8 - 1 Copyright © 2002 by Harcourt, Inc.All rights reserved. Chapter 2: DCF Applications Application 1: Capital budgeting Application 2: Bond Valuation

8 - 1

Copyright © 2002 by Harcourt, Inc. All rights reserved.

Chapter 2: DCF Applications

Application 1: Capital budgetingApplication 2: Bond ValuationApplication 3: Investment Performance

AnalysisApplication 4: Equity / stock valuations

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What is capital budgeting?

Analysis of potential additions to fixed assets.

Long-term decisions; involve large expenditures.

Very important to firm’s future.

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Steps

1. Estimate CFs (inflows & outflows).2. Assess riskiness of CFs.3. Determine k = WACC (adj.).4. Find NPV and/or IRR.5. Accept if NPV > 0 and/or IRR > WACC.

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.

k1CF

NPV tt

n

0t

NPV: Sum of the PVs of inflows and outflows.

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What is Project L’s NPV?

10 8060

0 1 2 310%

Project L:

-100.00

9.09

49.59

60.1118.79 = NPVL NPVS = $19.98.

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Calculator Solution

Enter in CFLO for L:

-100

10

60

80

10

CF0

CF1

NPV

CF2

CF3

I = 18.78 = NPVL

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Rationale for the NPV Method

NPV = PV inflows – Cost= Net gain in wealth.

Accept project if NPV > 0.

Choose between mutually exclusive projects on basis ofhigher NPV. Adds most value.

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Internal Rate of Return: IRR

0 1 2 3

CF0 CF1 CF2 CF3

Cost Inflows

IRR is the discount rate that forcesPV inflows = cost. This is the sameas forcing NPV = 0.

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.NPV

k1CF

tt

n

0t

.0

IRR1CF

tt

n

0t

NPV: Enter k, solve for NPV.

IRR: Enter NPV = 0, solve for IRR.

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What’s Project L’s IRR?

10 8060

0 1 2 3IRR = ?

-100.00

PV3

PV2

PV1

0 = NPV

Enter CFs in CFLO, then press IRR:IRRL = 18.13%. IRRS = 23.56%.

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40 40 40

0 1 2 3IRR = ?

Find IRR if CFs are constant:

-100

Or, with CFLO, enter CFs and press IRR = 9.70%.

3 -100 40 0

9.70%

INPUTS

OUTPUTN I/YR PV PMT FV

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Rationale for the IRR Method

If IRR > WACC, then the project’s rate of return is greater than its cost--some return is left over to boost stockholders’ returns.

Example: WACC = 10%, IRR = 15%. Profitable.

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IRR Acceptance Criteria

If IRR > k, accept project.

If IRR < k, reject project.

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Bonds and Their Valuation

Key features of bondsBond valuationMeasuring yieldAssessing risk

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Key Features of a Bond

1. Par value: Face amount; paid at maturity. Assume $1,000.

2. Coupon interest rate: Stated interest rate. Multiply by par to get $ of interest. Generally fixed.

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3. Maturity: Years until bondmust be repaid. Declines.

4. Issue date: Date when bondwas issued.

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Financial Asset Values

PV =

CF

1+k... +

CF

1+k1 n

12

21

CF

kn .

0 1 2 nk

CF1 CFnCF2Value

...

+ ++

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The discount rate (ki) is the opportunity cost of capital, i.e., the rate that could be earned on alternative investments of equal risk.

ki = k* + IP + LP + MRP + DRP.

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V

k kB

d d

$100 $1,

1

000

11 10 10 . . . +

$100

1+ kd

= $90.91 + . . . + $38.55 + $385.54= $1,000.

++++

100 100

0 1 2 1010%

100 + 1,000V = ?

...

What’s the value of a 10-year, 10% coupon bond if kd = 10%?

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10 10 100 1000N I/YR PV PMT FV

-1,000

The bond consists of a 10-year, 10% annuity of $100/year plus a $1,000 lump sum at t = 10:

$ 614.46 385.54

$1,000.00

PV annuity PV maturity value PV bond

===

INPUTS

OUTPUT

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What is the “yield to maturity”?

YTM is the rate of return earned on a bond held to maturity. Also called the “promised yield.”

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What’s the YTM on a 10-year, 9% annual coupon, $1,000 par value bond

that sells for $887?

0 1 9 10

90 90 90

kd=?

1,000PV1 . . .PV10

PVM

887 Find kd that “works”!

...

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10 -887 90 1000N I/YR PV PMT FV 10.91

V

INT

k

M

kB

dN

dN

1 11

... +INT

1+ kd

887

90

1

1000

11 10 10

k kd d

+90

1+kd

,

Find kd

+ + + +

++++

INPUTS

OUTPUT

...

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If coupon rate < kd, discount.

If coupon rate = kd, par bond.

If coupon rate > kd, premium.

If kd rises, price falls.

Price = par at maturity.

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Find YTM if price were $1,134.20.

10 -1134.2 90 1000N I/YR PV PMT FV

7.08

Sells at a premium. Because coupon = 9% > kd = 7.08%, bond’s value > par.

INPUTS

OUTPUT

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Definitions

Current yield = .

Capital gains yield = .

= YTM = + .

Annual coupon pmtCurrent price

Change in priceBeginning price

Exp totalreturn

Exp Curr yld

Exp capgains yld

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Current yield =

= 0.1015 = 10.15%.

Find current yield and capital gains yield for a 9%, 10-year bond when the bond sells for $887 and YTM = 10.91%.

