Milind Shrikhande
Associate Professor of Finance

☺ Syllabus
☺ Course overview
☺ Lecture Sequence: Options…

☺ Expectations
☺
Be here
☺
Ask questions
☺
Work practice problems
☺ Required skills
☺
Spreadsheet (Excel) and Internet
☺ Required materials
☺
Text: Bodie, Kane and Marcus 6 th edition
☺
Solutions manual

☺ Grading
☺
3 Quizzes @ 20% each
Similar to or related to practice problems and examples
No make-ups
☺
Final exam (comprehensive) @ 30%
☺
Stock-Trak assignment @ 10%
☺ Make-up Policy
☺
No make-up quizzes
☺
Everyone must take the final exam

☺ Grading – Typical Department Policy
☺
No more than 35% A
☺
Majority (approximately 50%) B
☺
Lagging performance earns a C or lower
☺ Administrative – Withdrawal with a WF
☺
Beyond 3 absences from class
☺
Withdrawal after the semester midpoint
☺
Withdrawal while doing failing work

☺ Materials
☺
(Financial) Calculator – bring every day
☺
Text – leave it where you read it
☺
Lecture notes, handouts – provided
☺ Office Hours
☺
Drop-in, phone, e-mail and by appointment

☺ Discounted cash flows
The value of an asset is related to the stream of expected cash flows that it generates, and should reflect compensation for time and risk .
☺ Arbitrage pricing
When two assets have exactly the same stream of cash flows (magnitude, date, state) their prices should be identical.

Bonds Stocks Derivative
CF stream
Time line
Risk coupons and face-value fixed maturity dividends no maturity default risk systematic risk contingent on contract and underlying asset fixed expiration contingent on contract and underlying asset

Discounted Cash Flows (DCF) Valuation
The Idea
The value of an asset is the present value of its expected cash flows.
The Philosophical Basis
Every asset has an intrinsic value that can be estimated, based upon the characteristics of the stream of cash flows that the asset generates.

☺ The magnitude of the expected CFs
☺ The timing of the expected CFs
☺ The risk level of the expected CFs

☺ Magnitude : investors prefer to have more rather than less.
☺ Timing : investors prefer a dollar today rather than a dollar some time in the future.
☺ Risk : investors would rather get a certain CF of
$1 than get a lottery ticket with an expected
(average) CF of $1.

CF
1
CF
2
CF
3
CF
4
CF
T
|--------|--------|--------|--------|---------------|---> t
0 1 2 3 4 … T
Value
 f CF t t
,

T k

PV = Present Value
FV = Future Value
CF t
= Cash Flow on date t t is the time (date) index ( t = 1, 2, …, T ) k = risk-adjusted discount rate
(risk-adjusted / opportunity cost of capital) rf = risk-free discount rate
(use as the discount rate if the probability of default is zero) g = growth rate

Compounding
Converts present cash flows into future cash flows.
Discounting
Converts future cash flows into present cash flows.
The Additivity Principal
Cash flows at different points in time cannot be compared or aggregated. All cash flows have to be brought to the same point in time before comparisons or aggregations can be made.

$100 FV
|--------|-----> t k = 5%
0 1
FV

100 1.05 $105
$100 FV
|--------|--------|---> t k = 5%
0 1 2
FV
  2 
$110.25
PV FV
|--------|--------|-----------|---> t
0 1 2 … T
FV

PV (1
 k )
T

In a study of returns on stocks and bonds between 1926 and 1997, Ibbotson and
Sinquefield found that on average stocks made 12.4% annual return, treasury bonds made 5.2% and treasury bills made 3.6% .
Assuming that these returns continue into the future, what will be the value of $100 invested in each category for 1year, 5 years, 10 years?

