tuck bridge finance module 1

8/4/2019 Tuck Bridge Finance Module 1

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CLASS 1

INTRODUCTION AND

BASIC CONCEPTS

Bridge Program 2005

Finance module

Finance, Bridge Program 2005 1


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Contents

1 Overview of Finance module 3

2 Basic concepts 11

3 Bonds 19



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1 Overview of Finance module

1.1 Contact information

Diego Garca, Assistant Professor.

Office: Woodbury 205.

Email: [email protected].

Office hours: by appointment.

Class web page

http://diego-garcia.dartmouth.edu/bridge.html:

Copies of all assignments and slides.

Solutions and slides posted after class.



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1.2 Goals of the Finance module

1. Introduce basic concepts in modern Finance theory.

Discounting, interest rates, inflation.

Risk and return. Principles of investment decisions.

2. Basic goal: learn how to price things.

Discounted cash flow approach.

Rely on economic concepts and probability tools

to quantify prices.



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1.3 The bookThe book that we will use is not in publishable form, i.e. it is

work in progress.

Positives:

Its free!

Chapters are short: dont get distracted with side notes,

anecdotes and/or optional parts.

Negatives:

There are still some typos and incomplete sections.

Note: I have brief comments about the readings in the

summary about each class in the syllabus.



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1.4 What is expected of you Attendance. If you miss class Ive been told

you could get in trouble.

Readings. You should have read the chapters

assigned for each day.

Assignments. You should at least have made a

serious attempt at their solution. I will randomly

pick up 10 assignments each day.

I suggest 2-3 hours pre-class prep and 1 hour post-class

(go over slides and solutions to assignments).



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1.5 Outline of the 8 classes

Class Topic Must-Read Recommended

1 Introduction and basic concepts 2, 3, 4.1-4.4 1-4

2 NPV analysis 5.1, 6.4-6.6 5-6

3 Capital budgeting 7.1, 8.1-8.3 7-8

4 Introduction to investments 11.1, 12-13, 14.1 11-14

5 Diversification 15, 16.4 15-16

6 CAPM 17.1-17.4, 18.1 17-18

7 Capital structure and risk 20.1, 21 20-22

8 Review 10.2, 29 9-10, 29

Class 8, as well as two other review sessions, will be run by the

TAs for the course.



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1.6 Who am I?

Diego Garca. Call me Diego.

Call me Diego.

PhD in Finance, UC Berkeley 2000.MA in Statistics, BA in Business Administration.

Born and raised in Asturias, Northwest region of

Spain.

Fifth year teaching at the Bridge Program. Teach

Corporate Finance (core) in the MBA program.



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1.7 Research interests

Random keywords:

Football and stock returns.

Markets for information; competition betweenmutual funds.

Information aggregation in financial markets.

Overconfidence and asset prices.

Private information and contracting (venture

capital financing, capital budgeting).



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Other bits and pieces

I use 10% and 0.10 interchangebly.

I like to write 1 instead of 1000000.

I make 1s with heads. I randomize whether to give 7s a

middle stroke or not.

I will round in the board either up or down - watch out.

Office hours: email me and set up a time (lowest cost).

Can always try me at my office (but no AC).

I am pretty good at answering email. Dont hesitate to

write if you need clarifications or have questions.

I will cold-call you quite a bit. Sometimes I will not agree

with your answer. Please do not take my harshness the

wrong way, English is a foreign language for me.



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2 Basic concepts

2.1 Defining Finance

Finance is the study of how people allocate scarce

resources over time. Costs (payroll, current stock prices) and benefits

(sales, dividends/future stock prices) are distributed

over time.

Actual timing and size of future cash flows are oftenknown only probabilistically: there is risk that

investors need to deal with.



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Finance

Finance is a subfield of Economics: focus on risk

and timing of economic decisions.

Main goal of Finance is to evaluate (price) uncertain

cash flows.

When implementing decisions, people make use of

the Financial System defined as the set of markets

and other institutions used for financial contracting

and exchange of assets and risks.

I will not spend time on institutional details (or

rather little time). If you are serious about having a

career in Finance you should look these up.



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2.2 The players

Resources are allocated (and funds flow) from the

surplus unit to the deficit unit: directly, through markets,

through intermediaries.

Financial intermediary: a firm whose primary business isto provide financial services and financial products.

Some players: commercial banks, depository savings

institutions, thrift institutions, insurance companies,

pension and retirement funds, mutual funds, investment

banks, venture capital firms, investment management

firms.



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2.3 A road-map

This is basically the plan for this week:

Understand investment decisions ignoring risk: NPV

rule, yield curve. Risk and investment decisions: mean-variance

efficiency, CAPM.

We start slow (Mon-Tu) and then start moving quickly

(Thu).

Try to have fun.



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2.4 Rates of return

Imagine at date t we get to invest CFt, for a dollar return

CFT at date T.

The holding rate of return for this investment is

CFt(1 + rt,T) = CFT; rt,T =CFT

CFt 1.

This is a convention that turns out to be very useful interms of comparing different investment opportunities.



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An example with risk

Imagine a stock that can be priced at $20 with 40% or $30 with60% probability next year. Ignore dividends. The current stock

price is $25.

The expected price of this stock is E[P] = (0.6)30 + (0.4)20 = 26.

Its expected return is E[R] = (26 25)/25 = 4%.

Imagine a stock that can be priced at $50 with 40% or $60 with

60% probability next year. Ignore dividends. The current stock

price is $55.

The expected price of this stock is E[P] = (0.6)60 + (0.4)50 = 56.

Its expected return is (56 55)/55 = 1.81%.

Which of the two stocks is riskier?

Tough to say without learning about risk (classes 4-7).



