Post on 16-Dec-2015
Finance and the Financial Manager
Chapter 1
1.1 What is a Corporation?
1.2 The Role of the Financial Manager
Two Basic Questions1 Investment Decision
2 Financing Decision
1.3 Who is the Financial Manager
Financial
ManagerFirm's
Operations
Financial
Markets
(1)(2)
(3)
(4a)
(4b)
1.4 Goal of the Firm ?
1.5 Agency Problem
Monitoring by board of directors1
Compensation package2
Active outside takeover market5
Efficient outside managerial labor market4
Monitoring by outside large blockholders
(Bank, insurance Co., pension, mutual fund)
3
B. How to solve agency problem?
A. Separation between Ownership and Management
Present Value and The Opportunity Cost of Capital
Chapter 2
C. PV and Rate of Return
B. Risk and Present Value
PV = C / (1+r)
2.1 Introduction
A. Present Value
NPV = PV - C0
r:
D. The Opportunity Cost of Capital
1 From your Investment
C0 : $ 100,000
Slump : $ 80,000
Boom : $ 140,000 Normal : $ 110,000
C1 :
E(C1)
From Stock Market2
Find stock X which has same risk as your project :
P0 : $ 95.65
Slump : $ 80
Boom : $ 140Normal : $ 110
P1 :
E(P1) = 1/3 (80 + 110 + 140) = 110
E(R) = = 0.15 15% k110 - 95.6595.65
Q : What is the Present Value of your project?
PV of project =
NPV =
How to Calculate Present Values
Chapter 3
3.1 Cash Flows in Several Periods (*)
3.2 Perpetuities and Annuities (*)
3.3 Growing Perpetuities (*)
3.4 Compounding Interest (*)
3.5 Nominal and Real Interest
A. Real CF = Nominal CF
(1+inflation rate)
B. (1+Real Rate) = (1+ Nominal rate)(1+inflation rate)
3.6 Bond Valuation
PVbond =C
1+rC
(1+r)2
C+F(1+r)n+ + … ... +
= C PVAF + F PVF
(Ex) Coupon rate: 10%, r=5%, face value=$1,000 N=7years
PVbond = 100 5.786 + 1100 0.711 = $1360.7
The Value of Common Stocks
Chapter 4
• NYSE• AMEX• OTC (NASDAQ)
B. Secondary Market
A. Primary Market
4.1 How Common Stocks are Traded?
(Ex) P0 = $100 , P1 = $110 , DIV = $5
r =
= Holding Period Return = E(R)
E(R) = (P1 - P0 + DIV) / P0 = r
r: market capitalization rate
4.2 Stock Valuation
A. Today’s Price
P1 - P0
P0
DIVP0
+=
Q: What happen if P0 is different from $100 ?
$ 100 ; equilibrium price if 15% is an appropriate discount rate
P0 = (P1 + DIV) / (1+r) = (110 + 5 ) / 1.15 = 100
B. What determines next year’s price ?
P0 = [D0 • (1 + g)] / (r - g) = D1 / (r - g)
Assume: Dividend grows at a constant rate; g
P0 = (P1 + D1) / (1 + r), P1 = (P2 + D2) / (1 + r)
P0 = D1 / (1 + r) + (P2 + D2) / (1 + r)2
= D1 / (1 + r ) + D2 / (1+r)2
+ D3 / (1 + r)3 + ………
Valuation Model
=
t=1Dt / (1 + r)t
D1 / P0 : Dividend Yield
g : Dividend Growth
r = D1 / P0 + g
4.3 Simple Way to Estimate r
EX : Pinacle West Corp (p 69)P0 = $41, Div1 = $1.27, g = 5.7%
r =
g = Plowback ratio * ROE =
ROE = EPS / Book Equity per Share = 0.1
Plowback Ratio = 1- Payout ratio = 0.53
Payout ratio = DIV1 / EPS = 0.47
Alternative Approach:
r = 0.031 + 0.053 = 0.084 or 8.4%
Some Warnings about Constant-Growth Formulas
1. Individual stock’s r is subject to estimation errorsPortfolio approach
2. Growth rate can rarely sustained indefinitelyEx. Growth-tech
DIV1=$0.05, P0=$50, Plowback Ratio=80%, ROE=25%
g =
r =
YEAR1 YEAR2 YEAR3 YEAR4
Book equity
Earning pershare, EPS
Return on Equity, ROE
Payout ratio
Dividends pershare, DIV
Growth rateof dividends
10.00 12.00 14.40 15.50
2.50 3.00 2.30 2.49
.25
.20
.25 .16 .16
.20 .50 .50
.50 .60 1.15 1.24
- .20 .92 .08
Ex: at t=3 and thereafter ROE =16% Firm responds by plowing back 50% of earnings
g =
Table 4.2
• General DCF formula to find the capitalization rate r:
DIV1
1+rP0 =DIV2
(1+r)2+ +DIV3 + P3
(1+r)3
P3 =
P0 =
50 =
4.4 The link between stock price and earning per Share
Growth stock vs Income stock
A. Income Stock
No Growth Perpetuity Model
P0 =EPS1
r = rDIV1
(EX) Expected Return = Dividend Yield = 10/100 =.10 = r
Price = DIV1 / r = EPS1 / r =
B. Growth Stock (r=10%)
NPV =
$ 1 (each year)
Invest $10 into project with permanent return of 10%
at t = 1: (once & for all)
This investment contributes “0” to value.
(EX) Return on project is higher or lower than 10%;
NPV? (go to table 4-3)
Table 4-3Effect on stock price investing an additional $10 in year 1 at different rates of return.Notice that the earnings-price ratio overestimates r when the project has negative NPVand underestimates it when the project has positive NPV.
Project's impact Project Rate Incremental Project NPV on Share Price Share Price EPS1
of Return Cash Flow, C in Year 1ain Year 0 b
in Year 0, P0
P0 r
.05 $ .50 - $ 5.00 - $ 4.55 $ 95.45 .105 .10
.10 1.00 0 0 100.00 .10 .10
.15 1.50 + 5.00 + 4.55 104.55 .096 .10
.20 2.00 + 10.00 + 9.09 109.09 .092 .10
.25 2.50 + 15.00 + 13.64 113.64 .088 .10
a Project costs $ 10.00 (EPS1). NPV = - 10 + C / r, where r = .10
b NPV is calculated at year 1. To find the impact on P0, discount for 1 year at r = .10
In general :
P0 = PVGOEPS1
r +
PVGO : Present Value of Grow Opportunity
Sum of all NPVs (per share)
EPS1
rCapitalized value of average earning under a no-growth policy
:
P0 = PVGOEPS1
r +
Divide each side by EPS
P/E = 1r
PVGOE
+
Q : Japanese firm : P/E 50U.S. firm : P/E 17
Is Japanese firm growing fast?
Determinants of P/E Ratio
1. Cost of Capital(r): “-” 2. Conservative accounting procedure(EPS): “-”3. Growth opportunities(PVGO): “+”
If EPS1 = $ 8.33, Payout ratio = D1 / EPS1 = 5 / 8.33 = 0.6
If ROE = .25, g =
P0 = D1 / (r - g) =
r = 15 % , D1 = $ 5
P0 =
EX : Fledgling Electronics Case (p73)
Analyze: $ 44.44Plowback Ratio = .4, 8.33 * .4 = $ 3.33 Invest: $ 3.33 at 25% (ROE) .25 * 3.33 = $ .83
at t = 1; NPV1 = -3.33 + .83 / .15 = 2.22 at t = 2; Invest 3.33 * 1.1 = 3.69 (g = 10%)
NPV2 = -3.33 * 1.1 + (.83 * 1.1) / .15 = 2.44
PVGO = NPV1 / (r - g) = 2.22 / (.15 - .1) = $ 44.44
This is growth stock, not because g = 10%, but because
Table 4-4 Estimated PVGOs (p.76)
Market PVGO, Stock Capitalization PVGO Percent of
Stock Price, P0 EPS* Rate, r** =P0 - EPS/r Stock Price P / EIncome Stocks: AT & T $52.00 $2.85 .094 $21.70 41.7 18.2
Conagra 26.00 1.33 .106 13.50 51.7 19.5
Duke Power 60.00 3.58 .094 21.90 36.5 16.8 Exxon 64.00 2.89 .099 34.70 54.3 22.1
Growth Stocks:
Compaq 30.00 0.69 .123 24.40 81.3 43.5 Merck 120.00 4.43 .118 82.50 68.7 27.1 Microsoft 101.00 2.08 .165 85.10 84.2 48.6
Wal-Mart 60.00 0.73 .094 52.20 87.1 82.2
* EPS defined as the average earnings under a no-growth policy. As an estimate of EPS, we use the forecasted earnings per share for the 12 months ending March31, 1999. Source: Value Line.* The market capitalization rate was estimated using the capital asset pricing model. We describe this model and how to use it in Section 8.2 and 9.2. EX: market risk premium = 6%
C. Some Example of Growth Opportunities
Why NPV leads to better
Investment Decisions
than Other Criteria
Why Net Present Value Leads to Better Investment Decisions than Other Criteria
Chapter 5
5.1 Review of Basics
1 Forecast Cash Flow
2 Determine appropriate Cost of Capital
3 Discount with Cost of Capital
Q : Why NPV ?
• All cash flows are considered
• Time Value of Money
• NPV is not affected by manager’s taste, accounting method, profitability of existing business, and profitability of other independent business
CASH FLOWS, DOLLARSPayback NPV at
Project C0 C1 C2 C3 Period, Years 10 Percent
B - 2,000 + 500 + 500 + 5,000 3 2,642
C - 2,000 500 +1,800 + 5,000 2 -58
D - 2,000 + 1,800 + 500 + 0 2 +50
5.2 Payback Period
• Number of years it takes before cumulative cash flow recovers initial investment
5.3 Book Rate of Return
Book Rate of Return Book incomeBook assets
=
Cash flow vs. Book Income
Problems :
Computing the average book rate of return on an investment of $9000 in project A CASH FLOWS, DOLLARS
Project A Year 1 Year 2 Year 3
Revenue 12,000 10,000 8,000
Out-of-Pocket cost 6,000 5,000 4,000
Cash flow 6,000 5,000 4,000
Depreciation 3,000 3,000 3,000
Net income 3,000 2,000 1,000
Average book rate of return = average annual income
= 2,000
= .44average annual investment 4,500
Year 0 Year 1 Year 2 Year 3
Gross book value of investment $ 9,000 $ 9,000 $ 9,000 $ 9,000
Accumulated depreciation 0 3,000 6,000 9,000
Net book value of investment $ 9,000 $ 6,000 $ 3,000 $ 0
Average net book value = $ 4,500
Example
(Rule) Accept IRR>k NPV>0
Reject IRR<k NPV<0
C0 = - 4,000 k: cost of capitalC1 = 2,000 C2 = 4,000
5-3 Internal Rate of Return: IRR Discount rate that makes NPV = 0
NPV = -4,000 + (1+IRR)
2,000+
4,000
(1+IRR)2= 0
-2000
-1500
-1000
-500
0
500
1000
1500
2000
2500
10Discount rate (%)
Net Present Value, dollars
IRR=28%
20 30 50 60 80 90 1007040
Pitfall 1. Lending vs. Borrowing?
