Fi8000Fi8000Valuation ofValuation of

Financial AssetsFinancial Assets

Milind ShrikhandeMilind ShrikhandeAssociate Professor of FinanceAssociate Professor of Finance

TodayToday

☺SyllabusSyllabus

☺Course overviewCourse overview

☺Lecture Sequence: Options…Lecture Sequence: Options…

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☺ ExpectationsExpectations☺ Be hereBe here☺ Ask questionsAsk questions☺ Work practice problemsWork practice problems

☺ Required skillsRequired skills☺ Spreadsheet (Excel) and InternetSpreadsheet (Excel) and Internet

☺ Required materialsRequired materials☺ Text: Bodie, Kane and Marcus 6Text: Bodie, Kane and Marcus 6thth edition edition☺ Solutions manualSolutions manual

SyllabusSyllabus

☺ GradingGrading☺ 3 Quizzes @ 20% each3 Quizzes @ 20% each

Similar to or related to practice problems and examplesSimilar to or related to practice problems and examples

No make-upsNo make-ups

☺ Final exam (comprehensive) @ 30%Final exam (comprehensive) @ 30%☺ Stock-Trak assignment @ 10%Stock-Trak assignment @ 10%

☺ Make-up PolicyMake-up Policy☺ No make-up quizzesNo make-up quizzes☺ Everyone must take the final examEveryone must take the final exam

SyllabusSyllabus

☺Grading – Typical Department PolicyGrading – Typical Department Policy☺ No more than 35% ANo more than 35% A☺ Majority (approximately 50%) BMajority (approximately 50%) B☺ Lagging performance earns a C or lowerLagging performance earns a C or lower

☺Administrative – Withdrawal with a WFAdministrative – Withdrawal with a WF☺ Beyond 3 absences from classBeyond 3 absences from class☺ Withdrawal after the semester midpointWithdrawal after the semester midpoint☺ Withdrawal while doing failing workWithdrawal while doing failing work

SyllabusSyllabus

☺MaterialsMaterials☺ (Financial) Calculator – bring every day(Financial) Calculator – bring every day☺ Text – leave it where you read itText – leave it where you read it☺ Lecture notes, handouts – providedLecture notes, handouts – provided

☺Office HoursOffice Hours☺ Drop-in, phone, e-mail and by appointmentDrop-in, phone, e-mail and by appointment

Approaches to ValuationApproaches to Valuation

☺Discounted cash flowsDiscounted cash flowsThe value of an asset is related to the stream of The value of an asset is related to the stream of expected cash flowsexpected cash flows that it generates, and that it generates, and should reflect compensation for should reflect compensation for time time and and riskrisk..

☺Arbitrage pricingArbitrage pricingWhen two assets have exactly the same stream When two assets have exactly the same stream of cash flows (magnitude, date, state) their of cash flows (magnitude, date, state) their prices should be identical.prices should be identical.

Valuation of Financial AssetsValuation of Financial Assets

BondsBonds StocksStocks DerivativeDerivative

CF streamCF streamcoupons coupons

and and

face-valueface-valuedividendsdividends

contingent on contingent on contract and contract and underlying underlying

assetasset

Time lineTime line fixed fixed maturitymaturity

no no maturitymaturity

fixed fixed expirationexpiration

RiskRisk default riskdefault risk systematic systematic riskrisk

contingent on contingent on contract and contract and underlying underlying

assetasset

Discounted Cash Flows (DCF) ValuationDiscounted Cash Flows (DCF) Valuation

The IdeaThe IdeaThe value of an asset is the present value The value of an asset is the present value

of its expected cash flows.of its expected cash flows.

The Philosophical BasisThe Philosophical Basis Every asset has an intrinsic value that can Every asset has an intrinsic value that can

be estimated, based upon the be estimated, based upon the characteristics of the stream of cash flows characteristics of the stream of cash flows

that the asset generates.that the asset generates.