Holding
Period
1
Stocks
$112.40
T.
Bonds
$105.20
T.
Bills
$103.60
5
10
$179.40
$128.85
$119.34
$321.86
$166.02
$142.43

PV $100
|--------|-----> t k = 5%
0 1
PV

100
1.05

$95.24
PV $100
|--------|--------|-----> t k = 5%
0 1 2
PV

100
1.05
2

$90.70
PV FV
|--------|--------|------------|---> t
0 1 2 … T
PV

FV
(1
 k )
T

CF
1
CF
2
CF
3
CF
4
CF
T
|--------|--------|--------|--------|--------------|---> t
0 1 2 3 4 … T
PV

(
1
)

(
2
 
PV CF
T
)

(1
CF

1 k )

(1
CF
 k
2
)
2
CF
T
(1
 k )
T
 t
T 

1
CF t
(1
 k ) t

1.
How much will you pay today for a project that is expected to pay a dividend of $500,000 three year from now, if the appropriate (riskadjusted) annual discount rate for this project is 10%?
2.
What is the value of a project that is expected to pay $150,000 one year from now and
$500,000 three years from now, if the appropriate (risk-adjusted) annual discount rate for this project is 10%?

1.
PV = $500,000/(1+0.1) 3 = $375,657.40
2.
PV = $150,000/(1+0.1) 1 + $500,000/(1+0.1) 3
= $136,363.64 + $375,657.40
= $512,021.04

special cases
A growing perpetuity:
CF CF(1+g) … CF(1+g) (t-1) …
|---------|---------|-------------------|-------------------> time
0 1 2 … t …
PV

(1
CF
 k )

CF
(1
(1
 k

)
2 g )
 t



1
CF (1
 g )
(1
 k ) t
CF (1
 g )
(1
 k ) t

...

CF k
 g
(if k
 g )

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

Current dividend per share = $2.73
Expected growth rate g = 6% = 0.06
CF
1
= $2.73 ·(1+0.06) = $2.8938
Discount rate k = 12.23% = 0.1223
PV

2.8938

$46.45

In fact, the stock was actually trading at $70 per share. This price could be justified by using a higher expected growth rate.
70 g

2.73(1
 g )
0.1223
 g

8%

special cases
A growing annuity:
CF CF(1+g) … CF(1+g) (T-1)
|---------|---------|-------------------|-------------------> time
0 1 2 … T
PV

(1
CF
 k )

CF
(1
(1
 k

)
2 g ) CF (1
 g )
( T

1)
(1
 k )
T
 t
T 

1
CF (1
 g )
( t

1)
(1
 k ) t

CF k
 g



1



1

1
 g k
 T



Suppose you are trying to borrow $200,000 to buy a house on a conventional 30-year mortgage with monthly payments.
The monthly interest rate on this loan is
0.7%. What is the monthly payment on this loan?

PV = $200,000
T = 30·12 = 360 k = 0.7% = 0.007
g = 0
$200, 000

CF
0.007




1




CF

$1, 523.7
1



360
 



The frequency of compounding affects both the future and present values of cash flows.
The quoted annual interest rate may be compounded more frequently than once a year. This will affect the effective annual interest rate which is determined by the specified frequency of compounding.

A government note pays a coupon (interest) of 4.75% of par value. This means that a
$1,000 face-value note pays $47.50 in annual interest in two semiannual installments of $23.75 each.
The quoted annual interest rate is 4.75%, but it is compounded semiannually . What is the effective annual interest rate ?

1
 effective rate

1 quoted
 rate m

 m
1
 effective rate effective rate


1
0.0475
2


2
4.8064%
 quoted
 rate

Frequency annual
Semi-annual monthly weekly continuous
Quoted
Rate
10%
10%
10%
10%
10% m
1
2
12
52
∞
Effective
Rate
10.00%
10.25%
10.47%
10.51%
10.52%

1
 effective rate

1 quoted
 rate m

 m
As m goes to infinity (m
 
) we get
1
 effective rate
 e

1
 effective m period
 rate
 effective period
 rate
 m
If one sub-period is a monthe and m=12, then
1
 effective
 annual
 rate
 effective
 monthly
 rate

12
If one sub-period is 6 months and m=4, then
1
 effective year
 rate
 effective months
 rate

4

The quoted annual rate is also called the
APR (Annual Percentage Rate)
The Effective Annual Rate is the EAR
We will use the notation r q,annual r eff,annual
= quoted annual rate
= effective annual rate r annual
= annual rate (when r q,annual
= r eff,annual
)

The quoted annual rate of return is 10%, compounded semiannually . Calculate the following rates: a.
Effective rate for 1 year (10.25%) b.
Effective rate for 2 years (21.55%) c.
Effective rate for 18 months (15.76%) d.
Effective rate for 6 months (5%) e.
Effective rate for 2 months (1.64%)