CASH FLOWS, DOLLARS
NPV atProject C0 C1 IRR, Percent 10 Percent
A - 1,000 + 1,500 + 50B + 1,000 - 1,500 + 50
CASH FLOWS, DOLLARSNPV at
Project C0 C1 C2 C3 IRR, Percent 10 PercentC + 1,000 - 3,600 + 4,320 - 1,728 + 20 - .75
-20
0
20
40
60
10
Discount rate (%)
Net Present Value, dollars
20 30 50 60 80 90 1007040
Pitfall 2. Multiple Rates or Return
Pretax
Tax
Net
1 42 53 60
-1,000 300 300 300 300 300 300
+500 -150 -150 -150 -150 -150
-1,000 800 150 150 150 150 -150
CASH FLOWS, DOLLARSNPV at
Project C0 C1 C2 IRR, Percent 10 Percent
D + 1,000 - 3,000 + 2,500 none + 339
1000
NPV
500
0
-500
-1000
Discount Rate
IRR=15.2%
IRR=-50%
Pitfall 3. Mutually Exclusive Projects
3.1 Different scale
CASH FLOWS, DOLLARS NPV at
Project C0 C1 IRR, Percent 10 Percent
E - 10,000 + 20,000 100F - 20,000 + 35,000 75
CASH FLOWS, DOLLARS NPV at
Project C0 C1 IRR, Percent 10 Percent
F-E - 10,000 + 15,000 50 + 3,636
CASH FLOWS, DOLLARS IRR, NPV at
Project C0 C1 C2 C3 C4 C5 Etc. Percent 10 Percent
G - 9,000 +6,000 +5,000 +4,000 0 0 … 33 3,592
H - 9,000 +1,800 +1,800 +1,800 +1,800 +1,800 … 20 9,000
I -6,000 +1,200 +1,200 +1,200 +1,200 … 20 6,000
3.2 Different pattern of cash flow over time
10,000
NPV, dollars
0
-5000
Discount Rate,
percent
33.3
15.6
+5,000+6,000
10 20 30 40 50Project G
Project H
(generally)
IRR vs. r1
r2 ?
r3
NPV = - C0 + C1 / (1+r1) + C2 / (1+r2)2 + …
Pitfall 4. What happens if term structure is not flat?
CASH FLOWS, MILLIONS OF DOLLARS NPV at
Project C0 C1 C2 10 Percent
A - 10 + 30 + 5 21
B - 5 + 5 + 20 16
C - 5 + 5 + 15 12
5.5 Limited Resource (Capital Rationing)
<$10> t=0
CASH FLOWS, MILLIONS OF DOLLARS NPV at Profitability
Project C0 C1 C2 10 Percent Index
A - 10 + 30 + 5 21 2.1
B - 5 + 5 + 20 16 3.2
C - 5 + 5 + 15 12 2.4
D 0 - 40 + 60 13 0.4
<$10> t=0, t=1
• More Elaborate Capital Rationing Models We
accept proportion A of project A.
NPV of accepting A of A
Previous Example
NPV =
Constraint: (Costs)
at t = 0, 10 A + 5 B + 5 C + 0 D 10
at t = 1, 40 D 30A + 5 B + 5 C + 10
0 A , B , C , D 1
Maximize: 21 A + 16 B + 12 C + 13 D
Subject to : 10 A + 5 B + 5 C + 0 D 10
-30 A - 5 B - 5 C + 40 D 10
0 A , B , C , D 1
Making Investment Decisions with the Net Present Value Rule
Chapter 6
• How to apply the rule to practical investment problems?
• Question
What should be discounted?
CF: relevance, completeness, consistency, accuracy
How NPV rule should be used when there are
project interactions?
• Estimate Cash Flow on an Incremental Basis
Average vs. incremental
Include all incidental effects
Do not forget NWC requirement
Forget sunk cost
Include opportunity costs
Beware of allocated overhead costs
Consider spillover effect “erosion”
• Treat Inflation consistently. – Real CF : discount with real rate – Nominal CF: discount with nominal rate
(Ex) C0 C1 C2 C3
Real CF -100 + 35 +50 +30 rN = 15%, I = 10%
NPV =
NPV =
6.2 Example - IMFC Project
• Initial investment: $ 10 mil
• Salvage value at year 7: $ 1 mil (sold)
• Depreciation: 6 year straight line with arbitrary
salvage of : $ 500,000
annual depreciation = = $ 1.583
mil
9.5 mil
6
Table 6 - 1 Nominal Cashflow
Ex: forecast of inflation: 10%
IM&C's guano project - revised projections reflecting (figures in thousands of dollars)
PERIOD
0 1 2 3 4 5 6 71. Capital investment 10,000 -1,949*
2. Accumulated
depreciation 1,583 3,167 4,750 6,333 7,917 9,500 0
3. Year-end book value 10,000 8,417 6,833 5,250 3,667 2,083 500 0
4. Working capital 550 1,289 3,261 4,890 3,583 2,002 0
5. Total book value
(3 + 4) 10,000 8,967 8,122 8,511 8,557 5,666 2,502 0
6. Sales 523 12,877 32,610 48,901 35,834 19,717
7. Cost of goods sold 837 7,729 19,552 29,345 21,492 11,830
8. Other costs ** 4,000 2,200 1,210 1,331 1,464 1,611 1,772
9. Depreciation 1,583 1,583 1,583 1,583 1,583 1,583
10. Pretax profit
(6 - 7 - 8 - 9) -4,000 -4,097 2,365 10,144 16,509 11,148 4,532 1,449**
11. Tax at 35% -1,400 -1,434 828 3,550 5,778 3,902 1,586 507
12. Profit after tax -2,600 -2,663 1,537 6,594 10,731 7,246 2,946 942* Salvage value.
** The difference between the salvage value and the ending book value of $ 500 is a taxable profit
0 1 2 3 4 5 6 7
1. Sales
2. Cost of goods and sold
3. Other costs
4. Tax on operations
5. Cash flow from operation6. Change in working capital7. Capital investment and Disposal8. Net cash flow9. Present value at 20%
Net present value = +3,519(sum of 9)
4,000
-1,400-2,600
-10,000
-12,600
-12,600
523
837
2,200
-1,434-1,080
-550
-1,630
-1,358
12,887
7,729
1,210
828
3,120
-739
2,381
1,654
32,610
19,552
1,331
3,550
8,177
-1,972
6,205
3,591
48,901
29,3451,464
5,778
12,314
-1,629
10,685
5,153
35,834
21,492
1,611
3,902
8,829
1,307
10,136
4,074
19,717
11,830
1,772
1,586
4,529
1,581
6,1102,046
2,002
1,442
3,444961
Period
IM&G’s guano project-cash-flow analysis(thousand)
• Cash flow = Sales - CGS - Other costs - Taxes
• Net cash flow = Cash flow from operation
Networking capital
[- Initial Investment + Recovery of Salvage Value]
• NPV =
6.3 Project Interacting
Choosing between Long & Short Equipment
C1C0 C3C2PV
at 6%
A
B
+15 +5 +5 +5
+10 +6 +6
28.37
21.00
Equivalent Annual Cost
C1C0 C3C2PV
at 6%
Machine A
EACA
+15 +5 +5 +5
+10 +6 +6
28.37
21.00Machine B
EACB
x x x
y y
28.37
21.00
Risk, Return & opportunity
Cost of Capital
Risk and Return & Opportunity Cost of Capital
Chapter 7&8
7.1 Seventy-Two year of Capital Market
0.1
10
1000
1925 1933 1941 1949 1957 1965 1973 1981 1989 1997
1,828 S&P
5,520 Small Cap
55.38 Corporate Bonds
39.07Government Bonds14.25 Treasury Bills
Dollars
0.1
10
1000
1925 1933 1941 1949 1957 1965 1973 1981 1989 1997
613.5 Small firms
203.2 S&P 500
6.16 Corporate bonds4.34 Government bonds
1.58 Treasury bills
Dollars
PORTFOLIO
AVERAGE ANNUALRATE OR RETURN
NOMINAL REAL
AVERAGE RISK PREMIUM(EXTRA RETURN VS.
TRESURY BILLS)
Treasury bills
Government bonds
Corporate bonds
Common stocks (S&P 500)
Small firmcommon stock
3.8
5.6
6.1
13.0
17.7
.7
2.6
3.0
9.7
14.2
0
1.8
2.3
9.2
13.9
Average rate of return on Treasury bills, Government bonds, Corporate bonds, and common stocks, 1926-1997
(Percent per year)
7.2 Measuring Portfolio Risk
• Variance (Standard Deviation)
• Expected = Ri * Pi = E (R) = R
• Variance = (Ri - R)2 * Pi = 2 = V
• Risk
Systematic Risk: market risk
macro-economic variables
Unsystematic Risk: firm unique or specific risk
PORTFOLIO
Treasury billsLong-term government bondsCorporate bondsCommon stock (S&P 500) Small-firm common stocks
3.2
STANDARD DEVIATION() VARIANCE(2)
9.28.7
20.333.9
10.284.675.7
412.11149.2
PERIOD
1926-1929
MARKET SD()
1930-19391940-19491950-19591960-19691970-19791980-19891990-1997
23.9%41.617.514.113.117.119.414.3
STOCK
AT&TBristol-Myers SquibbCoca-ColaCompaq Exxon
22.6
STANDARD DEVIATION() STOCK
STANDARD DEVIATION()
17.1
19.7
42.0
13.7
General ElectricMcDonald’sMicrosoftReebok Xerox
18.820.8
29.4
35.4
24.3
Stock
BPDeutscheBank
FiatHudsonBay
16.3
SD()
23.2
35.2
26.3
30.1KLM
MARKET
UKGermany
Italy
Canada
Netherlands
12.2
11.3
24.5
11.7
14.2
SD() Stock SD() MARKET SD()
LVMHNestle
Sony
TelefoniadeArgentina
25.818.9
27.5
52.2
FranceSwitzerland
Japan
Argentina
16.6
14.6
17.4
28.6
0
5 10 15
Number of Securities
Por
tfol
io s
tand
ard
devi
atio
n
Market risk
Uniquerisk
n = 2
7.3 Calculating Portfolio Risk
Itself Variance; 2(,)
Between A, B Covariance; 2(,)
A B
A
B
A
B
Weights; A , B , A + B = 1
A
B
A
B
2A
AB
BA 2B
Portfolio Risk =
Example;
Bristol-Myers :
McDonald’s :
0.55
0.45
0.171
0.208
BM = 0.15
2p =
n=3
Variance:
Covariance:
n=4
Variance:
Covariance:
lim VP N
VP = 2P =
2P = VP =
(Ex) mutual fund
Limits to Diversification
N * (1/N)2 2 + (N2 - N) * (1/N2) cov
2 : average variancecov : average covariance
(1/N) 2 + (1 - 1/N) cov
= 1
2P = X1
2 12 + X2
2 22 + 2X1X2 1 2 * 1
= (X1 1 + X2 2 )2
( a b)2 a2 + b2 2ab
P = X1 1 + X2 2 , when = 1
There is:• no diversification• no risk reduction
* Portfolio risk is simply weighted average of individual risk; linear combination !