Inputs for DCF ValuationInputs for DCF Valuation

☺The The magnitudemagnitude of the expected CFs of the expected CFs

☺The The timingtiming of the expected CFs of the expected CFs

☺The The riskrisk level of the expected CFs level of the expected CFs

Assumptions Underlying DCF Assumptions Underlying DCF ValuationValuation

☺ MagnitudeMagnitude: investors prefer to have more rather : investors prefer to have more rather than less.than less.

☺ TimingTiming: investors prefer a dollar today rather : investors prefer a dollar today rather than a dollar some time in the future.than a dollar some time in the future.

☺ RiskRisk: investors would rather get a certain CF of : investors would rather get a certain CF of $1 than get a lottery ticket with an expected $1 than get a lottery ticket with an expected (average) CF of $1.(average) CF of $1.

The Mechanics of DCFThe Mechanics of DCF

CFCF1 1 CFCF2 2 CFCF3 3 CFCF4 4 CFCFTT

|--------|--------|--------|--------|---------------|---> |--------|--------|--------|--------|---------------|---> tt

0 1 2 3 4 … T0 1 2 3 4 … T

( , 1,..., ; )tValue f CF t T k

NotationNotation

PVPV = Present Value = Present ValueFVFV = Future Value = Future Value

CFCFtt = Cash Flow on date = Cash Flow on date tt

tt is the time (date) index ( is the time (date) index (t = 1, 2, …, Tt = 1, 2, …, T))kk = risk-adjusted discount rate = risk-adjusted discount rate (risk-adjusted / opportunity cost of capital)(risk-adjusted / opportunity cost of capital)

rfrf = risk-free discount rate = risk-free discount rate (use as the discount rate if the probability of (use as the discount rate if the probability of defaultdefault is zero) is zero)

gg = growth rate = growth rate

The Mechanics of Time ValueThe Mechanics of Time Value

CompoundingCompounding Converts present cash flows into future cash flows.Converts present cash flows into future cash flows.

DiscountingDiscountingConverts future cash flows into present cash flows.Converts future cash flows into present cash flows.

The Additivity PrincipalThe Additivity PrincipalCash flows at different points in time cannot be Cash flows at different points in time cannot be

compared or aggregated. All cash flows have to be compared or aggregated. All cash flows have to be brought to the same point in time before brought to the same point in time before

comparisons or aggregations can be made.comparisons or aggregations can be made.

Compounding a Cash FlowCompounding a Cash Flow$100$100 FVFV

|--------|-----> |--------|-----> t k = 5%t k = 5%

0 10 1

$100 $100 FVFV

|--------|--------|---> |--------|--------|---> t k = 5%t k = 5%

0 1 20 1 2

PV FVPV FV

|--------|--------|-----------|---> |--------|--------|-----------|---> tt

0 1 2 … T0 1 2 … T

2

100 1.05 $105

100 1.05 $110.25

(1 )T

FV

FV

FV PV k

ExampleExample

In a study of returns on stocks and bonds In a study of returns on stocks and bonds between 1926 and 1997, Ibbotson and between 1926 and 1997, Ibbotson and Sinquefield found that on average Sinquefield found that on average stocksstocks made made 12.4%12.4% annual return, annual return, treasury bondstreasury bonds made made 5.2%5.2% and and treasury billstreasury bills made made 3.6%3.6%..

Assuming that these returns continue into the Assuming that these returns continue into the future, what will be the value of $100 invested future, what will be the value of $100 invested in each category for 1year, 5 years, 10 years?in each category for 1year, 5 years, 10 years?

SolutionSolution

Holding Holding PeriodPeriod StocksStocks

T.T.

BondsBonds

T.T.

BillsBills

11 $112.40$112.40 $105.20$105.20 $103.60$103.60

55 $179.40$179.40 $128.85$128.85 $119.34$119.34

1010 $321.86$321.86 $166.02$166.02 $142.43$142.43

Discounting a Cash FlowDiscounting a Cash FlowPV $100PV $100

|--------|-----> |--------|-----> t k = 5%t k = 5%

0 10 1

PVPV $100$100

|--------|--------|-----> |--------|--------|-----> t k = 5%t k = 5%

0 1 20 1 2

PV FVPV FV

|--------|--------|------------|---> |--------|--------|------------|---> tt

0 1 2 … T0 1 2 … T

2

100$95.24

1.05

100$90.70

1.05

(1 )T

PV

PV

FVPV

k

The Present Value The Present Value of a Stream of Cash Flowsof a Stream of Cash Flows

