Finance Lecture Slides SEC01 Coursera Update

COURSERA

LECTURE NOTES

AN INTRODUCTION TO CORPORATE FINANCE

Franklin Allen

Wharton School

University of Pennsylvania

Fall 2013

WEEK 1

Section 1

Introduction

Copyright 2013 by Franklin Allen

An Introduction to Corporate Finance - Section 1 - Page 1

Section 1: Introduction

Supplemental Reading: BMA Chapter 1

Purpose of the Course

The purpose of the course is to give you a framework for thinking about how a firm

should make investment and financing decisions to create value for its shareholders. In order to

do this we will not only need to look at the firm but also to consider how financial markets work

and how investors in those markets should make decisions. By the end of the course you should

have a framework for thinking about business problems.

Review of Background Material

Microeconomics

You need to know about indifference curves and utility maximization subject to a budget

constraint.

If we have two commodities, apples and bananas say, we can represent a person's

preference for these commodities by indifference curves


An indifference curve is the locus of combinations of apples and bananas such that the

person is indifferent. It is assumed more is preferred to less, so moving in a northeasterly

direction utility is increasing.

We are all constrained by a budget constraint: we can't spend more than our income on

apples and bananas. It must be the case that

PA A + PB B ≤ I

where PA, PB are the prices of apples and bananas respectively, A and B are the quantities

purchased, and I is income.

This can be represented on our usual diagram.

utility increasing

Bananas

Apples


utility maximizing choice

B

A

demand for

bananas

demand for

apples

If we add indifference curves to this diagram of the budget constraint we can use it to find

the combination of A and B a person will choose if he maximizes his utility.

In the next section we will be using these concepts a lot, so if you are at all shaky on them, you

should review them as soon as possible.

consumption bundle

must be on the line or

below

B

A

AP

I

BP

I

AA

B

P

IB

P

PA


Future Values and Present Values

One of the most important ideas in finance is present value. If you put $1 in the bank

today at 10% interest, then in a year's time you’ll have $1.10. This involves going forward

through time.

FV = 1 x 1.10 = $1.10

An equivalent notion is to go backwards through time and say that the present value of $1.10 in

one year's time if the interest rate is 10% is $1 now, i.e.,

PV = 1.10 = $1

1 + 0.10

In general, $C1 one year from now if the interest rate is r has

PV = C1

1 + r

Suppose you put $1 in the bank today at 10% interest, then in two years time you’ll have

FV = $1x1.102=$1.21

Alternatively we can say that the present value of $1.21 in two year’s time if the interest rate is

10% is $1 now, i.e.,

PV = 1.21 = $1

(1 + 0.10)2

In general, $C2 two years from now if the interest rate is r has

PV = C2

(1 + r)2

Similarly, $Ct t years from now has

PV = Ct

(1 + r)t


Suppose next we have a stream of cash flows C1, C2, C3, … , CT. We can represent this

on a time line:

Date 0 1 2 3 … T

| | | | |

Cash C1 C2 C3 CT

Flows

The equivalent in terms of today’s money of this stream of cash flows is

)r + (1

C + ... +

)r + (1

C +

)r + (1

C +

r + 1

C = PV

T

T

3

3

2

21

Summing Geometric Series: Perpetuities

Fairly soon we'll be talking a lot about PV's, and one of the things it will be useful to

know is how to sum a geometric series.

A special case of a sequence of cash flows that is of interest is when the cash flow at

every date is the same, i.e. Ct = C for every date t and this stream goes on forever. This is called a

perpetuity.

Date 0 1 2 3 … ∞

| | | |

Cash C C C …

Flows

(1) PV = C + C + C + ....

1 + r (1 + r)2 (1 + r)

3

Multiplying (1) by (1 + r) gives:

(2) (1 + r)PV = C + C + C + C + ....

1 + r (1 + r)2 (1 + r)

3


Subtracting (1) from (2):

rPV = C

PV = C

r

As an example, suppose C = $20 and r = 0.10 then PV = 20/0.10 = $200.

Another way to see what is going on here is to consider the case where you put $200 in

the bank at 10% forever and receive $20 per year forever. A stream of $20 forever is therefore

equivalent to $200 today. In general, if you put PV in the bank you receive C = rPV forever so

PV = C/r.

Now that's the last time I'm going to go through the algebra of that or any other derivation

of a formula on the board. In the future I'll just refer you back to this lecture for perpetuities and

give you the general outline for other cases. However at this point you should memorize the fact

that for perpetuities you just divide by the interest rate. There will be derivations of formulas in

the appendix for Section 3 and in the solutions to Problem Set 2. If at any point you find yourself

thinking where does that formula come from you can check it out.

Statistics

We won't be using the statistics for some time and when we get to the point we do need

it, I'll review it. For those of you who want some more time to refresh your memory, I'll just list

the basic concepts you'll need to understand:

Random Variable

Probability


Expectation

The Mean or Average

Variance

Standard deviation

Covariance

Correlation

That's the basic background knowledge you'll need. If you are at all doubtful about any of

the concepts, review them soon.

Finance Lecture Slides SEC01 Coursera Update

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