Special Cases
= - 1
2P = X1
2 12 + X2
2 22 - 2X1X2 1 2
= (X1 1 - X2 2 )2
P = X1 1 - X2 2 , when = -1
• Risk may be completely eliminated by combining
X1, X2 (Ex)
• Portfolio Risk is (again) a linear combination of
individual risks.
A B
E(R) 10% 12%
2 9% 16%
AB = -1
Find the weights, A, B for Minimum Variance Portfolio. ( p = 0)
What is the risk & return of that portfolio?
* General case : -1
We need Calculus.
Example
• Efficient Frontier
Ep • B
A •
P
AB = 1
= -1 • BEp
P
= -1 A •
Generally 1
P
Ep • B
A •
09 11 13 15 17 19 21
10
12
14
16
18
20
22
0 P
E(RP)
P
Efficient Portfolio
E(RP)
2P = X1
2 12 + X2
2 22 + 2X1X2 1 2 12
(risk-free asset : 2 = 0 )
- Lending2
P = X12 1
2 P = X1 1 (linear combination)
EP = X1R1 + X2Rf
- Borrowing 2
P = ( X* + 1 )2 12 + ( -X* )2 2
2 + 2( 1+X* )( -X* ) 12
P = (1+X*) 1
EP = (1+X*) R1 - X* Rf
Portfolio Risk : Linear combination of individual risk
We Introduce Borrowing & Lending (p193)
Combination of Risky(A) and Risk Free Asset
Rf
A•
New Efficient Portfolio
Rf
A•
C
•
•
•
•Old EfficientPortfolio
B
T D
Rf
•T
EM
EP
PM
• Risk-return relationship for efficient portfolios
• Intercept: Rf price of time
• slope: (EM - Rf) / M price of risk Ep = Rf + [ (EM - Rf) / M ] x P
T is a market portfolio; MCapital Market Line CML
• Capital Asset Pricing Model: CAPM Apply Portfolio Theory to evaluate all risky assets
We can eliminate unsystematic risk by combining securities. (it cancels each other)
We can not eliminate systematic risk since it moveswith market as a whole
Systematic Risk vs. Unsystematic Risk
Therefore,
= Rf +
= Rf +
= Rf + amount of risk Price of risk
• Systematic Risk = Market risk = Covariance(iM)
Required Rate of Returnon Risky Asset
Risk-free Rate(Rf)
RiskPremium= +
= Rf +
STOCK
AT&TBristol-Myers SquibbCoca-ColaCompaq Exxon
.65
BETA STOCK
.95
.98
1.13.73
General ElectricMcDonald’sMicrosoftReebok Xerox
1.29.95
1.26
.871.25
BETA
STOCK
.74
BETA STOCK
1.05
1.11
.51
1.13
1.001.01
1.03
BETA
BPDeutscheBank
FiatHudsonBayKLM
LVMHNestle
Sony
Telefonia deArgentina 1.31
STOCK
AT&TBristol-Myers SquibbCoca-ColaCompaq Exxon
.65
BETA
.95
.981.13.73
General ElectricMcDonald’sMicrosoftReebok Xerox
1.29.95
1.26.87
1.25
EXPECTED RETURNrf+(rm - rf)
10.7%13.113.314.511.315.813.115.612.513.9
Summary
“”
1) Covariance risk (normalized) iM
2M
2) Sensitivity of stock i’s return with respect to
market
Ex:
Security Market Line: SML
1) CAPM Line2) Equilibrium Line; If asset is correctly priced (in its equilibrium), in terms of CAPM, it falls on this line.
Below this line : Above this line :
E(Ri)
i0 1
?
?
Rf
E(R)
0 1.0
rm
rf
• A
• B
• C
0.5 1.5
Market lineAvg Risk Premium 1931-91
Portfolio Beta1.0
30
20
10
0
Investors
Market Portfolio
Beta vs. Average Risk Premium
12
3
4
5 6 78
9
10
Avg Risk Premium 1931-65
Portfolio Beta1.0
Market Line30
20
10
0
Investors
Market Portfolio12
34 5 6
7 89
10
Avg Risk Premium 1966-91
Portfolio Beta1.0
30
20
10
0
Investor
Market Portfolio
Market Line
12 3 4 5
6 7 89
10
8.4 Some Alternative Theories
Arbitrary Pricing Theory
Assumes that each stock’s return depends partly on macroeconomic factors or noise (event that are unique to company)
Expected Premium
= r - rf = b1 (r1- rf ) + b2 (r2 - rf )
+ b3 (r3 - rf ) + … …
R = a + b1rf1 + b2rf2 + b3rf3 + … … noise
APT example1. Identify the Macroecnomic Factors
• Yield Spread• Interest Rate• Exchange Rate• Real GNP• Inflation
2. Estimate the Risk Premium for Each Factor
Factor Estimated risk premium(rfactor - rf)Yield spread
Interest rateExchange rateReal GNPInflationMarket
5.10%-.61-.59.49
-.836.63
3. Estimate the Factor Sensitivity
Factor risk
(b)
Estimated risk premium(rfactor - rf)
Yield spread
Interest rate
Exchange rate
Real GNP
Inflation
Market
5.10%
-.61
-.59
.49
-.83
6.63
Total
Factor Factor risk premium
[b(rfactor - rf)]
1.04
-2.25
.70
.17
-.18
.32
5.30%
1.37
-.41
.08
.15
2.04
8.53%
Capital Budgeting and Risk
Chapter 9
Firm Value = PV(AB) = PV(A) + PV(B) = sum of separate assets
PV(A), PV(B) are valued as if they were mini-firms
in which stockholders invest directly.
Each project should be evaluated at its own Cost of Capital
(implication of Value Additivity Principle)
Are the New Projects More Risky or Less Risky than its Existing Business?
r
rf
•A
• B
Cost of Capital
• True Cost of Capital
- depends on the use to which the capital is put
- Project beta ()
Expected Return = r = rf + (project beta) (rm - rf) • “” of project or division
- Look at an average of similar companies
(or industry beta) - Firm’s borrowing policy (leverage) affects its stock
beta
- Project beta shifts over time.
Industry Beta and Divisional Cost of Capital
Individual measurement error
Portfolio error cancelled out
If you consider across-the-board expansion,
such as new division,
What is the “” for new division?
Answer:
• Measuring Betas
– Using monthly stock return on IBM
– Using monthly market return
(Ex) 60 months
R1
IBM R1M
R2IBM R2
M
R60
IBM R60M
… …
… …
( = alpha)
Average rate of price appreciation or depreciation,
born by stock-holders when investors in the market
as a whole earn nothing.
R-squared R2
The proportion of variance of stock price change
that can be explained by market movement.
means systematic risk / total risk
= -0.65% ; -0.65 12 -7.8%
Alpha = -.65Change in market index
Beta = 1.30
Change in prices of DEC common stock
9.2 Capital Structure & Company Cost of Capital(COC)
Cost of Capital; hurdle rate minimum return required to make firm value unchanged.
Depends on
also depends on
* Financial leverage does not affect the risk or the
expected return on the firm’s assets.
But,
How Changing Capital Structure Affects Expected Return?
CompanyCost of Capital
(WACC) = r d r eD
D + E +
EE + D
= r Asset = r portfolio
(EX) B/S (market value)A 100 D 40
100 100
r d = 8% r e = 15%
r Asset =
60E
• (Now) : Issue 10 equity, Retire 10 debt
* The change in financial structure does not affect
rAssets =
B/S (market value)A 100 D 30
100 100
70E
does affect
(Ex) lower leverage: rD 7.3% (Given)
How does Changing Capital Structure Affect Beta?
Assets = Portfolio =DV
EV
D + E
V = D + E D = 0.2 E = 1.2
A =
After refinancing; D 0.1(Given)
Expected return (%)
rdebt=8
rassets=12.2
requity=15
20
0 .2debt=Beta
.8assets= equity=1.2
Before Refinancing
20
0
Expected return (%)
.1debt=
rdebt=7.3
rassets=12.2
requity=14.3
Beta .8assets= equity=1.1
After Refinancing
9.3 How to Estimate the company Cost of Capital
• Pinnacle West’s Common Stock
.15.51Average Portfolio
21.37.ResourcesL&PP
21.43.Corp.West Pinnacle
23.70. EnergyPECO
15.39. EnergyOGE
19.35.System ElectricNE
18.65.Inc. GPU
19.66.Associate UtilitiesEastern
17.56. EnergyDTE
20.65. EdisonConsolidated
18.30. HudsonCentral
19.60. ElectricBoston
ErrorStandard.Beta
requity = rf + equity [ rm - rf]
= 0.045 + 0.51 0.08 = 0.0858
8.6%
rd = 6.9%, re = 8.6%, = 0.43, = 0.57
WACC = Company Cost of Capital
= rd + re
DV
EV
DV
EV
9.4 Discount Rates for International Projects
• Foreign investments are not always riskier.
.47.1203.80Taiwan
.35.1472.36Kazakhstan
.62.1603.80Brazil
1.46.4163.52Argentina
Betacoefficient
Correlation Ratio
• Foreign Investment in the US
09 11 13 15 17 19 21
10
12
14
16
18
20
22
Taiwan Index
US Index
0 P
E(RP)
9-4 Setting Discount Rate when you can’t calculate
Think about the determinant of asset beta
Avoid fudge factors
Do not add fudge factors to the discount rate instead adjust cash flow forecasts
(Ex) dry hole, FDA approval, politica1 unstability in foreign country etc
(Ex)
Q: What are industries which are risky,
but have low ?