CFCF1 1 CFCF2 2 CFCF3 3 CFCF4 4 CFCFTT

|--------|--------|--------|--------|--------------|---> |--------|--------|--------|--------|--------------|---> tt

0 1 2 3 4 … T0 1 2 3 4 … T

1 2

1 22

1

( ) ( ) ... ( )

...(1 ) (1 ) (1 ) (1 )

T

TtT

T tt

PV PV CF PV CF PV CF

CFCF CF CF

k k k k

ExamplesExamples

1.1. How much will you pay today for a project that How much will you pay today for a project that is expected to pay a dividend of $500,000 is expected to pay a dividend of $500,000 three year from now, if the appropriate (risk-three year from now, if the appropriate (risk-adjusted) annual discount rate for this project adjusted) annual discount rate for this project is 10%?is 10%?

2.2. What is the value of a project that is expected What is the value of a project that is expected to pay $150,000 one year from now and to pay $150,000 one year from now and $500,000 three years from now, if the $500,000 three years from now, if the appropriate (risk-adjusted) annual discount appropriate (risk-adjusted) annual discount rate for this project is 10%?rate for this project is 10%?

SolutionsSolutions

1.1.

PV = $500,000/(1+0.1)PV = $500,000/(1+0.1)33 = $375,657.40 = $375,657.40

2.2.

PV = $150,000/(1+0.1)PV = $150,000/(1+0.1)11 + $500,000/(1+0.1) + $500,000/(1+0.1)33

= $136,363.64 + $375,657.40= $136,363.64 + $375,657.40

= $512,021.04= $512,021.04

Cash Flow Streams – Cash Flow Streams – special casesspecial cases

A growing perpetuityA growing perpetuity::

CFCF CF(1+g)CF(1+g) … … CF(1+g)CF(1+g)(t-1) (t-1) ……

|---------|---------|-------------------|-------------------> |---------|---------|-------------------|-------------------> timetime

0 1 2 … t …0 1 2 … t …

( 1)

2

( 1)

1

(1 ) (1 )... ...

(1 ) (1 ) (1 )

(1 ) (if )

(1 )

t

t

t

tt

CF CF g CF gPV

k k k

CF g CFk g

k k g

ExampleExample

In 1992, Southwestern Bell paid dividends In 1992, Southwestern Bell paid dividends per share of $2.73. It’s earnings and per share of $2.73. It’s earnings and dividends had grown at 6% a year between dividends had grown at 6% a year between 1988 and 1992 and were expected to grow 1988 and 1992 and were expected to grow at the same rate in the long term. The rate of at the same rate in the long term. The rate of return required by investors on stocks of return required by investors on stocks of equivalent risk was 12.23%.equivalent risk was 12.23%.

What should be the value of the stock?What should be the value of the stock?

SolutionSolution

Current dividend per share = $2.73Current dividend per share = $2.73

Expected growth rate g = 6% = 0.06Expected growth rate g = 6% = 0.06

CFCF11 = $2.73 ·(1+0.06) = $2.8938 = $2.73 ·(1+0.06) = $2.8938

Discount rate k = 12.23% = 0.1223Discount rate k = 12.23% = 0.1223

2.8938$46.45

0.1223 0.06PV

Example - continuedExample - continued

In fact, the stock was actually trading at $70 per In fact, the stock was actually trading at $70 per share. This price could be justified by using a share. This price could be justified by using a higher expected growth rate.higher expected growth rate.

2.73(1 )70

0.1223

8%

g

g

g

Cash Flow Streams – Cash Flow Streams – special casesspecial cases

A growing annuityA growing annuity::

CFCF CF(1+g)CF(1+g) … … CF(1+g)CF(1+g)(T-1)(T-1)

|---------|---------|-------------------|-------------------> |---------|---------|-------------------|-------------------> timetime

0 1 2 … T0 1 2 … T

( 1)

2

( 1)

1

(1 ) (1 )...