$90 $887

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YTM = Current yield + Capital gains yield.

Cap gains yield = YTM – Current yield = 10.91% – 10.15% = 0.76%.

Could also find value in Years 1 and 2,get difference, and divide by value inYear 1. Same answer.

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Semiannual Bonds

1. Multiply years by 2 to get periods = 2n.2. Divide nominal rate by 2 to get

periodic rate = kd/2.3. Divide annual INT by 2 to get PMT = INT/2.

2n kd/2 OK INT/2 OK

N I/YR PV PMT FV

INPUTS

OUTPUT

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2(10) 13/2 100/220 6.5 50 1000N I/YR PV PMT FV

-834.72

Find the value of 10-year, 10% coupon,semiannual bond if kd = 13%.

INPUTS

OUTPUT

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You could buy, for $1,000, either a 10%, 10-year, annual payment bond or an

equally risky 10%, 10-year semiannual bond. Which would you prefer?

The semiannual bond’s EFF% is:

10.25% > 10% EFF% on annual bond, so buy semiannual bond.

%.25.1012

10.011

m

i1%EFF

2m

Nom

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If $1,000 is the proper price for the semiannual bond, what is the proper price for the annual payment bond?

Semiannual bond has kNom = 10%, with EFF% = 10.25%. Should earn same EFF% on annual payment bond, so:

10 10.25 100 1000N I/YR PV PMT FV

-984.80

INPUTS

OUTPUT

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A 10-year, 10% semiannual coupon,$1,000 par value bond is selling for$1,135.90 with an 8% yield to maturity.It can be called after 4 years at $1,050.

What’s the bond’s nominal yield tocall (YTC)?

8 -1135.9 50 1050N I/YR PV PMT FV 3.568 x 2 = 7.137%

INPUTS

OUTPUT

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kNom = 7.137% is the rate brokers would quote. Could also calculate EFF% to call:

EFF% = (1.03568)2 – 1 = 7.26%.

This rate could be compared to monthly mortgages, etc.

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Bond Ratings Provide One Measure of Default Risk

Investment Grade Junk BondsMoody’s Aaa Aa A Baa Ba B Caa C

S&P AAA AA A BBB BB B CCC D

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Provisions in the bond contractSecured vs. unsecured debtSenior vs. subordinated debtGuarantee provisionsSinking fund provisionsDebt maturity

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Dollar-weighted returnsInternal rate of return considering

the cash flow from or to investmentReturns are weighted by the amount

invested in each stockTime-weighted returnsNot weighted by investment amountEqual weighting

Performance Valuations:Dollar- and Time-Weighted Returns

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Text Example of Multiperiod Returns

Period Action

0 Purchase 1 share at $50

1 Purchase 1 share at $53

Stock pays a dividend of $2 per share

2 Stock pays a dividend of $2 per share

Stock is sold at $108 per share

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Period Cash Flow

0 -50 share purchase

1 +2 dividend -53 share purchase

2 +4 dividend + 108 shares sold

%117.7

)1(

112

)1(

5150

21

r

rr

Internal Rate of Return:

Dollar-Weighted Return

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Time-Weighted Return

%66.553

25354

%1050

25053

2

1

r

r

Simple Average Return:

(10% + 5.66%) / 2 = 7.83%

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Averaging Returns

Arithmetic Mean:

n

t

t

n

rr

1

Geometric Mean:

1)1(/1

1

nn

ttrr

Text Example Average:

(.10 + .0566) / 2 = 7.81%

[ (1.1) (1.0566) ]1/2 - 1

= 7.83%

Text Example Average:

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Past Performance - generally the geometric mean is preferable to arithmetic

Predicting Future Returns- generally the arithmetic average is preferable to geometric.

Geometric has downward bias

Comparison of Geometric and Arithmetic Means

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1) Sharpe Index

rp - rf

p

rp = Average return on the portfolio

rf = Average risk free rate

p= Standard deviation of portfolio

return

Risk Adjusted Performance: Sharpe

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2) Treynor Measure rp - rf

ßp



ßp = Weighted average for portfolio

Risk Adjusted Performance: Treynor

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= rp - [ rf + ßp ( rm - rf) ]

Risk Adjusted Performance: Jensen

3) Jensen’s Measure

p

p = Alpha for the portfolio


ßp = Weighted average Beta


rm = Avg. return on market index port.

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Appraisal Ratio

Appraisal Ratio = p / (ep)

Appraisal Ratio divides the alpha of the portfolio by the nonsystematic risk

Nonsystematic risk could, in theory, be eliminated by diversification

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It depends on investment assumptions1) If the portfolio represents the entire investment for

an individual, Sharpe Index compared to the Sharpe Index for the market.

2) If many alternatives are possible, use the Jensen or the Treynor measureThe Treynor measure is more complete because it adjusts for risk

Which Measure is Appropriate?

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Decomposing overall performance into components

Components are related to specific elements of performance

Example componentsBroad AllocationIndustrySecurity ChoiceUp and Down Markets

Performance Attribution

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Set up a ‘Benchmark’ or ‘Bogey’ portfolio

Use indexes for each componentUse target weight structure

Process of Attributing Performance to Components

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Calculate the return on the ‘Bogey’ and on the managed portfolio

Explain the difference in return based on component weights or selection

Summarize the performance differences into appropriate categories

Process of Attributing Performance to Components

Documents

8 - 1 Copyright © 2002 by Harcourt, Inc.All rights reserved. Chapter 2: DCF Applications Application 1: Capital budgeting Application 2: Bond Valuation