• Determinants of Asset Beta:
Operating Leverage
Cyclicality: Firms whose revenue depend on business cycle high
Commitment to fixed production charges
• High fixed cost ratio High operating leverage
High Asset Beta
Why ?
$
Q
Unit VariableCost
Break Even Point Analysis
FixedCost
TotalCost
Profit
Loss
FC
TC
TR
Low Fixed Cost(high Variable Cost) Low OL
BEF
FC
TC
TR
High Fixed Cost(Low Variable Cost) High OL
9-6 Another Look at Risk and Discounted Cash flow
Risk-adjusted:
t=1PV = [Ct / (1+r)t], r = rf + (rM - rf)
n
(Ex) r = 6 + 0.75 8 = 12% Year CF PV 1 100 89.3 2 100 79.7 3 100 71.2 240.2
x = 94.658 (x = certainty equivalent cash flow)
1001.12
100(1.12)2
= 89.3 =x
(1.06)2
x = 100 (1.06/1.12)2 = 89.57
• General Solution
Certainly equivalentCash Flow at time t
RiskyCash Flow at time t
1+rf
1+r
t
We call t =
=
1+rf
1+r
t
Certainty equivalent coefficient 1 = (1.06 / 1.12) = 0.946 2 = (1.06 / 1.12)2 = 0.896 3 = (1.06 / 1.12)3 = 0.848
Valuing CE cash flow
PV = CE(CF)(1 + rf)
CF1 + r
=
(Example) E(C) = -1,000,000 0.5 = -500,000
r = 25%
Convert into Certainty Equivalent cash flow:
5001.25
125(1.25)t
t=2NPV = -125 - +
= -125 or -$125,000?
NPV = -1000 + (250/0.1) = +1500 (50% chance)
NPV = 0 (50% chance)
E(NPV) = 1500 0.5 = 750 (if = 0.5)
NPV = -125 + = 225.5 or $225,000(750 0.5)
1.07
Success
Failure
Making Sure Managers Maximize NPV
Chapter 12
12.1 Incentives
A. Agency Problems in Capital Budgeting
• Reduced Effort
• Perquisites
• Empire Building
• Entrenchment
• Avoiding Risk
B. Monitoring
C. Compensation
6.120.11702,30347-Walt Disney
2.78.9420,13298UAL
5.87.15963,4335Safeway
5.121.20885,423,119 MorrisPhilip
8.111.47680,51,727Microsoft
5.1423.0219,221,688Merck
3.1321.8138,181,327Johnson & Johnson
8.117.867,4312,743-IBM
7.1515.224,18599-Packard-Hewlett
7.95.982,8873,527- MotorsGeneral
7.1217.753,5672,515 ElectricGeneral
1.912.158,2721,719 MotorFord
0.912.223,0246,81ChemicalDow
9.7%36.0%$10,814$2,442ColaCoca Capital
ofCost
Capital
on Return
Invested
CapitalEVA
Corporate Financing and Market Efficiency
Chapter 13
• So far, we assume ‘all equity’ financing.
Stockholders supply all the firm’s capital, bear all the business risks, and receive all the rewards.
<Questions>
How to spend $? How to raise $?
?
B/S
13.1 We always come back to NPV
(ex) Government offer: $100,000, 10yrs at 3%Market fair rate: 10%
NPV = Amount borrowed - PV of interest payments
- PV of loan payment
3,000(1.10)t= +100,000 -
t=1
10- 100,000
(1.10)10 = $43,200
Difference between Investment & Financing Decisions Easy reverse Abandonment value is O.K. Lose or make money is not easy
80
130
180
Month
Lev
el
80
130
180
230
Month
Lev
el
13.2 Efficient Market Hypothesis
• Definition
Stock price reflects information immediately and completely
• Level of Efficiency- Weak Form
Stock price reflects previous price movement immediately and completely
- Semi-Strong Formall publicly available information
- Strong Formall information (public, private, and insider)
• Test of Market Efficiency
- Weak form
- Semi-Strong form
- Strong form
• Market Anomaly
- Small firm Effect
- January Effect
- Weekend Effect
Q: Is market inefficient?
The Dividend Controversy
Chapter 16
Q1 : How company set dividend?
Q2 : How dividend affect stock price?
- So far:
independent
Investment Financing
If dividend affects firm value, attractiveness of new project depends on where the money is coming from.
DividendDecision Mixed with
FinancingInvestment
decision
Given capital budgeting & financing decision,what is the effect of change in dividend?
16.1 How dividends are paid? Board of directorsRecord date
Legal Limitation Companies are allowed to pay a dividend out of surplus
but they may not distribute legal capital (par value of all outstanding shares)
Share Repurchase ’80: Ford: $1.2 bil, Exxon: $15 bil, IBM, COCA etc.
Just after 1987 Crash: Citi Corp $6.2 bil
How to Repurchase? 1. Open market repurchase 2. Tender Offer 3. Direct negotiation
16.2 Information content of Dividend
Signaling Model
Other Signaling Tools
GreenmailTarget of a takeover attempt buys off the hostile bidder by repurchasing any shares that it has acquired with premium at the expense of existing shareholders.
16.3 Dividend Controversy
MM(1961) - Dividend irrelevance
In a world without taxes and transaction costs(efficient and perfect capital market)
(Ex) B/S (Market Value)Cash 1,000FA 9,000
0 D10,000+NPV E
10,000 + NPV 10,000 + NPV
Pay dividend by issuing new shares($1,000)We want to continue project w/t cash($1,000)
• Value of original shareholders’ shares (Ex Post)
= Value of company - Value of new shares = (10,000 + NPV) - 1,000 = $ 9,000 + NPV
$1,000 cash dividend = $1,000 capital loss
Investment and borrowing policies are unaffected by dividend[overall value 10,000 + NPV, is unchanged]
* Crucial Assumption New stock holders pay fair-price
Old stockholders have received $1,000 dividend and $1,000 capital loss
Dividend policy doesn’t matter.
(Ex)
N = 1,000 shares
NPV = $2,000
Vold* =
Vold =
Number of new sharessold
=
16.4 The Rightist
Trade a safe receipt with an uncertain future gain?
Sell it!
– Market Imperfection
• Transaction costs• Temporarily depressed price• Information asymmetry about future Earning
16.4 The Leftist
Tax Argument
Weakened after 1986 ‘Tax Reform Act’
16.6 Middle of the Roaders• Without tax and transaction cost (perfect & efficient market), company’s
value is not affected by dividend policy (irrelevant): MM (1961)
• Even if with tax and other imperfections,
Q: If company increase stock price by paying more or less dividend, why have not they already done so?
(perhaps)
– “Supply Effect”
Does Debt Policy Matter?
Chapter 17
B/S
AssetStructure
CapitalStructure
Mix of differentsecurities
“Maximize V”
MM Proposition IFirm can not change the total value of securities just bysplitting its cash flows into different streams. (RHS)Firm value is determined by its real assets. (LHS)
17.1 The Effect of Leverage in a Tax Free Economy
VU: Value of unlevered firm
EL = VL - DL
1) 1% of unlevered firm
$ investment $ return (NOI)
.01 VU .01 profit
2) 1% of equity & debt of levered firm (I: interest)
$ invest $ return Debt .01 DL .01 I
Equity
NI.01 EL
.01(DL + EL)
= .01 VL
same profit (NOI) VU = VL
.01 (profit -I).01 profit
same cost (same investment)
3) Buy 1% of equity of levered firm
$ investment $ return
.01 EL .01 (profit -I) = .01 (VL - DL)
4) Alternative way: Borrow .01 DL on your account Buy 1% of equity of unlevered firm
$ investment $ return
same cost (same investment)
-.01 DL -.01 I.01 VU .01 profit.01(VU - DL) .01 (profit - I)
Same profit
VU = VL
Borrowing Equity
Example of Proposition I (p.477)
All Equity
E(EPS) = $1.5, P = $10, E(R) = 1.5/10 = 15%
N = 1,000
P = $10
VU = $10,000
NOI($) 500 1,000 1,500 2,000
EPS($) .5 1.0 1.5 2.0
ROE(%) 5 10 15 20
A
Issue: debt $5000, k = 10%, repurchase: 500 shares
B
NOI($) 500 1,000 1,500 2,000
Interest 500 500 500 500
NI($) 0 500 1,000 1,500
EPS($)
ROE(%) 0 10 20 30
0 1 2 3
N = 500P = $10, k = 10%Market value of stock: $5,000Market value of debt : $5,000
.50
1.00
1.50
2.00
2.50
3.00
500 1000 1500 2000
Equal proportions debt and equity
All equity
Expected EPS with debt and equity
Expected EPS with all equity
Expectedoperatingincome
Personal LeverageC
Borrow $10, then invest $20 in two unlevered shares(Initially, I have $10)
Earnings on two shares($)
Interest($) at 10%
Net Earnings($)
Return on $10 investment
500 1,000 1,500 2,000NOI($)
1 2 3 4
-1 -1 -1 -1
0 1 2 3
0% 10% 20% 30%
17.2 How Leverage Affects Return
E(EPS)
P
E(ROE)
Current structureall equity
Proposed structure
$1.5 $2.0
$10 $10
15% 20%
V=10,000
D=5,000
E=5,000
NOI = $1,500
N =1,000
Kd = 10%
Leverage increases EPS, but not P.
The change in EPS is exactly offset by a change in the rate at which the earning are capitalized. 15% 20%
Expected return on asset(rA) Market value of all security
NOI=
• In a perfect market, borrowing decision does not affect operating income or total market value of its securities.
• Borrowing decision does not affect expected return on firm’s assets(rA).
Assumption:
rE rA= + DE
(rA - rD)
Expectedreturn onequity
Expected return on assets
rAD
D+E= rD
ED+E+ rE
Debt/EquityRatio
= +Expectedreturn onassets
Expectedreturn ondebt
-
• Proposition II (MM)
The expected return on equity (rE) of a levered firm increases in proportion to debt to equity ratio (D/E)
& the rate depends on the spread between rA and rD. (Ex)
rA = 15% D = 5,000
rD = 10% E = 5,000
rE =
• Figure 17-2
MM’s proposition II. The expected return on equity rE increases
linearly with the debt-equity ratio so long as debt is risk-free. But if leverage increases the risk of the debt, debtholders demand a higher return on the debt. This causes the rate of increase in rE to
slow down.
r
DE
rD
Risk free debt
Risky debt
rA Expected Return on Assets=
rE Expected Return on Equity=
rD Expected Return on Debt=
The Risk-Return Trade-off
AD
D+E= D +
ED+E
E
E A +DE
(A D)-=
Investors (stock-holders) require higher returns on levered equity
17.3 The Traditional Position
Moderate degree of financial leverage
may increase rE although not to the degreepredicted by MM proposition II
Excessive debt raise rE faster
rA (=WACC) decline & later rise.