(1 ) (1 ) (1 )

(1 ) 1 1

(1 ) 1

T

T

TtT

tt

CF CF g CF gPV

k k k

CF g CF g

k k g k

ExampleExample

Suppose you are trying to borrow $200,000 Suppose you are trying to borrow $200,000 to buy a house on a conventional 30-year to buy a house on a conventional 30-year mortgage with monthly payments.mortgage with monthly payments.

The monthly interest rateThe monthly interest rate on this loan is on this loan is 0.7%. What is the monthly payment on this 0.7%. What is the monthly payment on this loan?loan?

SolutionSolution

PV = $200,000PV = $200,000

T = 30·12 = 360T = 30·12 = 360

k = 0.7% = 0.007k = 0.7% = 0.007g = 0g = 0

3601

$200,000 10.007 1 0.007

$1,523.7

CF

CF

The Frequency of CompoundingThe Frequency of Compounding

The frequency of compounding affects both The frequency of compounding affects both the future and present values of cash flows.the future and present values of cash flows.

The The quoted annual interestquoted annual interest raterate may be may be compounded more frequently than once a compounded more frequently than once a year. This will affect the year. This will affect the effective annual effective annual interest rateinterest rate which is determined by the which is determined by the specified frequency of compounding.specified frequency of compounding.

ExampleExample

A government note pays a coupon (interest) A government note pays a coupon (interest) of 4.75% of par value. This means that a of 4.75% of par value. This means that a $1,000 face-value note pays $47.50 in $1,000 face-value note pays $47.50 in annual interest in two semiannual annual interest in two semiannual installments of $23.75 each.installments of $23.75 each.

The The quoted annual interest ratequoted annual interest rate is 4.75%, is 4.75%, but it is but it is compounded semiannuallycompounded semiannually. What . What is the is the effective annual interest rateeffective annual interest rate??

SolutionSolution

2

1 1

0.04751 1

2

4.8064%

mquoted rate

effective ratem

effective rate

effective rate quoted rate

The Frequency of CompoundingThe Frequency of Compounding

FrequencyFrequency Quoted Quoted RateRate

mm Effective Effective RateRate

annualannual 10%10% 11 10.00%10.00%

Semi-annualSemi-annual 10%10% 22 10.25%10.25%

monthlymonthly 10%10% 1212 10.47%10.47%

weeklyweekly 10%10% 5252 10.51%10.51%

continuouscontinuous 10%10% ∞∞ 10.52%10.52%

Continuous CompoundingContinuous Compounding

1 1

As m goes to infinity (m ) we get

1

m

quoted rate

quoted rateeffective rate

m

effective rate e

The Frequency of Compounding The Frequency of Compounding - continued- continued

12

1 1 1

If one sub-period is a monthe and m=12, then

1 1

If one sub-period is 6 months and m=4, then

1

meffective m period rate effective period rate

effective annual rate effective monthly rate

effective

42 1 6year rate effective months rate

Terminology and NotationTerminology and Notation

The quoted annual rate is also called the The quoted annual rate is also called the APR (Annual Percentage Rate)APR (Annual Percentage Rate)

The Effective Annual Rate is the EARThe Effective Annual Rate is the EAR

We will use the notationWe will use the notation

rrq,annualq,annual = quoted annual rate = quoted annual rate

rreff,annualeff,annual = effective annual rate = effective annual rate

rrannualannual = annual rate (when r = annual rate (when rq,annualq,annual = r = reff,annualeff,annual))

ExampleExample

The The quoted annual ratequoted annual rate of return is 10%, of return is 10%, compounded semiannuallycompounded semiannually. Calculate the . Calculate the following rates:following rates:

a.a.Effective rate for 1 year (10.25%)Effective rate for 1 year (10.25%)

b.b.Effective rate for 2 years (21.55%)Effective rate for 2 years (21.55%)

c.c.Effective rate for 18 months (15.76%)Effective rate for 18 months (15.76%)

d.d.Effective rate for 6 months (5%)Effective rate for 6 months (5%)

e.e.Effective rate for 2 months (1.64%)Effective rate for 2 months (1.64%)