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2.5 Compounding interest rates

What is the total two-year Holding Rate of Return, if one earns

a one-year rate of return of 20% in each year?

It is not 20% + 20% = 40%! If one invests $100 at a 20% rate of

return today (year 0), one will have $120 in year 1. Investing

$120 at a 20% rate of return from year 1 to year 2, one will end

up with

$120(1 + 20%) = $144

The compounding formula translates many individual period

rates of returns into a single total holding period rate of return:

(1 + rt,t+N) = (1 + rt,t+1) (1 + rt+1,t+2) (1 + rt+N1,t+N).



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2.6 Annualized rates

If the total return is 173% over the three year period, what

would your average annualized interest return be?

The answer is not 173%/3 57.7%, because if you earned

57.7% per year, you would have ended up with

(1 + 57.7%) (1 + 57.7%) (1 + 57.7%) 1 = 287%,

not 173%!

To find the annualized rate, which I will call r3, we need to solve

the equation

(1 + r3) (1 + r3) (1 + r3) = (1 + 173%)

(1 + r3)3 = (1 + 173%)

(1 + rt)t = (1 + r0,t).

so r3 39.76%.



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3 Bonds

A bond is a contract (piece of paper) that promises its holder a

fixed set of cash flows over its life.

Cash flows typically decomposed into:

1. Coupon payments: a percent (the coupon rate) of the

principal of the bond.

2. Principal repayment: paid at the maturity of the bond.

Example: a 2-year 10% coupon bond with a face value of $1000

would give its owner $100 1 year from today, plus $1100

(100+1000) 2 years from today.

Notation on bonds: c is coupon rate, F is face value, T is

maturity.



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ExampleConsider a zero-coupon bond (c = 0) with a face value of

F = 100 and price P = 90 which matures in 5 years (T = 5).

This bonds entitles its holder to receive $100 5 years from

today, after paying $90.

Total (net) return (100 90)/90 11.11%.

Total (gross return) 100/90 1.1111.

Annualized return r5 solves

(1 + r5)5 = 1.1111;

so r5 2.1296%.



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Some definitions

The term structure of interest rates is a graph which gives you

the annualized risk-free return one can guarantee himself for

different horizons (typically from 1-month up to 30-years).

We call these annualized rates spot rates.

What is current long-rate (30-year spot)?

Say around 4.3%.

What is current short-rate (3-month spot)?

Say around 2.9%.Note: yields-to-maturity on coupon bonds (data reported by

financial press) are (slightly) different than spot rates.



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3.1 Assignment 1

If you had $100 today, how much could you guarantee yourself

to have by November 2046. What is the total holding return?

The annualized return?

To get $100 in November 2046 we need to pay today $91.219.

91.219(1+r5/4411/46) = 100; 1+r5/4411/46 =100

91.219= 1.0963;

so the total holding return is about 9.63%.

If you invested $100 you would end up with $109.63.

The annualized return is given by

(1 + r11/46)2.5 = 1.0963; r11/46 = 1.0963

1/2.5 1 = 3.74%.



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If you had $100 today, how much could you guarantee yourself

to have by August 2049. What is the total holding return? The

annualized return?

To get $100 in August 2049 we need to pay today $77.781.

77.781(1+r5/448/49) = 100; 1+r5/448/49 = 10077.781

= 1.2857;

If you invested $100 you would end up with $128.57.

In annualized terms

(1 + r8/49)5.25 = 1.2857; r8/49 = 1.2857

1/5.25 1 = 4.90%.



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Summarzing the term structure

One can express the term structure of interest rates in terms of:

Total holding return from now till time T (i.e. 28.57%).

Annualized holding return from now till time T (i.e. 4.90%).

Cost today of $1 in time T (i.e. 0.7778).

They all convey the same information, sometimes one is easier

to use than another (computation wise).

The annualized returns are the most common way to describeinvestment opportunities.



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Computing the term structure

What is the term structure of interest rates?

Graph plotting annualized return on risk-free government bonds.

What is the coupon on the bonds given in the problem

(STRIPS)?

Zero!

Zero-coupon bonds have c = 0: these bonds promise payment F

at maturity. If its price is P, then holding period return is

r0,T =F

P 1

The annualized rate, or spot rates, is simply

rT =

F

P

1/T 1



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Computing the term structure

How do we compute the term structure of interest rates?Use formula

rT =

F

P

1/T 1

where F = 100, P is the price of each of the bonds, and T is

their time to maturity.

Recall we call rTs spot rates.

Only trick to automate the process (copy formulae in Excel) is

to get time to maturity of the bonds from data in form Jul 47.

My solution:=IF(B5=Jul,7,IF(B5=Aug,8,IF(B5=Oct,10,...)))

Once we have the months in numeric form it is easy to calculate

the time to maturity for each bond.



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Main topics for class 1

Rules of the game.

Basic concepts:

compounding,

annualized interest rates,

the term structure of interest rates.



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Key ideas for class 1

Annualizing interest rates.A 5-year return of 80% is about a 12.47% annual

return.

(1 + r0,T) = (1 + rT)T

How to look up zero-coupon bond prices and infer

annualized rates of return.

Suppose bond with F = $100 maturing in August

2009 we need to pay today $80.

80(1+r5/058/09) = 100; 1+r5/058/09 =100

80= 1.25;

In annual terms r8/09 5.39%.



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Main topics for class 2 and 3

The NPV rule.

Annuities and perpetuities.

Assignment 2:

1. Recap from todays concepts - bond pricing.

2. Mortgage calculations.

Assignment 3:

1. Corporate projects and the NPV rule. Focus your energies on the assignment. Try to read

ahead (classes 4 and 5).


tuck bridge finance module 1

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