A
r
DE
rD
Traditionalist believe there is an optimal debt-equity ratio that minimizes rA
rA (MM)=
rE (MM)=
rD
rE (traditional)=
rA (traditional)=
debtequity=
Transaction Costs
Imperfections may allow firms that borrow
to provide valuable service.
(Ex. Economies of scale in borrowing)
Levered Shares might trade at premium compared to their theoretical valuein perfect market
Smart financial engineer already recognize this and shift capital structure to satisfy this client.
B
How Much Should a Firm Borrow?
Chapter 18
Question: Why do we worry about debt policy?
Evidence:
1. D/E ratio are different across the industry.
2. Imperfections:
• Tax• Bankruptcy Costs (T.C.)• Cost associated with financial distress• Potential conflicts of interests between security holders• Interactions of investment and financing decision
18.1 Corporate Taxes
Income statement
of Firm UIncome statement
of Firm L
Earnings before interest and taxesInterest paid to bondholders
Pretax income
Tax at 35%
Net income to stockholders
Total income to bothbondholders and stockholders
Interest tax shield (.35interest)
$1,000 $1,000
0 80
1,000 920
350 322
$650 $598
$0 + 650 = $650 $80 + 598 = $678
0 28
Interest Payment D=
PV(Tax shield) =
rD
(rDTC D)•
rD
TC D=
PV(Tax shield) =0.35 0.08 1000
$350=0.08
Normal Balance Sheet(Market Values)
Asset value (present valueof after-tax cash flows)
DebtEquity
Total assets Total value
Expanded Balance Sheet(Market Values)
Pretax asset value (present
value of pretax cash flows)
Debt
Government ‘s claim(present value of futuretaxes)
Total pretax assets Total value
Equity
Book ValuesNet working capital
Total assets
Market Values
Total assets Total value
$2,64417,599Long-term assets
$20,243
Long-term debtOther long-term
liabilitiesEquity
$1,3476,282
12,614
$20,243
Net working capitalMarket value of long-term assets
$134,156
$2,644
131,512
$134,156
Long-term debt
Other long-term liabilities
Equity
$1,347
6,282
126,527
Table 18.3(a)
Book Values
Net working capital
Total assets
Market Values
Total assets Total value
$2,64417,599Long-term assets
$20,243
Long-term debtOther long-term
liabilitiesEquity
6,282
11,614
$20,243
Net working capitalMarket value of long-term assets
$2,644
131,512
Long-term debt
Other long-term liabilities
Equity
6,282
Additional tax shields
Table 18.3(b)
MM & Taxes: MM Prop I with corporate tax.
VL = VU + PV (Tax Shield)
100% debt?
18.2 Corporate and Personal Taxes
Operating income$1.00
Corporate tax
Income aftercorporate tax
Personal tax
Income after all taxes
Corporate Borrowing is better If (1 - TP) > (1- TPE) * (1 - Tc)
Relative Tax Advantage of Debt =
Special Cases:
1. TPE = TP, RTAD =
MM’s original
2. (1 - TP) = (1 - TPE) * (1 - Tc) RTAD = 1.0 Debt policy is irrelevant! This case happen when Tc < TP & TPE is small.
(1 - TP)(1 - TPE) • (1 - Tc)
1(1 - TC)
(Ex) Tc = 35%, TP = 39.6% What TPE makes debt policy irrelevant?
18.3 Cost of Financial Distress
Value of firm(levered)
Value of allequity PV(tax shield)
PV (costs of financial distress)
= +
-
Debt
Mar
ket V
alue
of
The
Fir
m
Bankruptcy Costs
Payoff
Payoff tobondholders
ACE LIMITED(limited liability)
1,000
500
Assetvalue1,000500
Payoff
Payoff tobondholders
ACE LIMITED(unlimited liability)
1,000
500
Assetvalue1,000500
Assetvalue
PayoffPayoff tostockholders
1,000
01,000500
-1,000
Assetvalue
Payoff
Payoff tostockholders
1,000
01,000500
-1,000
Direct: legal fee, court fee, etc.Indirect: difficult to measure
SHARE PRICE
FRIDAYAPR 10, 1987
MONDAYAPR 13, 1987 CHANGE
NUMBER OF SHARES
(MILLIONS)
CHANGE IN VALUE
(MILLIONS)
Texaco
Pennzoil
Total
$31.875 $28.50 -$3.375 242 -$ 817
-62892.125 77.00 -15.125 41.5
-$1,445
Table 18.4
• Financial Distress without BankruptcyWhen firms get into trouble, stockholders’ & bondholders’ interests conflict. reduce value of firm
Circular File company (Book Values)
Net working capital $ 20
Fixed assets 80
Total assets $100
$ 50
50
$100
Bonds outstandingCommon stock
Total value
Circular File company (Market Values)
Net working capital $20
Fixed assets 10
Total assets $30
$25
5
$30
Bonds outstandingCommon stock
Total value
Risk Shift: The First Game
C0 C1
-$10$120
$ 0
(p=10%)
(p=90%)
If r=50%,
NPV = -10 +1200.1+0
1.5= -$2
Circular File company (Market Values)
Net working capital $10
Fixed assets 18
Total assets $28
$20
8
$28
Bonds outstandingCommon stock
Total value
(Ex1)
High Risk Project
Good (p=0.5) Bad (p=0.5)
VD
S
S =
2,000 300
D =
V =
(Ex2): Amount of Debt = $600
Low Risk Project
Good (p=0.5) Bad (p=0.5)
V
D
S
S =
1,400 1,000
D =
V =
Refusing to contribute equity capital: The second game
Good project with NPV= + $5 by investing $10
Net working capital $20
Fixed assets 25
Total assets $45
$33
12
$45
Bonds Common stock
Total value
Firm value increase by $15Bond value increase by $8Stock value increase by $7
Cost of Distress Vary with Type of Asset
Firms with intangibles having value only as a part of going concern, high technology, investment opportunities, human capital, lose more in the financial distress.
Trade off Theory of Capital Structure
Trade-off between interest tax shield and the costsof financial distress
• Company with safe, tangible asset and plenty of taxable income High debt ratio
• Unprofitable company with risky, intangible assets
Equity finance• Trade-off theory explains what kinds of companies “go private in LBO”
• Trade-off theory cannot explain why some most successful companies thrive with little debt.
18.4 The Pecking Order of Financing Choice, Information Asymmetry
Asymmetric information affects the choice between internal and external financing andbetween new issues of debt and equity securities
Pecking order: internal fund, new issue of debt,finally new issue of equity
(Exception) Firm with already excessive debt High-tech, high-growth company
Implication of Pecking Order1. Firms prefer internal financing2. Firms adopt target payout ratio & try to avoid sudden changes in dividend3. Sticky dividend policy
4. If external finance is required, debt, convertible bond, then equity
Financial Slack: Cash, marketable securities, readily saleable real assets, & ready access to the debt marketor to bank financing
More valuable to firm with plenty of positive-NPVgrowth opportunity
Interactions of Investment and Financing Decisions
Chapter 19
Introduction
• So far, all equity financing All financing decisions are irrelevant
• In this chapter,we consider capital budgeting decision when investment and financing decision interact and can not be separated
APV = BaseNPV
NPV offinancing decisionscaused by project acceptance
+
(value additivity principle)
19.1 After-tax WACC
WACC = rDDV
rEEV
+
WACC = rD (1-Tc) DV
rEEV
+
Sangria Corporation
(Book Values, millions)
Asset $100
Total assets $100
$50
50
$100
DebtEquity
Total value
(Market Values, millions)
Asset $125
Total assets $125
$50
75
$125
DebtEquity
Total value
WACC =?
rD =0.08 rE =0.146 TC=0.35
DV = E
V =
WACC =
Invest: $12.5 million
Pretax cashflow: $2.085 (perpetual)
Tax: 35%
$ 7.5 million (Equity)$ 5 million (Debt)
After-tax cashflow: $1.355 million
NPV =
Return on Investment =
Return on Equity:
NOI
I
Earning After tax
-Tax
2.085-0.4 (=0.085)
1.685
1.095
Expected return on Equity 1.0957.5= = 0.146
E(RE) = rE NPV=0
-0.59 (=1.6850.35)
19.2 Using WACC - Some tricks of the trade
Current Assets, Current liabilities, including cash, inventory, including accounts payable and accounts receivable and short-term debtPlant and equipment Long-term debt (D) Preferred stock (P)Growth opportunities Equity (E)
Firm value (V)
Total capitalization (V)
Industry Cost of Capital
Cost of capital of new subsidiaryCompany’s WACC vs. a weighted-average costof capital of for a portfolio of industry
An Application of the Railroad IndustryAggregate industry capital structure in 1979
DebtEquity
$24,383 bil$57,651 bil
29.7%70.3%
rd=7.2%, g=11.5%, D/P= 2.3%, TC = 35%
WACC =
rE =
Valuing Companies:
WACC vs. Flow-to-Equity Method
WACC• Debt ratio is expected to be constant
• Calculate tax as if firm is all equity-financed
• Usually forecast to a median-time horizon and add a terminal value to the cashflow in the horizon year• Discount at WACC evaluation of the assets and operation of the firm
Flow-to Equity Method
• Evaluation of equity
• Discount the cashflow to equity, after interest and taxes, at the cost of equity• Leverage change cost of equity change two methods give different answer
rE=rA + (rA-rD)(1-TC)DE
19.3 Adjusting WACC when debt ratios or business risks change
Rate of return
r
Debt-Equity Ratio
WACC
Opportunity cost of capital (r)
Cost of Equity(rE)
Cost of Debt(rD)
(Ex) DV = 0.4
DV = 0.2
Step1: unlevering the WACC
Calculate opportunity cost of capital
rDDV
rEEV
+r =
Step2: Estimate rD at 20% debt ratio, & Calculate new rE
rADE
+=rE (rA- rD)
* If taxes are left out, WACC equals the r and is independent of leverage
Step3: Recalculate the WACC at the new financing weight
Step1: current = 0.4DV
r =
Step2: rd = 8%, when = 0.2
rE=
Step3:
WACC=
DV
Rate of return, percent
Debt-Equity Ratio(D/E)
WACC
Opportunity cost of capital (r)
Cost of Equity(rE)
Cost of Debt(rD)8
10
12
14
.25
8.0
11.410.84
13.0
14.6
.67(D/V = .2) (D/V = .4)
Unlevering and Relevering
- Unlevering
asset = debt ( ) + equity( )DV
EV
- Relevering
equity = asset + (asset - debt)DE
or (1+ ) asset , if debt = “0” DE
*. Underlying assumption: Rebalancing Maintain the same market-value debt ratio
19.4 The Adjusted Present Value Rule
Base-NPV
NPV = -10 + [1.8 / (1.12)t ] = $0.17 mil • Issue costs. 5% of gross proceeds of issue
APV = base NPV - issue cost = .17 mil - 526,000 = -356,000 Reject it!
