of return;

• If you follow the NPV rule, you are $11,818 richer;

• Is it worth making the additional $10,000 investment in F?– you look at the IRR on the incremental flows.

Internal Rate of ReturnPitfall 3 - Mutually Exclusive Projects

Opportunity Cost matters

• if the opportunity cost of capital were 20 percent, investors would place a higher value on the shorter-lived project G.

• But in our example the opportunity cost of capital is not 20 percent but 10 percent.

• Investors are prepared to pay relatively high prices for longer-lived securities, and so they will pay a relatively high price for the longer-lived project.

Continue

• At a 10 percent cost of capital, an investment in H has an NPV of $9,000 and an investment in G has an NPV of only $3,592;

• Assume, it is a shortage of capital which forces the choice between G and H.;

• When this implicit assumption is brought out, H is better if there is no capital shortage.

Incremental Flows• First, you check that project G has a

satisfactory IRR. • Then you look at the return on the additional

investment in H.• The IRR on the incremental investment in H is

15.6 percent. Since this is greater than the opportunity cost of capital, you should undertake H rather than G.

Internal Rate of ReturnPitfall 4 - Term Structure Assumption• We assume that discount rates are stable during

the term of the project. • This assumption implies that all funds are

reinvested at the IRR. • This is a false assumption.• In a situation where it is important, we have to

compare the project IRR with the expected IRR (yield to maturity) offered by a traded security

Internal Rate of Return• that;– (1) is equivalent in risk to the project

and. – (2) offers the same time pattern of cash

flows as the project.

• Calculating the IRR can be a laborious task. Fortunately, financial calculators can perform this function easily.

Profitability Index

• When resources are limited, the profitability index (PI) provides a tool for selecting among various project combinations and alternatives

• A set of limited resources and projects can yield various combinations.

• The highest weighted average PI can indicate which projects to select.

Profitability Index

ExampleWe only have $300,000 to invest. Which do we select?

Proj NPV Investment PIA 230,000 200,000 1.15B 141,250 125,000 1.13C 194,250 175,000 1.11D 162,000 150,000 1.08

Investment

NPVIndexity Profitabil

Profitability IndexExample - continuedProj NPV Investment PIA 230,000 200,000 1.15B 141,250 125,000 1.13C 194,250 175,000 1.11D 162,000 150,000 1.08

Select projects with highest Weighted Avg PIWAPI (BD) = 1.13(125) + 1.08(150) + 0.0 (25) (300) (300) (300) = 1.01

Profitability IndexExample - continuedProj NPV Investment PIA 230,000 200,000 1.15B 141,250 125,000 1.13C 194,250 175,000 1.11D 162,000 150,000 1.08

Select projects with highest Weighted Avg PIWAPI (BD) = 1.01WAPI (A) = 0.77WAPI (BC) = 1.12

Linear Programming

• Maximize Cash flows or NPV• Minimize costs

ExampleMax NPV = 21Xn + 16 Xb + 12 Xc + 13 Xd

subject to10Xa + 5Xb + 5Xc + 0Xd <= 10-30Xa - 5Xb - 5Xc + 40Xd <= 12

Vegetron Case

YEAR1 2 3 4 5

1.Revenue 180 180 180 180 1802. Operating costs 70 70 70 70 703. Depreciation a 80 80 80 80 804. Net income 30 30 30 30 305. Start-of-year book value 400 320 240 160 80

Book rate of return 7.50% 9.40% 12.50% 18.75% 37.50%(4÷5)

Table 5.1

Vegetron CaseTable 5.2

YEAR1 2 3 4 5 6 7

1.Reyenue 140 140 140 140 140 140 1402. Operating costs 55 55 55 55 55 55 553. Depreciation a 57 57 57 57 57 57 574. Net income 28 28 28 28 28 28 285. Start-of-year book value 400 343 286 229 171 114 57

6. Book rate of return 7.00% 8.20% 9.80% 12.20% 16.40% 24.60% 49.10% (4÷5)