• Additions to the Firm’s debt capacity APV = base NPV + PV tax-shield
t=1
10
Table 19-1 Calculating the present value of interest tax shields on debt supported bythe solar heater project (dollar figures in thousands)
Debt Outstanding Interest Present Value Year at Start of Year Interest Tax Shield of Tax Shield
1 $ 5,000 $400 $140 $129.62 4,500 360 126 108.03 4,000 320 112 88.94 3,500 280 98 72.05 3,000 240 84 57.2
6 2,500 200 70 44.17 2,000 160 56 32.68 1,500 120 42 22.79 1,000 80 28 14.010 500 40 14 6.5
Total: $576
Assumptions:1. Marginal tax rate = Tc = .35; tax shield = .35 x interest.2. Debt principal repaid at end of year in ten $500,000 installments.3. Interest rate on debt is 8 percent.4. Present value calculated at the 8 percent borrowing rate. The assumption here is that the tax shields are just as risky as the interest payments generating them.
• APV = 170,000 + 576,000 = $746,000
• The value of interest Tax Shield (ITS).– We treat the interest tax shield as safe cash-inflow
& discount at 8%.– We assume firm can capture interest tax shields of
35cents on every dollar of interest.
• You can’t use interest tax shield unless you pay taxes.
• Corporate tax favors debt. Personal tax favors equity.
• A project’s debt capacity depends on how well it does.
APV for the Perpetual Crusher projectBase case NPV = - 10 + 1.355/0.12 = $1.29 mil
Financing Rule 1: Debt fixedFinancing Rule 2: Debt rebalanced
Under rule 1 PV (tax shield) = [0.350.08 5] ÷ 0.08 = $1.75 mil APV = 1.29 + 1.75 = $3.04 mil
Under rule 2 Debt is rebalanced to 40% of actual project value.
debt levels are not known & depend on the project’s actual performance. cost if capital is 12%
PV(tax shield) = (0.35 0.08 5) 0.12 = $1.17 mil APV = 1.29 + 1.17 = $2.36 mil
A. Technical Point on Financing Rule 2
• Discount at opportunity cost of capital
• Multiply the resulting PV by (1+r) and
divide by (1+rD)
PV(approx) =0.140.12 = 1.17
PV(exact) = 1.17 1.121.08
= 1.21
APV = 1.29 + 1.21 = $2.5 mil
APV and hurdle Rates
APV tells whether a project makes a net contribution
to the value of the firm
It tells break-even cashflow
APV = - Investment + PVTaxShield
CFr
(Ex) APV = - 10 + PVCF
0.12TaxShield
APV = - 10 + 0.97 = 0CF
0.12
CF = 1.084 IRR = 10.84%
General Definition of Adjusted Cost of Capital
• The Opportunity Cost of Capital (r)
• The Adjusted Cost of Capital (r*)
The expected rate of return offered in capital markets
by equivalent-risk assets.
This depends on the risk of the project’s cash flows.
Adjusted opportunity cost or hurdle rate that reflectsthe financing side effects of an investment project
Spotting and Valuing Options
Chapter 20
20.1 Call vs. Put
Call: Right to buy underlying asset at a specified price
Put: Right to sell underlying asset at a specified price
American: Exercise anytime
European: Exercise only at an expiration date
Exercise Date Exercise Price
Price of Call Options
Price of Put Options
October 1998
January 1999
January 1999
$80
80
85
$8.875
11.375
8.625
$3.25
4.75
6.875
Share Price
Value of Call
85
85
(a)Share Price
Value of Put
85
85
(b)
Value of Share
85
85
(c)
Share Price
Selling Calls, Puts, and Shares
(c)
Share Price
Value of Call Seller’s Position
-85
(a)
085
Share Price
Value of Put Seller’s Position
-85
(a)
085
085
-85
Value of Stock Seller’s Position
Share Price
Buy Share
Value of Share
$85 Future Stock Price
Sell call
Your Payoff
$85 Future Stock Price
Your Payoff
$85 Future Stock Price
+ =
Buy Share
Value of Share
$85 Future Stock Price
Buy Put
Your Payoff
$85 Future Stock Price
Your Payoff
$85 Future Stock Price
+ =
Bank deposit paying $85
Value of Share
$85
Buy Call
Your Payoff
$85 FutureStockPrice
Your Payoff
$85 FutureStockPrice
+ =$85
FutureStockPrice
Put - Call Parity
C + PV (Ex) = P + S
Today
V1=C+PV(EX)
V2=P+S
Expiration Date
S* EX S* < EX
The Difference between Safe & Risky Bonds
Bond holder: Effectively acquire a firm
Stock holder: Effectively purchase a call optionon the assets of firm(PB=promised payment to bondholders)
Asset value $30 Bond: Asset - Call$25
$30
5
$30
Stock: CallFirm: Asset
Circular File Co. (MV)
S
Ex= $500 V (Promised Payment to Bondholders)
Stockholders’ PositionV<50 S =
V50 S =
B
Ex= $500 V (Promised Payment to Bondholders)
Bondholders’ PositionV<50 B =
V50 B =
PB: Promised Payment to Bondholders (safe)
V : Firm value (asset)
S : Stock value
B : Risky bond value
C+ PV(EX) = P + S
S+ PV(PB) = P + V
S+ B = V
B = V - S = PV(PB) - P
Value of risky debt =
Value of risklessdebt
“p”-
?
Asset value $30 Bond value =$25
$30
5
$30
Circular File Co. (Market Value)
present value of promised
payment - value of put
Stock value = asset value - present value
of promised payment +
value of put
Spotting the Option
(Ex) Incentive program:
Paid bonus of $50,000 for every $ that
price of stock exceeds $120. Maximum
bonus is set at $2 millionPay off
1200 Stock Price
$40
160
Pay off
1200 Stock Price160
Buy call with exercise price of $120 and Sell call with exercise price of $160
* Any set of contingent payoffs can be valued as a mixture of simple options on that assets
Share PriceExercise price
Valueof call
A
C
BUpper bound:Value of callequals shareprice
Lower bound:Value of callequals payoffif exercisedimmediately
20.3 What determines option values?
Payoff to call option on firm
Y’s shares
Probabilitydistribution of future price of firm Y’s shares
Payoff tooption on Y
Exercise price
Probabilitydistribution of future price of firm X’s shares
Payoff tooption on X
Exercise price
Payoff to call option on firm
X’s shares
Share PriceExercise price
Value of callson shares of firms X and Y
X
Upper bound
Lower boundY
What the price of a call options depends on
1. Increase in variables:If there is an increase in:
Stock price (P)Exercise price(EX)Interest rate (rf)Time to expiration(t)Volatility of stock price ()
Positive NegativePositivePositivePositive
The changes in the calloption price are:
2. Other properties:a. Upper bound. The option price is less than the stock priceb. Lower bound. The option price never falls below the payoff to immediate exercise (P-EX or zero, whichever is larger)c. If the stock is worthless, the option is worthlessd. As the stock price becomes very large, the option price approaches the stock price less the present value of the exercise price
20.4 An Option-Valuation Model
Constructing Option Equivalents fromcommon stocks & borrowing
Stock PriceToday
$85
Stock Price6 months later Call
$68
$106.25
rf =2.5%
Exercise price = $85
• Hedge ratio (Option delta):
Number of shares that are needed to replicate on call
Optiondelta = Spread of share prices
Spread of option prices
=
• How much to borrow?Present value of the different between the payoff fromthe option and the payoff from the option delta numberof shares
PV(37.78) = $36.86 Amount of borrowing
Option Equivalents:
Buy shares and borrow $36.86 today59
Today
Buy shares
Borrow $36.36
6 month later S* = $68 S* = $106.25
Value of call today= value of shares - $36.86 bank loan
=
59
Arbitrage Opportunity
EX 1: If call is priced at $12 : overpriced
Strategy: Sell a call option Buy 5/9 share & borrow 36.86 today
Today
+12
-47.22
6 month later S* = $68 S* = $106.25
+36.86
+ $ 1.64
EX 2: If call is priced at $9 : underpriced
Strategy: Buy a call option Sell 5/9 share of stock short & lend(deposit) $36.86 today
Today
- 9
+47.22
6 month later S* = $68 S* = $106.25
-36.86
+ $ 1.36
Risk-Neutral Valuation: All investors are indifferent about risk
Expected Return on any risky assets = rf =
E(R) = Pu Ru + Pd Rd
where, Pu + Pd = 1 Pu = probability of stock price increase in the hypothetical risk-neutral world Pu =
at t=1
at t=0
E(C1) =
C0 =
E(R) = Pu ( ) + Pd ( ) =
Ru =106.25-85
85 =
Rd =68-85
85 =
Pd =
Valuing the Intel Put Option
t=0
$85
S P
$68
$106.25
shares Intel share &
Lend $46.07 How is it computed?
Optiondelta = Spread of share prices
Spread of option prices
= =
EX=$85
Today
Sell shares
Lend $46.07
6 month later S* = $68 S* = $106.25
49
Value of put = - of share + $46.07 bank loan
=
49
20.5 The Black -Scholes Formula
Construct a situation where the stock price ischanging continuously and generate a continuumof possible six month prices
Replicate a call option by a levered investment in the stock by adjusting the degree of leverage continuously
Value of call = (delta Share price) - (bank loan)
[N(d1) P] [N(d2) PV(EX)]
where
d1
Log[P/PV(EX)] t
+2
t=
d2 t= d1 -
N(d) = cumulative normal probability density function
EX = exercise price of option; PV(EX) is calculated by discounting at the risk-free interest rate, rf
t = number of periods to exercise date
P = price of stock now = standard deviation per period of (continuously compounded) rate of return on stock
Value of call=[N(d1) P] + [N(d2) PV(EX)]
Real Options
Chapter 21
Option to make follow-on investment if the immediate investment project succeeds.
Option to abandon a project
Option to wait before investing
Option to vary the firm’s output or its production methods
Real Option
21.1 The value of follow-on investment
Table 21-1 Summary of cash flows and financial analysis of the Mark I microcomputer
(millions of dollars)
Year1982 1983 1984 1985 1986 1987
After-tax operating
cash flow (1) * -200 +110 +159 +295 +185 0
Capital Investment (2) 250 0 0 0 0 0Increase in working
capital (3)0 50 100 100 -125 -125
Net Cash Flow
(1) - (2) - (3)-450 +60 +59 +195 +310 +125
NPV at 20% = - $46.45, or about -$46 million
• Table 21-2. Valuing the option to invest in the Mark II microcomputer.
Assumptions1. The decision to invest in the Mark II must be made after
3 years, in 1985.
2. The Mark II investment is double the scale of the Mark I (note the expected rapid growth of the industry). Investment required is $900 million (the exercise price), which is taken as fixed.
3. Forecasted cash inflows of the MarkII are also double those of the MarkI, which present value of about $800 million in 1985 and 800/(1.2)3 = $463 million in 1982.
4. The future value of the Mark II cash flows is highly uncertain. This value evolves as a stock price does with a standard deviation of 35 percent per year.(Many high-technology stocks have standard deviation higher than 35%.)
5. The annual interest rate is 10 percent.
• Interpretation
The opportunity to invest in the Mark II is a 3-year call option on asset worth $463 million with a $900 million exercise price.
• Valuation
PV(EX) = 900(1.1)3 = 676
Call value = N(d1)P - N(d2) • PV(EX)
d1 = log[0.685] / 0.606 + 0.606 /2 = -0.3216d2 = d1 - 0.606 = -0.9279
N(d1) = 0.3739 N(d2) = 0.1767
Call value = 0.3739463 - 0.1767676 = $53.59 mil
21.2 The Option to Abandon
Good Demand
Bad Demand
Tech A Tech B
$18.5 $18
8.5 8
If we bail out Tech B for $10 mil when bad demand Exercise option to sell assets
Value of Tech B = DCF + Value of the abandonment Put
(Value of Flexibility)
Valuing the Abandonment Putt=1 Pr Payoff Put
Good DemandBad Demand
0.5 $ 18
0.5 $ 8
EX = $10, r = 8.3%, rf = 5%
PV=
E(R) = Pu ( ) + Pd ( ) = = rf
Pu = Pd =
E(P) = 0.46 + 0.54 =
P =1+rf
E(P)=
Value of project =
21.3 The Timing Option: rf = 5%
t = 0
If invest $180,project worth $200
GoodDemand
BadDemand
Project Value
Cash flow
Value of Call
$250 $25
$160 $16
t = 1
If undertake project today,
capture either $25, or $16 at t=1
If delay, miss out on this cashflow at t=1, but will have more information on how the project is lively to work out
Project NPV0
Value of option
to invest
Investment nowor never
Investment canbe postponed
RG=
RB=
E(R) = PG ( ) + PB ( ) = = rf
PG = PB =
t=1, E(C) =
t=0, Value of call =
Q: Do you undertake project now?
Warrants and Convertibles
Chapter 22
22.1 What is warrant?
Value of warrant
Exercise price = $15
Actual warrant value prior to expiration
Theoretical value (lower limit on warrant value)
Stock price
• Two Complications: Dividends and Dilution• Example: Valuing United Glue’s Warrants
Number of shares outstanding (N) Current stock price (P)
Number of warrants issued per share outstanding (q)
Total number of warrants issued (Nq)
Exercise price of warrants (EX)
Time to expiration of warrants (t) Annual standard deviation of stock price changes
Rate of interest (r): United stock pays no dividends.
()
1 million
$12
.10
100,000
$10
4 years
.40
10%
……………………..…………..
…………..
……….
……………
……………
……………
…………………………..
United Glue’s market value balance sheet (in $ millions)
Before the Issue
Existing assets
Total
$16
$16
$ 4 Existing loans
Common stock (1 million shares at $12 a share)
12
$16
After the Issue
Existing assets Existing loans$16 $ 4New assets financedby debt and warrants 2
New loan without warrants
1.5
Total
Total debt5.5.5 Warrants
12 Common stockTotal $18 $18 Total
United Glue has just issued a $ 2million package of debt and warrant
Suppose
$ 1.5 mil: value of debt without warrants
$ 0.5 mil: value of warrants
Each warrant costs investors =
Value of warrant from Black-Scholes formula
=
• Dilution Effect
Nq =
Nq EX =
V: value of equity
V = Total asset - debt
Share price afterexercise =
Warrant valueat maturity = Max (P - EX, 0)
= Max V + Nq•EXN + Nq
- EX, 0
Max V/N + EX1 + q
, 0=
Max VN
, 0=1
1 + q - EX
$ 12.5 mil: Current equity value of alternative firm (=18 mil - 5.5 mil) Current share priceof alternative firm = V
N= 12.5
1 mil= $12.5
Suppose of alternative firm: = 0.41
Black-Sholes value of call:
Value of warrant = 1
1 + q Value of call on
alternative firm
=
deal for United
22.2 What is a Convertible Bond
• Difference between convertible bond vs. bond-warrant package
Bond value:
Conversion value:
• The price of convertible bond depends on its bond value and its conversion value
0
1
2
3
1 2 3 4 5Value of firm ($ million)
Bon
d va
lue,
$th
ousa
nd
0
1
2
3
1 2 3 4 5Value of firm ($ million)
Con
vers
ion
valu
e, $
thou
sand
0
1
2
3
1 2 3 4 5Value of firm ($ million)
Val
ue o
f co
nver
tible
,$
thou
sand
ConvertBond paid
in full
Default
• Value at Maturity
Default
Bond paid in full
0
1
2
3
1 2 3 4 5Value of firm ($ million)
Bon
d va
lue,
$th
ousa
nd
0
1
2
3
1 2 3 4 5Value of firm ($ million)
Low
er li
mit
on C
onve
rtib
le,
$th
ousa
nd
Bond Value
Conversion Value
0
1
2
3
1 2 3 4 5Value of firm ($ million)
Val
ue o
f co
nver
tible
,$
thou
sand
Lower limit on value
Value of convertible
• Value before Maturity
A B CStock price
Value of Convertible
Bond Value
Conversion Value
Call price
Forcing Conversion
Value of convertible
bond
Value of straight
bondConversion
optionRedemption
option= + -
22.3 Difference between Warrants and Convertibles
1. Warrants are usually issued privately
2. Warrants can be deleted
3. Warrants may be issued on their own
4. Warrants are exercised for cash
5. A package of bond & warrants may be taxed differently
22.4 Why do companies issue
Warrants and Convertibles?
Valuing Debt
Chapter 23
• Present Value of Bond
Q: What determines the discount rates?
PV C(1+r1)
=C
(1+r2)2C
(1+r3)3+ + + … (1000+C)(1+rn)n+
r1 , r2 , r3 , …. rn : discount rates for cashflows to be received by the bond holders in periods 1, 2, …,n.
(Ex) Same security offers different yields at a different time.
Bonds maturing at different dates offer different rate of interestBorrowing rate of government is lower than your borrowing rate
23.1 Real and Nominal Rates of Interest
Real Rate: compensation for time value of money
Nominal Rate = Real Rate + Perspective Rate of Inflation
How Real Rate is determined?
Supply of capital: time preference for today’s consumption over future consumption
Demand of capital: Availability for profitable investment opportunities ( Positive NPV Projects)
S
D
rr1
S
D
rr2
23.2 Term Structure and Yield to Maturity
PV = C1+r1
PV =C
1+r1
C(1+r2)2
r1, r2 : Spot rate
The series of spot rates r1, r2 … Term structure of interest rates
+
• Yield to MaturityRate of return to bondholders if he/ she keeps the bonduntil maturity
Price of Bond =C
(1+y)C
(1+y)2+ + … C+F(1+y)n+
PRESENT VALUE CACULATIONS5s of ‘08 10s of ‘08
PERIOD INTEREST RATE Ct PV AT rtCt PV AT rt
t = 1
t = 2
t = 3
t = 4
t = 5
r1 = .05
r2 = .06
r3 = .07
r4 = .08
r5 = .09 Totals
$ 50
50
50
50
1,050$1,250
$ 47.62
44.50
40.81
36.75
682.43$852.11
$ 100
100
100
100
1,100$1,500
$ 95.24
89.00
81.63
73.50
714.92$1,054.29
YIELD TO MATURITYBond Price Percent (IRR)
5s of ‘0810s of ‘08
85.21%105.43
8.78%8.62
23.3 Duration and Volatility
Duration: Average time to each payment
D =1 PV(C1)
V+ … +
2 PV(C2)V
…
YEAR CtPV(Ct) AT 5.5%
1
2
3
4
5
6
137.5
137.5
137.5
137.5
137.5
1137.5
PROPORTION OF TOTAL VALUE
[PVt/V]PROPORTION OF TOTAL
VALUE TIME
130.33
123.54
117.10
110.99
105.21
824.97
.092
.087
.083
.079
.075
.584
.092
.175
.249
.314
.373
3.505
V = 1,412.13 1.000 Duration = 4.708 years
(A) 13 ¾s of 2004 (B) 7 ¼s of 2004
VB =
DB = 5.115 years
vs.
(EX) 1% changes in yield
13 ¾s of 2004 7 ¼s of 2004NEW PRICE CHANGE NEW PRICE CHANGE
Yield falls, 0.5%Yield rises, 0.5%
144.41138.11
Difference 6.30
+2.26%- 2.20
4.46%
111.42106.15
5.27
+2.46%- 2.39+4.85%
Volatility (%) Duration1+yield
VA =
DA = 4.708 years
• Hedging
By equalizing the duration of the asset and that of the liability,we can immunize against any change in interest rate
(EX) Aztec Learning has just purchased some equipment andArranged to rent it out for $ 2mil a year over eight years at 12%
Aztec finances by issuing a packaging of one year and six-year bond, each with 12% coupon to set up hedged position, find out proportion of one year and six year bond
Solution
PV of rental income =
Duration of Rental income =Duration of one year bond =Duration of 6-year bond =
Let : x is the proportion raised by 6-year bond1-x is the proportion raised by 1 year bond
Duration Package = x duration of6-year bond + (1-x) duration of
1 year bond3.9 years = x 4.6 years + (1-x) 1 years
23.4 Explaining the Term StructureTopic Why do we observe different shape of term- structure?
Ms. Long: invest $1,000 for 2 years 1,000
1,000
Forward Rate
The extra return that Ms. Long gets by lending for 2 years rather than 1 Implicit & guaranteed
(1+r2)2 = (1+ r1 ) (1+f2)
f2 =(1.105)2
1.1- 1 0.11 11%
=
=
Expected Payoff: L1 Certain Payoff: L2
1,000 (1+r1) [1+E(1r2)] vs.1,000 (1+r2)2
1,000 (1+ r1 )(1+f2)or
Strategy L1 gives higher-return if
Mr. Short: invest 1 year
Buy 1 year bond:
Buy 2 year bond & sell it after 1 year
PV of 2 year bond at year 1 =
Certain Payoff: S1 Expected Payoff: S2
1,000 (1+r1) vs. or
Strategy S2 is better if
1,000 (1+r2)2
1+E(1r2)
1,000 (1+ r1 )(1+f2)1+E(1r2)
• The Expectations Hypothesis
Ms.Long and Mr. Short try to maximize their expected return
If f2 > E(1r2) prefer 2yr. bond price bond of 2yr return of 2yr. Bond and f2
Equilibrium: f2 = E(1r2)
If f2 < E(1r2) prefer 1 yr. bond
The only reason for upward sloping term structure is investor expect the relationship such that
f2 = E(1r2)
f2 > r1 , E(1r2) > r1
• Consider “risk”
Long Case: horizon 2 yr.If Ms. Long buys 1 year bond: first year return is certain
but, uncertain “reinvestment rate” at the end of year 1
Ms. Long holds 1 year bond only if E(1r2) f2
Short Case: horizon: 1 yr.If Mr. Short buys 2 year bond: he has to sell it next year at an
“unknown price”. Mr. Short holds 2 year bond only if E(1r2) f2
Other things equal, Ms. Long will prefer to buy year bond & Mr. Short will prefer to buy year bond
The Liquidity Preference (Theory)
If more companies want to issue 2 year bond thanthere are Ms. Long to hold them,
They need to offer “Bonus” to attempt some of theMr. Short to buy 2 year bond.
Any bonus shows up as a difference between f2 & E(1r1) Liquidity Premium
In reality, there are shortage of long-term lender,liquidity premium is positive.
f2 = E(1r2) + Liquidity Premium ( = LP2)
f2 = E(2r3) + LP3
23.5 Allowing for the risk of Default
Q: Why do some borrowers have to pay a higher rateof interest than others?
Default risk premium
Expected yield
other risk premium
Rf
Promised yield y
Yield= Rf+ Risk Premium
(EX) Rf = 9% Payoff (t=1)$ 1,090
0
Probability0.80.2
Expected payoff ($) at t=1:
If default is totally unrelated to other event of economy,= default risk is wholly diversifiable
PV =
Promised yield = (expected yield = 9%)
Since default occurs in recession, ,
PV =
Promised yield = (expected yield = 11%)
say risk premium=2%
Bond Ratings“relative quality” of bond by
MOODY’S STANDARD AND POOR’SAaaAaABaa
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Investment grade
Junkbonds
PERCENTAGE DEFAULTING WITHINRATING ATTIME OF ISSUE
1 YEAR AFTER ISSUE
5 YEAR AFTER ISSUE
10 YEAR AFTER ISSUE
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Moody’sStandard & Poor’s
Leasing
Chapter 25
A rental agreement that extends for a year or moreand involves a series of fixed payments
What to lease?
LesseeLessor : Leasing industry
Equipment manufacturersBanksIndependent leasing company
Operating Lease
Capital Lease(financial/ full payment)
25.2 Why lease ? – Convenient (short-term)– Cancellation option – Maintenance provided– Tax-shield can be used.– Etc.
25.3 Operating lease.In real life, idle time is considered.
In operating lease, the lessor absorbs idle risk, not the lessee.
The discount rate must include a premium sufficient to compensate its shareholder for the risk of idling.
– For operating lease: Lease vs. Buy
– For financial lease : Lease vs. Borrow
Table 25-1 Calculating the zero-NPV rental rate (or equivalent annual cost) for EstablishmentIndustries' pearly white stretch limo (figures in thousands of dollars)
Year0 1 2 3 4 5 6
Initial cost -75
Maintenance, insurance, selling, and administrative costs -12 -12 -12 -12 -12 -12 -12
Tax Shield on costs +4.2 +4.2 +4.2 +4.2 +4.2 +4.2 +4.2
Depreciation tax shield +5.25 +8.40 +5.04 +3.02 +3.02 +1.51Total -82.80 -2.55 .60 -2.76 -4.78 -4.78 -6.29
NPV at 7% = -$98.15
Break-even rent (level) 26.18 26.18 26.18 26.18 26.18 26.18 26.18
Tax -9.16 -9.16 -9.16 -9.16 -9.16 -9.16 -9.16
Break-even after tax 17.02# 17.02 17.02 17.02 17.02 17.02 17.02
NPV at 7% = $98.15* no inflation; r = 7%; Tc = 35%` * Table 6-5: depreciation
* First payment: immediate # 17.02 = 65% of 26.18 7% PVA 7yrs = 5.389 5.389 * 1.07 = 5.766
25. 4 Financial LeaseTable 25-2 Cash-flow consequences of the lease contract offered to Greymare Bus Lines(figures in thousands of dollars; some columns do not add due to rounding)
NPV of 'Lease' relative to 'Buy'
Year0 1 2 3 4 5 6 7
Cost of new bus +100Lost depreciation tax shield -7.00 -11.20 -6.72 -4.03 -4.03 -2.02 0Lease payment -16.9 -16.9 -16.9 -16.9 -16.9 -16.9 -16.9 -16.9Tax shield of lease payment +5.92 +5.92 +5.92 +5.92 +5.92 +5.92 +5.92 +5.92Cash flow of lease +89.02 -17.99 -22.19 -17.71 -15.02 -15.02 -13.00 -10.98* 5 yr: depreciation (Table 6.4), 7yrs/8 times payment, Tc = 35%, rD = 10%
* After tax: rD * (1 - Tc) = 6.5%
NPV lease = +89.02 - 17.99 - 22.19 - 17.71 - 15.02 - 15.02 - 13 - 10.98
1.065 (1.065)2
(1.065)3
(1.065)4
(1.065)5
(1.065)6
(1.065)7
= -0.7 -$700
Year
0 1 2 3 4 5 6 7
Lease cash flows, thousands +89.02 -17.99 -22.19 -17.71 -15.02 -15.02 -13.00 -10.98
Table 25-3: Equivalent loan; exactly same debt service on lease.
Year
0 1 2 3 4 5 6 7
Amount borrowed at year-end 89.72 77.56 60.42 46.64 34.66 21.89 10.31 0
Interest paid at 10% -8.97 -7.76 -6.04 -4.66 -3.47 -2.19 -1.03Interest tax shield at 35% +3.14 +2.71 +2.11 +1.63 +1.21 +.77 +.36Interest paid after tax -5.83 -5.04 -3.93 -3.03 -2.25 -1.42 -0.67Principal repaid -12.15 -17.14 -13.78 -11.99 -12.76 -11.58 -10.31Net cash flow of equivalent loan 89.72 -17.99 -22.19 -17.71 -15.02 -15.02 -13.00 -10.98
How much can I borrow when I pay same cash as lease payment?
Creating Equivalent Loan
25.5 When Do Financial Leases Pay? The value of the lease to the bus manufacturer would be(Tc=35%)
Value of lease to lessor
-89.02 +17.99
+1.065
= +.70 Zero sum gameSuppose that Greymare paid no tax (Tc = 0).
Then the only cash flows of the bus lease would be:
Year0 1 2 3 4 5 6 7
Cost of new bus +100
Lease payment -16.9 -16.9 -16.9 -16.9 -16.9 -16.9 -16.9 -16.9
These flows would be discounted at 10 percent,because rD (1-Tc)= rD when Tc =0
+22.19
(1.065)2
17.71
(1.065)3+
15.02
(1.065)4+
15.02
(1.065)5
13
(1.065)6+ +
10.98
(1.065)7=
t=0
10
(1.1)t
16.9100 -Value of lease = = +100 - 99.18 = +.82 or $820
The potential gains to lessor and lessee are higher when:
The lessor’s tax rate is substantially higher than the lessee’s
The depreciation tax shield is received early in the lease period
The lease period is long and the lease payments are concentrated toward the end of the period
The interest rate rD is high - if it were zero, there would be no advantage in present value terms to postponing tax
Mergers
Chapter 33
Selling Company Acquiring Company Payment, billions of dollars
NYNEX Bell Atlantic 21.0McDonnell Douglas Boeing 13.4Digital Equipment Compaq Computer 9.1Schweizerischer Union Bank of Swiz. 23.0Energy Group PCC Texas Utilities 11.0Amoco Corp. British Petroleum 48.2Sun America American Intl. 18.0BankAmerica Corp. Nationsbank Corp. 61.6Chrysler Daimler-Benz 38.3Bankers Trust Corp. Deutsche Bank AG 9.7Netscape America Online 4.2Citicorp Travelers Group Inc. 83.0
33.2. Sensible Motives for Mergers Economies of Scale
Vertical Integration
Complementary Resources
Unused Tax Shields
Surplus Fund Free Cash Flow ?
Eliminating Inefficiencies
Diversification
Increasing Earning Per Share
Lower Financing Cost
33.3 Estimating Merger Gains and Costs
A: Buyer B: Seller
Synergy Gain = PVA+B - (PVA + PVB)
Cost = Cash paid - PVB
NPV = Gain - Cost = PVAB - (Cash-PVB)
(Ex)
PVA = 200, PVB = $50, PVA+B = $275
Gain = PVAB = + $25
Cash = $65
Firm A Firm BMarket priceper share
Number of share
Market value of firm
$ 200 $ 100
1,000,000 500,000
$ 200 mil $ 50 mil
Cost = Cash - PVB = Cash - MVB + (MVB - PBB)
= 65 -50 + (50 - 44) = $21 mil
Cash payment depends on the relative bargainingpower of the two participants
• Stock offer
N : shares received by seller
PAB: combined firm’s worth
Cost= N PAB - PVB(Ex) N = 325,000
A’s price before merger: $200PVB = $50 mil
Apparent cost =
If PVAB = $275mil (due to synergy gain)
New share price =
Cost = 0.325 -50 =
Takeover Defense Preoffer Defenses
• Shark-repellent Charter Amendments– Staggered Board– Super Majority– Fair price
• Dual class stock• Poison Pill, Poison put• ESOP
Postoffer Defenses • Litigation• Asset Restructuring• Liability Restructuring
Divestitures (sell offs) and Spin offs.
- Synergy Motivated
- Focus
- Complementary Resources
- More Efficient Contracting (Better Organization Structure)
- Raising Capital
Question:
What is the source of gain and where it is created?
Leveraged Buyouts
• Debt financed (junk-bond)
• Going private
• MBO